Saturday, 23 February 2019

On This Day in Math - February 23

Gauss memorial in Brunswick

Pauca sed matura.
(Few, but ripe.)
~Carl F. Gauss, His motto. He would limit his publications to work he regarded as complete and perfect.

Rubik's cube has 54 squares
The 54th day of the year; 54 is the smallest number that can be written as the sum of 3 squares in 3 ways.(Well, go on, find all three ways!)
There are 54 ways to draw six circles through all the points on a 6x6 lattice. *

54 is the fourth Leyland number, after mathematician Paul Leyland. Leyland numbers are numbers of the form \(x^y + y^x \) where x,y are both integers greater than 1.

And the Sin(54o) is one-half the golden ratio.


Drawing by Athanasius Kircher, 1684
1668/9 Cheerleaders Rejoice, The Megaphone is born.. A Letter from Newton on this date is extended by John Collins. In it he mentions "Another useful Instrument lately invented here, is Sir Samuell Morelands loud speaking Trumpett, of which he hath written a Booke or history with the title of Tuba Stentorophonica value one shilling, by which persons may discourse at about a Mile and a halfes distance, if not more". A very similar type of instrument had been thought of by Athanasius Kircher. Two years earlier he described a device that could be used for both broadcasting on one end and “overhearing” on the other. The term ‘megaphone’ was seemingly coined by Thomas Edison 200 years later. *Wik The image at right shows "war tubas" to detect sound of enemy aircraft in the 1920' and 30's before radar. This one shows Emperor Showa inspecting mobile Japanese tubas, but they were common in many countries. *Chris Wild, The strange history of listening before radar.

1826 Lobachevsky first announced his principles of non-Euclidean geometry. This was done in a talk at his home University of Kazan. Unfortunately no record of the talk survives. *VFR
The first published treatise on hyperbolic geometry is Lobachevsky’s Elements of geometry, printed in installments in the Kazan Messenger in the years 1829-1830. Before that article, Lobachevsky wrote a memoir on the same subject, which he presented on the 12th (Old Style; 23rd New Style) of February 1826 to the Physico-mathematical Section of Kazan University. The title of the memoir is Exposition succinte des principes de la g´eom´etrie avec une d´emonstration rigoureuse du th´eor`eme des parall`eles (A brief Exposition of the principles of geometry with a rigorous proof of the theorem on parallels). The manuscript of the memoir does not survive; it was “lost” by the referees. *HYPERBOLIC GEOMETRY IN THE WORK OF J. H. LAMBERT ; ATHANASE PAPADOPOULOS AND GUILLAUME THERET

1855 At 1:05 a.m., Johann Carl Friedrich Gauss, Professor of Mathematics and Director of the Observatory at G¨ottingen, ceased breathing. His pocket watch, which he had carried with him most of his life, ceased ticking at almost exactly the same time. [Eves, Adieu, 43◦]*VFR

In 1896, the Tootsie Roll was introduced by Austrian immigrant Leo Hirshfield to the U.S. In a small store in New York City, he began producing his a chocolaty, chewy candy, which he named after a nickname of "Tootsie" for his five-year-old daughter, Clara. He was America's first candy maker to individually wrap penny candy. By 1905, production moved to a four-story factory in New York. During World War II, Tootsie Rolls were added to American soldiers' rations because of their ability to withstand severe weather conditions and give quick energy. Tootsie Rolls are made from a base of sugar, corn syrup, soy-bean oil, skim milk and cocoa. Current production is over 49 million pieces a day.*TIS Every year in Calculus as we were introducing Rolle's Thm, I would mention to my class the important contribution of his daughter, Tootsie.
Some nice "Tootsie Roll" math can be found at this blog from Christopher Danielson.

1912 Richard Courant gives his Inagural lecture, "On Existance Proofs in Mathematics,” at Gottingen. Existance proofs would run through his life’s works. A common joke years later, when he was not loved by all who knew him, was that Courant had proved by Counterexample, “Courant does not exist.” *Reid, Courant

1955 Germany issued a stamp for the centenary of the death of Gauss. [Scott #725] *VFR

In 1987, supernova 1987A in LMC was first seen. The brightest of the twentieth century, it was the first supernova visible with the naked eye since 1604. *TIS

2012 The near earth asteroid 2012 DA14 has an estimated diameter of about 44 meters and an estimated mass of about 120,000 metric tons. It was discovered on February 23, 2012, by the OAM Observatory, La Sagra in Spain (J75). Calculations show that on February 15, 2013, the distance between the asteroid and the Earth will be 0.07 LD (27,000 km; 17,000 mi) *Science Daily


1583 Jean-Baptiste Morin (23 Feb 1583 in Villefranche, Beaujolais, France - 6 Nov 1656 in Paris, France) French astrologer and astronomer who attempted to solve the longitude problem using lunar observations. He was certainly not the first to propose the method but he did add one important new piece of understanding, namely he took lunar parallax into account.
Since Morin put forward his method for a longitude prize, a committee was set up by Cardinal Richelieu​ to evaluate it. Étienne Pascal, Mydorge, Beaugrand, Hérigone, J C Boulenger and L de la Porte served on the committee and they were in dispute with Morin for the five years after he made his proposal.
Morin realised that instruments had to be improved, improved methods of solving spherical triangles had to be found and better lunar tables were needed. He made some advances in these areas but his method, although theoretically sound, could not achieve either the computational or observational accuracy to succeed. Morin refused to listen to objections to his proposal.
Even while the dispute was going on, in 1638, Morin attacked Descartes saying that he had realised as soon as they met how bad his philosophy was. These disputes alienated Morin from the scientific community. He was to spend the latter part of his life isolated from other scientists although Cardinal Richelieu's successor Cardinal Mazarin did award him a pension for his work on the longitude in 1645.*SAU

1723 Richard Price (23 February 1723 – 19 April 1791) was a British moral philosopher and preacher in the tradition of English Dissenters, and a political pamphleteer, active in radical, republican, and liberal causes such as the American Revolution. He fostered connections between a large number of people, including writers of the Constitution of the United States. He spent most of his adult life as minister of Newington Green Unitarian Church, where possibly the congregant he most influenced was early feminist Mary Wollstonecraft, who extended his ideas on the egalitarianism inherent in the spirit of the French Revolution to encompass women's rights as well. In addition to his work as a moral and political philosopher, he also wrote on issues of statistics and finance, and was inducted into the Royal Society for these contributions. Price was a friend of the mathematician and clergyman Thomas Bayes. He edited Bayes' most famous work "An Essay towards solving a Problem in the Doctrine of Chances" which contains Bayes' Theorem, one of the most fundamental theorems of probability theory, and arranged for its posthumous publication. Price wrote an introduction to Bayes' paper which provides some of the philosophical basis of Bayesian statistics.
Besides the above-mentioned, Price wrote an Essay on the Population of England (2nd ed., 1780) which directly influenced Thomas Robert Malthus.*Wik

1861 George Ballard Mathews, FRS (February 23, 1861 — March 19, 1922) was a London born mathematician who specialized in number theory.
After receiving his degree (as Senior Wrangler) from St John's College, Cambridge in 1883, he was elected a Fellow of St John's College. *Wik Mathews also wrote Algebraic equations (1907) which is a clear exposition of Galois theory, and Projective geometry (1914). This latter book develops the subject of projective geometry without using the concept of distance and it bases projective geometry on a minimal set of axioms. The book also treats von Staudt's theory of complex elements as defined by real involutions. The book contains a wealth of information concerning the projective geometry of conics and quadrics. *SAU

1905 Prime Number Theorist Derrick Lehmer (February 23, 1905 – May 22, 1991) Derrick Lehmer, one of the world's best known prime number theorists, is born in Berkeley, California. Before World War II, Lehmer invented a number of electromechanical sieves for finding prime numbers and made many important contributions in prime number theory throughout his life. Prime numbers are of interest in themselves as mathematical curiosities but are also of great importance to cryptography. The Computer Museum History Center has three Lehmer sieves in its permanent collection. Lehmer died in 1991.*CHM Lehmer's peripatetic career as a number theorist, with he and his wife taking numerous types of work in the United States and abroad to support themselves during the Great Depression, fortuitously brought him into the center of research into early electronic computing.His father Derrick Norman Lehmer, known mainly as a pioneer in number theory computing, also made major contributions to combinatorial computing. *Wik

1922 Anneli Cahn Lax (23 Feb 1922 in Katowice, Poland - 24 Sept 1999 in New York City, New York, USA) Anneli Cahn was born in Katowice, then a German city, but now part of Poland, on February 23, 1922. Her family fled Hitler’s regime in 1935 and settled in New York. She married Peter Lax, a fellow mathematician,
in 1948. Their lives together included a shared love for mathematics. Perhaps her most important contribution to mathematics was as editor of the New Mathematics Library. The launch of the Soviet satellite Sputnik in 1957 was a shock to the American scientific community, a shock felt on every level. Much thought was devoted to the education of a new generation who would accelerate the pace of American scientific productivity. Out of this endeavor grew the New Mathematical Library. The notion was to make accessible to interested high school students, and to a more general public, deep results in mathematics
described by research mathematicians. (This sort of work had long been going on in Eastern Europe.) Lax was asked to take over as general editor for this series, and under her guidance it grew to be the foremost mathematical expository
series in the language. Upon her death it was renamed in her honor. *Mark Saul, Obituary for the AMS VOl 47,#7

1947 Robert Edward Bowen called Rufus by his friends, because of his striking red hair and beard (23 Feb 1947 in Vallejo, California, USA - 30 July 1978 in Santa Rosa, California, USA) Rufus Bowen worked on dynamical systems and died of a cerebral hemorrhage at the age of 31. *SAU

1951 Shigefumi Mori (23 Feb 1951 Nagoya, Japan, ) Japanese mathematician who has made important contributions to the field of algebraic geometry. His major work, in which he proved the existence of minimal models for all three-dimensional algebraic varieties (Jan 1988), has been dubbed Mori's Program. Within ten years since his first published paper, Mori had thereby completed what many said could never be done. In 1979, Mori published his first major results, a proof of the Hartshorne conjecture, which stated that a certain class of algebraic varieties are projective in nature. In other words, these varieties or sets of solutions to given polynomial equations could be described using projective geometry. He was awarded the Fields Medal in 1990 for his work in algebraic geometry.*TIS


1468 Johannes Gutenberg, printer, died. *VFR

1560 Gaspar Lax (1487 in Sarinena, Aragon, Spain - 23 Feb 1560 in Zaragoza, Spain) Lax published several good mathematics books based on works by Boethius, Euclid, Jordanus and Campanus. He was one of the Spanish school of "calculatores" who studied mechanics, being particularly involved with numerical examples, and using as their main tools the elements of proportion theory and infinitesimal arithmetic. This school seems to have originated with Lax and other students of Maior who studied in Paris, then returned to Spain. *SAU

1603 François Viète (1540 – 23 February 1603), Seigneur de la Bigotière, was a French mathematician whose work on new algebra was an important step towards modern algebra, due to its innovative use of letters as parameters in equations. He was a lawyer by trade, and served as a privy Councillor to both Henry III and Henry IV. A popular story about Viete as a codebreaker for Henry III is worth resharing: "While working for King Henry III, he discovered the key to a Spanish cipher of 500 characters, and so was able to read the secret correspondence of his enemies. Philipp II of Spain was so sure that his code was invulnerable that when he heard of this, he complained to the Pope that the French were using sorcery against him, contrary to good Christian morals."
Vieta's most significant contributions were in algebra. While letters had been used to describe an unknown quantity by earlier writers, Vieta was the first to also use letters for the parameters or constant coefficients in an equation. Vieta gave a solution of the problem of Apollonius, to construct a circle tangent to three given circles, and also made a study of ``solid" problems such as the trisection of the angle and the construction of the regular heptagon, which use a marked ruler in addition to the Euclidean tools of ruler and compass. (His method was similar to the Greek method called "neusis" {neuein "incline towards"} which had been used by early mathematicians such as Archimedes but gradually the technique dropped out of favor and use.)
Vieta calculated the value of \( \pi \) to ten decimal places, using the method of Archimedes, and also gave an infinite product formula for \( \pi \) one of the earliest occurrences of an infinite product.
*Robin Hartshorne

1844 Duncan Farquharson Gregory (13 April 1813 in Edinburgh, Scotland - 23 Feb 1844 in Edinburgh, Scotland) Scottish mathematician who was one of the first to investigate modern ideas of abstract algebra.In this work Gregory built on the foundations of Peacock but went far further towards modern algebra. Gregory, in his turn, had a major influence on Boole and it was through his influence that Boole set out on his innovative research. *SAU

1855 Karl Friedrich Gauss (30 Apr 1777 in Brunswick, Germany , 23 Feb 1855 at age 77). His poorly educated mother couldn’t remember his birthdate, but could relate it to a movable religious feast. To confirm the date of his birth Gauss developed a formula for the date of Easter. *VFR
He transformed nearly all areas of mathematics, for which his talent showed from a very early age. For his contributions to theory in magnetism and electricity, a unit of magnetic field has been named the gauss. He devised the method of least squares in statistics, and his Gaussian error curve remains well-known. He anticipated the SI system in his proposal that physical units should be based on a few absolute units such as length, mass and time. In astronomy, he calculated the orbits of the small planets Ceres and Pallas by a new method. He invented the heliotrope for trigonometric determination of the Earth's shape. With Weber, he developed an electromagnetic telegraph and two magnetometers. *TIS; He proved that the heptadecagon (17 gon) was constructable (see April 8) with straight-edge and compass. Because of difficulties engraving the 17gon on his memorial, a seventeen pointed star was used instead.
The Star is located below his foot on the right of the monument pedestal. Dave Renfro has provided me a complete and elementary proof of the construction.

1917 Jean-Gaston Darboux (14 Aug 1842, 23 Feb 1917 at age 74)French mathematician whose work on partial differential equations introduced a new method of integration (the Darboux integral) and contributed to infinitesimal geometry. He wrote a paper in 1870 on differential equations of the second order in which he presented the Darboux integral. In 1873, Darboux wrote a paper on cycloids and between 1887-96 he produced four volumes on infinitesimal geometry, including a discussion of one surface rolling on another surface. In particular he studied the geometrical configuration generated by points and lines which are fixed on the rolling surface. He also studied the problem of finding the shortest path between two points on a surface.*TIS

1961 Mary Ann Elizabeth Stephansen (10 March 1872 in Bergen, Norway - 23 Feb 1961 in Espeland, Norway)received her Ph.D. in mathematics from the University of Zurich in 1902. She was the first woman from Norway to receive a doctoral degree in any subject. Her thesis area was in partial differential equations. It was not until 1971 that another Norwegian woman obtained a doctorate in mathematics. Stephansen taught at the Norwegian Agricultural College from 1906 until her retirement in 1937. She began as an assistant in physics and mathematics, then was appointed to a newly created docent position in mathematics in 1921. She published four mathematical research papers on partial differential equations and difference equations.
A extensive biography of Elizabeth Stephansen is available as a pdf document at the web site of Professor Kari Hag. This also includes description of her mathematical work. *Agnes Scott College Web site

1963 Antonio Signorini (2 April 1888 – 23 February 1963) was an influential Italian mathematical physicist and civil engineer of the 20th century. He is known for his work in finite elasticity, thermoelasticity and for formulating the Signorini problem.
The Signorini problem is the first variational inequality problem, : it consists in finding the elastic equilibrium configuration of an anisotropic non-homogeneous elastic body, resting on a rigid frictionless surface and subject only to its mass forces. The name was coined by Gaetano Fichera to honour his teacher, Antonio Signorini: the original name coined by him is problem with ambiguous boundary conditions. The problem was posed by Antonio Signorini during a course taught at the Istituto Nazionale di Alta Matematica in 1959. The problem was taken up, in particular, by one of his students, Gaetano Fichera.
On the first days of January 1963, Fichera was able to give a complete proof of the existence and uniqueness of a solution for the problem with ambiguous boundary condition, which he called "Signorini problem" to honour his teacher. The preliminary note later published as Fichera 1963 was written up and submitted to Signorini exactly a week before his death: He was very satisfied to see a positive answer to his question. *Wik

Credits :
*CHM=Computer History Museum
*FFF=Kane, Famous First Facts
*NSEC= NASA Solar Eclipse Calendar
*RMAT= The Renaissance Mathematicus, Thony Christie
*SAU=St Andrews Univ. Math History
*TIA = Today in Astronomy
*TIS= Today in Science History
*VFR = V Frederick Rickey, USMA
*Wik = Wikipedia
*WM = Women of Mathematics, Grinstein & Campbell

Friday, 22 February 2019

Two Problems About Squares, or Maybe Just One

It started with this problem, a decade ago when I student walked into class and said, "My Dad got this from a friend in the states and wondered if you could solve it, since  he got stuck."  It was lunch and, as often would happen, other students stopped in and joined in our exploration.  I don't even remember how the problem was posed, but by the end of the lunch, the students and I had found a good half dozen solutions to the problem and extensions of the problem.  I'll only tell you here that we began by discovering that the square of the distances connecting opposite vertices of the two squares were equal.  Then in forty + minutes of student led thinking that would make any teacher proud, we discovered much more, only some of which I remember.

So flash forward a decade, and I'm sliding down my twitter feed and there is a problem similar to the one below.  A random point in a square  and segments connecting it to the midpoints of the four sides of the square.  They gave areas of three of the four quadrilaterals shown below, and asked for the fourth.  I instinctively knew the answer, but I wasn't sure why I knew it.  I had never seen the problem, or had I.

The solution boiled down to realizing that the two opposing sections (red and blue or the two whites) would each add up to 1/2 the total area.  It's some pretty simple geometry, add dotted lines from the point to each corner of the square and think on it a while.  The triangle formed in the red area with it's base on the upper leg of the square and the triangle in the blue area with its base on the bottom side of the square are treated as corresponding, and together their heights add up to the length of a side of the square,s.  Sine each has a base of s/2 the formula for their combined area would be \( \frac{1}{2} ( \frac{s}{2}) s \)   = \( \frac{s^2}{4} \)   doing the same thing with the two corresponding triangles with bases on the left and right side gives you the rest to prove that these two opposite sections contain 1/2 the total area, and therefore, are equal to the remaining area.  

 My mind kept searching for why I knew the solution instantly, and all I could think about was the problem above with two squares. One about sums of squares, one about areas, but were they connected.  

I set my head to wondering, and within a few minutes I realized that if you draw the square connecting the midpoints of the sides of the square in the area problem, they also form a square.  And one of the quick deductions my students jumped to from the first problem above, was that the size of the square didn't matter, and so if you let it degenerate to a single point, the sum of the squares of segments connecting opposite vertices were equal.   So in this area problem, the sum of the squares of the segments connecting opposite midpoints were also equal.  But would the areas work in the original problem with two squares?

I created an area version of the four areas with a square cut out of a square.  Now I wondered if, in our rushed lunch, we had discovered a slightly altered version of this diagram and discovered that the four outside areas were in equal pairs.  Our version would have had the corners of the inner square connecting the corners of the outer square.  Using the square formed by the midpoints would reduce it to the former problem, and if that problem dividing the areas equally, adding back the four isosceles right triangles cut off would not create an imbalance in the areas since all four triangles outside the midpoints were congruent.  

I set about convincing myself that all the area properties true of the single point problem about areas were true in the two square part, and all the length properties of the two square problem were true about the area problem.   

I will add that the single point, or the inner square, do not have to be "inside" the square, as long as appropriate allowances are made for negative lengths and areas.  In fact, they don't have to be parallel to the sides of the original square, or even in the same plane as the original square, (although I did constrain my problems to offsets in parallel planes.)  

So the proof of the inner square area problem.  By drawing a diagonal line from the corner of the inner square to the corner of the outer square in two opposite pentagons, you divide each pentagon into a trapezoid and a triangle.  I used S for the length of the larger square, and 1 for the inner, (any other variable would have worked),  and so the area to be divided by the four pentagons was s2 -1.  We need to prove that the sum of two opposite pentagons if half this amount.  
Once more the triangles in each opposite region can be summed and their area will be \( \frac {(s)(s-1)}{4}\)  .  The trapezoids on opposite corners would have a combined area of \( \frac{1}{2} ( \frac{s}{2}+1)(s-1) \) 

On This Day in Math - February 22

Illustration from "On the forms of plane quartics", by Ruth Gentry

Suppose a contradiction were to be found in the axioms of set theory. Do you seriously believe that a bridge would fall down?
~Frank P. Ramsey

The 53rd day of the year; the month and day are both prime a total of 53 times in every leap year, but not today.

If you reverse the digits of 53 you get its hexadecimal representation; no other two digit number has this quality.

The sum of the first 53 primes is 5830, which is divisible by 53. It is the last year day for which n divides the sum of the first n primes.

53 is the smallest prime p such that 1p1 (ie, 1531) , 3p3, 7p7 and 9p9 are all prime.(Can you find the 2nd smallest?)


1535 On this day the contestants, Tartaglia and Fiore, were to deliver the answer to the 30 questions they were asking of their opponent to a notary. I assume the contest went on the same day, and it may not have taken long. Thony Christie at the Renaissance Mathematicus described it this way, "Tartaglia sat down and almost instantly gave the correct answers to Fiore’s entire list, who was completely unable to solve a single one of Tartaglia’s questions. This whitewash made Tartaglia a star amongst the reckoning masters." In Mario Livio's "The Equation That Couldn't be Solved" he says that Tartaglia finished all 30 of Fiore's questions in less than two hours. All 30 of Fiore's questions were of the form ax3 + bx = c, and Tartaglia had discovered a general solution for that type of cubic only eight days before the contest. 

1630 Popcorn was introduced to the English colonists at their first Thanksgiving dinner on this date (admit it, you thought it was in November) by Quadequina, brother of Massasoit. As his contribution to the dinner he offered a deerskin bag containing several bushels of “popped” corn. *Kane, Famous First Facts, p. 481 Popcorn is a type of corn with smaller kernels than regular corn, and when heated over a flame, it "pops" into the snack we know it as today. Native Americans were growing it for more than a thousand years before the arrival of European explorers. In 1964, scientists digging in southern Mexico found a small cob of popcorn discovered to be 7,000 years old. (don't you wonder if they tried to pop some of it?) Today, the United States grows nearly all of the world's popcorn. *TIS

1805 Francois Arago picked to head the completion of the measurement of the Paris Meridian. He was a 19yr old student at the Ecole Polytechnique. He was nominated by his professor, Dennis Poisson and appointed on Feb 2, 1805 to finish the work began by Mechain and Delambre. He would leave for Spain on Sept 3 of the following year *Amir D Aczel, Pendulum, pg 75-78

1876 The Johns Hopkins University Founded... commonly referred to as Johns Hopkins, JHU, or simply Hopkins, is a private research university based in Baltimore, Maryland, United States. Johns Hopkins maintains campuses in Maryland, Washington, D.C., Italy, China, and Singapore.
The university was founded on January 22, 1876 and named for its benefactor, the philanthropist Johns Hopkins. Daniel Coit Gilman was inaugurated as first president on February 22, 1876. On his death in 1873, Johns Hopkins, a Quaker entrepreneur and childless bachelor, bequeathed $7 million to fund a hospital and university in Baltimore, Maryland. At that time this fortune, generated primarily from the Baltimore and Ohio Railroad, was the largest philanthropic gift in the history of the United States.*Wik

1877 J. J. Sylvester, at a commencement address at Johns Hopkins, gave his view on the relation between teaching and research: “An eloquent mathematician must, from the nature of things, ever remain as rare a phenomenon as a talking fish, and it is certain that the more anyone gives himself up to the study of oratorial effect, the less he will find himself in a fit state of mind to mathematicize.” See Midonick, The Treasury of Mathematics, p. 768. *VFR

1880 American Poet Sidney Lanier (1842–1922) read his “Ode to The Johns Hopkins University”, which indicated the original faculty was “Led by the soaring-genius’d Sylvester.” [Osiris, 1(1936), p. 112] *VFR

1926 At its fiftieth anniversary celebration, Johns Hopkins University awarded a long overdue doctorate to Christine Ladd-Franklin. Now a sprightly 79, she attended the ceremonies to collect her degree 44 years late. [New York Times, 23 February 1926, p. 12. Thanks to Judy Green. Also see Rossiter, Women Scientists in America, p. 46.] *VFR She applied to Johns Hopkins University as a graduate student, a university not traditionally open to women. A fellow contributor to the publication, Educational Times, who was familiar with her work, James J. Sylvester, noticed her name on a list of applicants and urged the university to admit her. In 1878, she was accepted on the terms that she would only attend his lectures.

1965 Rwanda, in central Africa, issued a series of stamps honoring the National University of Rwanda at Butare. Included in the picture is a radical sign, in fact, this is the only stamp which includes a radical sign, a symbol which originated in Germany. For the complicated history of this symbol, see Math Words,
[Scott #84, 88] *VFR

1785 Jean-Charles-Athanase Peltier (22 Feb 1785; 27 Oct 1845 at age 60)
French physicist who discovered the Peltier effect (1834), that at the junction of two dissimilar metals an electric current will produce heat or cold, depending on the direction of current flow. In 1812, Peltier received an inheritance sufficient to retire from clockmaking and pursue a diverse interest in phrenology, anatomy, microscopy and meteorology. Peltier made a thermoelectric thermoscope to measure temperature distribution along a series of thermocouple circuits, from which he discovered the Peltier effect. Lenz succeeded in freezing water by this method. Its importance was not fully recognized until the later thermodynamic work of Kelvin. The effect is now used in devices for measuring temperature and non-compressor cooling units. *TIS

1796 (Lambert) Adolphe (Jacques) Quetelet (22 Feb 1796, 17 Feb 1874 at age 78) was a Belgian mathematician, astronomer, statistician, and sociologist known for his pioneering application of statistics and the theory of probability to social phenomena, especially crime. At an observatory in Brussels that he established in 1833 at the request of the Belgian government, he worked on statistical, geophysical, and meteorological data, studied meteor showers and established methods for the comparison and evaluation of the data. In Sur l'homme et le developpement de ses facultés, essai d'une physique sociale (1835) Quetelet presented his conception of the average man as the central value about which measurements of a human trait are grouped according to the normal curve. *TIS Quetelet created the Body Mass Index in a paper in 1832. It was known as the Quetelet Index until it was termed the Body Mass Index in 1972 by Ancel Keys.

1817 Carl Borchardt (22 Feb 1817 in Berlin, Germany - 27 June 1880 in Rudersdorf (near Berlin), Germany) was a German mathematician who worked in a variety of areas in analysis. He edited Crelle's Journal for more than 30 years.*SAU

1824 Pierre (-Jules-César) Janssen (22 Feb 1824, 23 Dec 1907) was a French astronomer who in 1868 devised a method for observing solar prominences without an eclipse (an idea reached independently by Englishman Joseph Norman Lockyer). Janssen observed the total Sun eclipse in India (1868). Using a spectroscope, he proved that the solar prominences are gaseous, and identified the chromosphere as a gaseous envelope of the Sun. He noted an unknown yellow spectral line in the Sun in 1868, and told Lockyer (who subsequently recognized it as a new element he named helium, from Greek "helios" for sun). Janssen was the first to note the granular appearance of the Sun, regularly photographed it, and published a substantial solar atlas with 6000 photographs (1904). *TIS

1849 Nikolay Yakovlevich Sonin (February 22, 1849 – February 27, 1915) was a Russian mathematician.
Sonin worked on special functions, in particular cylindrical functions. He also worked on the Euler–Maclaurin summation formula. Other topics Sonin studied include Bernoulli polynomials and approximate computation of definite integrals, continuing Chebyshev's work on numerical integration. Together with Andrey Markov, Sonin prepared a two volume edition of Chebyshev's works in French and Russian. He died in St. Petersburg.*Wik

1856 Micaiah John Muller Hill born. He worked in hydrodynamics, on the three-body problem, and has a differential equation named after him. *VFR He was Vice-Chancellor of the University of London from 1909 to 1911. His books on Euclids fifth and sixth books, and on the Theory of Proportion are available on the internet.

1857 Heinrich Rudolf Hertz (22 Feb 1857, 1 Jan 1894) was a German physicist who was the first to broadcast and receive radio waves. He studied under Kirchhoff and Helmholtz in Berlin, and became professor at Bonn in 1889. His main work was on electromagnetic waves (1887). Hertz generated electric waves by means of the oscillatory discharge of a condenser through a loop provided with a spark gap, and then detecting them with a similar type of circuit. Hertz's condenser was a pair of metal rods, placed end to end with a small gap for a spark between them. Hertz was also the first to discover the photoelectric effect. The unit of frequency - one cycle per second - is named after him. Hertz died of blood poisoning in 1894 at the age of 37. *TIS

1862 Ruth Gentry (February 22, 1862 - October 15, 1917) grew up in Indiana and received her A.B. degree at Indiana State Normal (now Indiana State University) in 1880. After ten years of teaching at preparatory schools, she earned a degree in mathematics from the University of Michigan in 1890. She spent the following year as a Fellow in Mathematics at Bryn Mawr, then became the first mathematician and the second recipient of the Association of College Alumnae European Fellowship, which she used in 1891-92 to attend lectures at the University of Berlin (but was not allowed to enroll for a degree). After a further semester attending mathematics lectures at the Sorbonne in Paris, Gentry returned to Bryn Mawr to become one of Charlotte Scott's first two graduate students. She received her Ph.D. in 1896 on the topic "On the Forms of Plane Quartic Curves." As she writes at the beginning of this thesis:
"Many papers dealing with curves of the fourth order, or Quartic Curves, are to be found in the various mathematical periodicals; but these leave the actual appearance of the curve as a whole so largely to the reader's imagination that it is here proposed to give a complete enumeration of the fundamental forms of Plane Quartic Curves as they appear when projected so as to cut the line infinity the least possible number of times, together with evidence that the forms presented can exist."
Gentry taught at Vassar College from 1896 until 1902, where she was the first mathematics faculty member to hold a Ph.D. degree. She was promoted to associate professor in 1900, but left Vassar two years later to become the associate principal and head of the mathematics department at a private school in Pittsburgh, Pennsylvania, a position she held until 1905. After that she spent some time as a volunteer nurse and traveled in the United States and Europe, but she became increasingly ill and died at the age of 55. She was a member of the American Mathematical Society from 1894 until her death in 1917 in Indianapolis, Indiana. *Agnes Scott College web page

1903 Frank Plumpton Ramsey (22 Feb 1903, 19 Jan 1930) English mathematician, logician and philosopher who died at age 26, but had already made significant contributions to logic, philosophy of mathematics, philosophy of language and decision theory. He remains noted for his Ramsey Theory, a mathematical study of combinatorial objects in which a certain degree of order must occur as the scale of the object becomes large. This theory spans various fields of mathematics, including combinatorics, geometry, and number theory. His papers show he was also a remarkably creative and subtle philosopher. *TIS His father Arthur, also a mathematician, was President of Magdalene College. His brother, Michael Ramsey, later became Archbishop of Canterbury. Suffering from chronic liver problems, Ramsey contracted jaundice after an abdominal operation and died on 19 January 1930 at Guy's Hospital in London at the age of 26. He is buried at the Parish of the Ascension Burial Ground in Cambridge, UK.*Wik

1928 BASIC co-inventor Thomas Kurtz is born. With John Kemeny, Kurtz developed the easy-to-learn programming language for his students at Dartmouth College in the early 1960s. He said: "If Fortran is the lingua franca ... BASIC is the lingua playpen." *CHM


1512 Amerigo Vespucci (9 Mar 1451, 22 Feb 1512 at age 60)Spanish astronomer whose name was given to the New World - America - because it was he and not Columbus, who realized and announced that Columbus had discovered a new continent. *TIS

1687 Francesco Lana de Terzi (Brescia, Lombardy 1631 – 22 February 1687 Brescia, Lombardy) was an Italian Jesuit, mathematician, naturalist and aeronautics pioneer. Having been professor of physics and mathematics at Brescia, he first sketched the concept for a vacuum airship and has been referred to as the Father of Aeronautics for his pioneering efforts, turning the aeronautics field into a science by establishing "a theory of aerial navigation verified by mathematical accuracy". He also developed the idea that developed into Braille. *Wik

1901 George Francis FitzGerald (3 Aug 1851 in Kill-o'-the Grange, Monkstown, Co. Dublin, Ireland - 21 Feb 1901 in Dublin, Ireland) Irish physicist whose suggestion of a way to produce waves helped lay a foundation for wireless telegraphy. He also first developed a theory, independently discovered by Hendrik Lorentz, that a material object moving through an electromagnetic field would exhibit a contraction of its length in the direction of motion. This is now known as the Lorentz-FitzGerald contraction, which Einstein used in his own special theory of relativity. He also was first to propose the structure of comets as a head made of large stones, but a tail make of such smaller stones (less than 1-cm diam.) that the pressure of light radiation from the sun could deflect them. FitzGerald also studied electrolysis as well as electromagnetic radiation.*TIS

1941 Dayton Clarence Miller (13 Mar 1866, 22 Feb 1941 at age 74)American physicist. Author of The Science of Musical Sounds (1916). Miller's collection of nearly 1,650 flutes and other instruments, and other materials mostly related to the flute, is now at the Library of Congress. To provide a mechanical means of recording sound waves photographically, he invented the phonodeik (1908). He became expert in architectural ecoustics. During WW I, he was consulted concerning using his photodeik to help locate enemy guns. Miller spent considerable research effort on repeating the Michelson and Morley experiment, proposed by Maxwell, to detect a stationary aether. He spent some time working with Morley (1902-4), then more time at Mt. Wilson, recording results favoring the presence of the aether.*TIS

1975 Oskar Perron ( 7 May 1880 in Frankenthal, Pfalz, Germany - 22 Feb 1975 in Munich, Germany)was a German mathematician best known for the Perron paradox:
Suppose the largest natural number is N. Then if N is greater than 1 we have N2 greater than N contradicting the definition. His publications cover a wide range of mathematical topics. His work in analysis is certainly remembered through the Perron integral. However he also worked on differential equations, matrices and other topics in algebra, continued fractions, geometry and number theory. *SAU

1984 Maxwell Herman Alexander "Max" Newman, FRS (7 February 1897 – 22 February 1984) was a British mathematician and codebreaker. After WWII he continued to do research on combinatorial topology during a period when England was a major center of activity, notably Cambridge under the leadership of Christopher Zeeman. Newman made important contributions leading to an invitation to present his work at the 1962 International Congress of Mathematicians in Stockholm at the age of 65, and proved a Generalized Poincaré conjecture for topological manifolds in 1966. He died in Cambridge.*Wik

Credits :
*CHM=Computer History Museum
*FFF=Kane, Famous First Facts
*NSEC= NASA Solar Eclipse Calendar
*RMAT= The Renaissance Mathematicus, Thony Christie
*SAU=St Andrews Univ. Math History
*TIA = Today in Astronomy
*TIS= Today in Science History
*VFR = V Frederick Rickey, USMA
*Wik = Wikipedia
*WM = Women of Mathematics, Grinstein & Campbell

Thursday, 21 February 2019

On This Day in Math - February 21

Durer Perspective

My mother said, "Even you, Paul, can be in only one place at one time." Maybe soon I will be relieved of this disadvantage. Maybe, once I've left, I'll be able to be in many places at the same time. Maybe then I'll be able to collaborate with Archimedes and Euclid.
~Paul Erdos

The 52nd day of the year; The month and day are simultaneously prime a total of 52 times in a non-leap year. *Tanya Khovanova, Number Gossip How many times in a leap year ?

52 is also the maximum number of moves needed to solve the 15 puzzle from the worst possible start. *Mario Livio

52 is the number of 8-digit primes (on a calculator) that remain prime if viewed upside down, in a mirror, or upside down in a mirror. *Prime Curios

There are 52 letters in the names of the cards in a standard deck: ACE KING QUEEN JACK TEN
(This also works in Spanish. any other languages for which this is true?) *Futility Closet  


1632 Galileo's epic Dialogue on the Two Chief World Systems is Published in Florence. After receiving, what Galileo viewed as permission to write about "the systems of the world" from the new pope, Urban VIII. Greeted with Praise from scholars across Europe, it would eventually be Galileo's downfall. *Brody & Brody, The Science Class You Wish You Had

1699 Newton elected the second foreign member of the French Academy. See January 28, 1699. [American Journal of Physics, 34(1966), 22] *VFR Thony Christie points out in a comment (below) that "Newton was appointed foreign associate of the Académie Royale des Sciences along with four others so to claim he was the second is more than somewhat dubious." (My Thanks)

1727/8 Isaac Greenwood began his “Publick” lectures at Harvard as the first Hollis Professor of Mathematics and Natural Philosophy. The lectures were open to the entire university. [I. B. Cohen, Some Early Tools of American Science, p. 35.] *VFR

1811, as Humphry Davy read a paper to the Royal Society, he introduced the name "chlorine" from the Greek word for "green," for the bright yellow green gas chemists then knew as oxymuriatic gas. In his paper, On a Combination of Oxymuriatic Gas and Oxygene Gas, Davy reported on his numerous experiments with oxymuratic gas, which appeared to have many of the reactive properties of oxygen. Hydrochloric acid was then known as muriatic acid, and when chlorine was first obtained from a reaction with the acid, the yellow green gas had been thought to be a compound containing oxygen. Later, Davy's careful work would show that the chlorine gas was in fact an element, unable to be decomposed into any simpler substances. *TIS

1831 Michael Faraday in a letter to William Whewell regarding a recent publication by Whewell (Journal of the Royal Institution of England (1831), 437-453.), “Your remarks upon chemical notation with the variety of systems which have arisen, had almost stirred me up to regret publicly that such hindrances to the progress of science should exist. I cannot help thinking it a most unfortunate thing that men who as experimentalists, philosophers are the most fitted to advance the general cause of science; knowledge should by promulgation of their own theoretical views under the form of nomenclature, notation, or scale, actually retard its progress. *Isaac Todhunter, William Whewell, (1876), Vol. 1., 307.

1845 The ship Charles Heddle sailed north from Mauritius and encountered a terrible storm. Striking sails and scudding before the wind they proceeded four times around the center in clockwise loops hundreds of miles wide. After six days a clearing sky allowed the Captain to take a reading and realize that as they circled, they had also been driven back nearly to their starting point. Reading the log of the Charles Heddle and other reports of this storm, Henry Piddington coined the word cyclone, from the Greek for "coils of a snake,". After he used the term in his "The Sailor's Horn-Book for the Law of Storms" it became a common term.

1908 Birth date of Dr. Irving Joshua Matrix, the greatest numerologist who (n)ever lived. At the age of seven he astonished his minister Father when he pointed out that 8 is the holiest number of all: “The other numbers with holes are 0, 6, and 9, and sometimes 4, but 8 has two holes, therefore it is the holiest.” Martin Gardner first drew attention to Dr. Matrix in his January 1960 column “Mathematical Games,” in Scientific American. For more details, see The Incredible Dr. Matrix, by Martin Gardner [p. 3-4]. *VFR

1953, Francis Crick and James Watson reached their conclusion about the double helix structure of the DNA molecule. They made their first announcement on Feb 28, and their paper, A Structure for Deoxyribose Nucleic Acid, was published in the 25 Apr 1953 issue of journal Nature. *TIS

1958: The Peace symbol is designed and completed by Gerald Holtom.
*History Time

1996 Cox Enterprises announces it was buying a one-third interest in Digital Domain, a computer-generated special effects company, in order to heighten the use of special effects in media. The deal reflected "another step in the rapid convergence of various computer, software, entertainment and media companies," The New York Times wrote. *CHM

2012 The engineering profession's highest honors for 2012, presented by the National Academy of Engineering (NAE), recognize ground-breaking contributions to the development of the modern liquid crystal display and achievements that led to a curriculum that encourages engineering leadership. The awards, announced today, will be presented at a gala dinner event in Washington, DC on February 21, 2012.
George H. Heilmeier, Wolfgang Helfrich, Martin Schadt, and T. Peter Brody will receive the Charles Stark Draper Prize a $500,000 annual award that honors engineers whose accomplishments have significantly benefited society "for the engineering development of the Liquid Crystal Display (LCD) that is utilized in billions of consumer devices." *AAAS/Science Newsletter, January 19, 2012


1591 Girard Desargues (21 Feb 1591 in Lyon, France - ? Sept 1661 in Lyon, France) He did noted work in projective geometry. *VFR Desargues' most important work, the one in which he invented his new form of geometry, has the title Rough draft for an essay on the results of taking plane sections of a cone (Brouillon project d'une atteinte aux evenemens des rencontres du Cone avec un Plan). A small number of copies was printed in Paris in 1639. Only one is now known to survive, and until this was rediscovered, in 1951, Desargues' work was known only through a manuscript copy made by Philippe de la Hire (1640 - 1718). The book is short, but very dense. It begins with pencils of lines and ranges of points on a line, considers involutions of six points (Desargues does not use or define a cross ratio), gives a rigorous treatment of cases involving 'infinite' distances, and then moves on to conics, showing that they can be discussed in terms of properties that are invariant under projection. We are given a unified theory of conics.
Desargues' famous 'perspective theorem' - that when two triangles are in perspective the meets of corresponding sides are colinear - was first published in 1648, in a work on perspective by Abraham Bosse. *SAU

1764 Ruan Yuan (Chinese characters: 阮元) (21 Feb 1764 in Yangzhou, Jiangsu province, China - 27 Nov 1849 in Yangzhou, Jiangsu province, China), was a scholar official in the Qing Dynasty in Imperial China. He won jinshi (high) honors in the imperial examinations in 1789 and was subsequently appointed to the Hanlin Academy. He was famous for his work Biographies of Astronomers and Mathematicians and for his editing the Shi san jing zhu shu (Commentaries and Notes on the Thirteen Classics) for the Qing emperor.*Wik

1849 Édouard Gaston (Daniel) Deville (21 Feb 1849; 21 Sep 1924 at age 75)
was a French-Canadian surveyor was a French-born Canadian surveyor of Canadian lands (1875-1924) who perfected the first practical method of photogrammetry, or the making of maps based on photography. His system used projective grids of images taken from photographs made with a camera and theodolite mounted on the same tripod. Photographs were taken from different locations, at precise predetermined angles, with measured elevations. Each photograph slightly overlapped the preceding one. With enough photographs and points of intersection, a map could be prepared, including contour lines. He also invented (1896) the first stereoscopic plotting instrument called the Stereo-Planigraph, though its complexity resulted in little use. *TIS

1915 Evgeny Mikhailovich Lifshitz FRS (February 21, 1915 – October 29, 1985) was a leading Soviet physicist of Jewish origin and the brother of physicist Ilya Mikhailovich Lifshitz. (Some commonly encountered alternative transliterations of his names include Yevgeny or Evgenii and Lifshits or Lifschitz.) Lifshitz is well known in general relativity for coauthoring the BKL conjecture concerning the nature of a generic curvature singularity. As of 2006, this is widely regarded as one of the most important open problems in the subject of classical gravitation.
With Lev Landau, Lifshitz co-authored Course of Theoretical Physics, an ambitious series of physics textbooks, in which the two aimed to provide a graduate-level introduction to the entire field of physics. These books are still considered invaluable and continue to be widely used. Landau's wife strongly criticized his scientific abilities, hinting at how much of their joint work was done by Lifshitz and how much by Landau. Despite the sniping, he is well known for many invaluable contributions, in particular to quantum electrodynamics, where he calculated the Casimir force in an arbitrary macroscopic configuration of metals and dielectrics.*Wik


1900 Charles Piazzi Smyth FRSE FRS FRAS FRSSA (3 January 1819, Naples, Italy – 21 February 1900), was Astronomer Royal for Scotland from 1846 to 1888, well known for many innovations in astronomy and his pyramidological and metrological studies of the Great Pyramid of Giza. *Wik

1901 George Francis Fitzgerald (3 Aug 1851, 21 Feb 1901 at age 49) Irish physicist whose suggestion of a way to produce waves helped lay a foundation for wireless telegraphy. He also first developed a theory, independently discovered by Hendrik Lorentz, that a material object moving through an electromagnetic field would exhibit a contraction of its length in the direction of motion. This is now known as the Lorentz-FitzGerald contraction, which Einstein used in his own special theory of relativity. He also was first to propose the structure of comets as a head made of large stones, but a tail make of such smaller stones (less than 1-cm diam.) that the pressure of light radiation from the sun could deflect them. FitzGerald also studied electrolysis as well as electromagnetic radiation.*TIS

1912  Émile Michel Hyacinthe Lemoine (22 Nov 1840 in Quimper, France - 21 Feb 1912 in Paris, France) Lemoine work in mathematics was mainly on geometry. He founded a new study of properties of a triangle in a paper of 1873 where he studied the point of intersection of the symmedians of a triangle. He had been a founder member of the Association Française pour l'Avancement des Sciences and it was at a meeting of the Association in 1873 in Lyon that he presented his work on the symmedians.
A symmedian of a triangle from vertex A is obtained by reflecting the median from A in the bisector of the angle A. He proved that the symmedians are concurrent, the point where they meet now being called the Lemoine point. Among other results on symmedians in Lemoine's 1873 paper is the result that the symmedian from the vertex A cuts the side BC of the triangle in the ratio of the squares of the sides AC and AB. He also proved that if parallels are drawn through the Lemoine point parallel to the three sides of the triangle then the six points lie on a circle, now called the Lemoine circle. Its centre is at the mid-point of the line joining the Lemoine point to the circumcentre of the triangle. Lemoine gave up active mathematical research in 1895 but continued to support the subject. He had helped to found a mathematical journal, L'intermédiaire des mathématiciens., in 1894 and he became its first editor, a role he held for many years. *SAU   His mathematical recreation books are still popular in France.

1912 Osborne Reynolds (23 Aug 1842 in Belfast, Ireland - 21 Feb 1912 in Watchet, Somerset, England) was an Irish mathematician best known for introducing the Reynolds number classifying fluid flow.*SAU

1926 Heike Kamerlingh Onnes (21 Sep 1853, 21 Feb 1926 at age 72)Dutch physicist who was awarded the 1913 Nobel Prize for Physics for his work on low-temperature physics in which he liquified hydrogen and helium. From his studies of the resistance of metals at low temperatures, he discovered superconductivity (a state in which certain metals exhibit almost no electrical resistance at a temperature near absolute zero).*TIS

1932 James Mercer FRS (15 January 1883 – 21 February 1932) was a mathematician, born in Bootle, close to Liverpool, England. He was educated at University of Manchester, and then University of Cambridge. He became a Fellow, saw active service at the Battle of Jutland in World War I, and after decades of suffering ill health died in London, England.
He proved Mercer's theorem, which states that positive definite kernels can be expressed as a dot product in a high-dimensional space. This theorem is the basis of the kernel trick (applied by Aizerman), which allows linear algorithms to be easily converted into non-linear algorithms. *Wik

1938 George Ellery Hale (29 Jun 1868, 21 Feb 1938 at age 69). U S astronomer known for his development of important astronomical instruments. To expand solar observations and promote astrophysical studies he founded Mt. Wilson Observatory (Dec 1904). He discovered that sunspots were regions of relatively low temperatures and high magnetic fields. Hale hired Harlow Shapley and Edwin Hubble as soon as they finished their doctorates, and he encouraged research in galactic and extragalactic astronomy as well as solar and stellar astrophysics. Hale planned and tirelessly raised funds for the 200-inch reflecting telescope at the Palomar Mountain Observatory completed in 1948, after his death, and named for him—the Hale telescope. *TIS

1962 Julio Rey Pastor (14 August 1888 – 21 February 1962) was a Spanish mathematician and historian of science. Rey proposed the creation of a "seminar in mathematics to arouse the research spirit of our school children.” His proposal was accepted and in 1915 the JAE created the Mathematics Laboratory and Seminar, an important institution for the development of research on this field in Spain.
In 1951, he was appointed director of the Instituto Jorge Juan de Matemáticas in the CSIC. His plans in Spain included two projects: the creation, within the CSIC, of an Institute of Applied Mathematics, and the foundation of a Seminar on the History of Science at the university. *Wik

1996 Hans-Joachim Bremermann​ (14 Sept 1926 in Bremen, Germany - 21 Feb 1996 in Berkeley, California, USA) was a German-American mathematician and biophysicist. He worked on computer science and evolution, introducing new ideas of how mating generates new gene combinations. Bremermann's limit, named after him, is the maximum computational speed of a self-contained system in the material universe.*Wik

2009 Ilya Piatetski-Shapiro (30 March 1929 – 21 February 2009) was a Russian-Jewish mathematician. During a career that spanned 60 years he made major contributions to applied science as well as theoretical mathematics. In the last forty years his research focused on pure mathematics; in particular, analytic number theory, group representations and algebraic geometry. His main contribution and impact was in the area of automorphic forms and L-functions.
For the last 30 years of his life he suffered from Parkinson's disease. However, with the help of his wife Edith, he was able to continue to work and do mathematics at the highest level, even when he was barely able to walk and speak.*Wik

Credits :
*CHM=Computer History Museum
*FFF=Kane, Famous First Facts
*NSEC= NASA Solar Eclipse Calendar
*RMAT= The Renaissance Mathematicus, Thony Christie
*SAU=St Andrews Univ. Math History
*TIA = Today in Astronomy
*TIS= Today in Science History
*VFR = V Frederick Rickey, USMA
*Wik = Wikipedia
*WM = Women of Mathematics, Grinstein & Campbell

Wednesday, 20 February 2019

On This Day in Math - February 20

A mathematician will recognise Cauchy, Gauss, Jacobi or Helmholtz after reading a few pages, just as musicians recognise, from the first few bars, Mozart, Beethoven or Schubert.
~Ludwig Boltzmann

The 51st day of the year; 51 is the number of different paths from (0,0) to (6,0) made up of segments connecting lattice points that can only have slopes of 1, 0, or -1 but so that they never go below the x-axis. These are called Motzkin Numbers.

\(\pi(51) = 15\), the number of primes less than 51 is given by it's reversal, 15.

Jim Wilder pointed out that 51 is the smallest number that can be writtenas a sum of primes  with the digits 1 to 5 each used once  2 + 3 + 5 + 41 = 51 (Students might explore similar problems using first n digits 2-9)

A triangle with sides 51, 52 and 53 has an integer area 1170 units2.

And like any odd number, it is the sum of two consecutive numbers, 25+26 , and the difference of their squares \(26^2 - 25^2\)

And I just found this unusual reference, "Don’t be baffled if you see the number 51 cropping up in Chinese website names, since 51 sounds like 'without trouble' or 'carefree' in Chinese." at the Archimedes Lab


1648 A letter from Fermat through Frenicle to Digby reached Wallis saying that Fermat had solved equations of the type x2-Ay2 = 1 for all non-square values up to 150. Thus begins the saga of the mis-naming of Pell's equation. *Edward Everett Whitford, The Pell Equation

1729 A Letter from Gabriel Cramer, Prof. Math. Genev. to James Jurin, M. D. and F. R. S. to be read at the Royal Society, gives an “account of an Aurora Borealis Attended with Unusual Appearances” . The borealis occurred on Feb 15, and the letter was sent on Feb 20. *Transactions of RSI

1807 Sophie Germain writes to Gauss informing him that she is the person who had written to him using the name M. LeBlanc. In closing she writes her hope that this will not change their correspondence. His Response on April 30 would assure her it had not.
*Sophie Germain: An Essay in the History of the Theory of Elasticity

In 1835, Charles Darwin, on his H.M.S. Beagle voyage reached Chile, and experienced a very strong earthquake and shortly afterward saw evidence of several feet of uplift in the region. He repeated measurement a few days later, and found the land had risen several feet. He had proved that geological changes occur even in our own time. Lyell's principles were based on the concept of a steady-state, nondirectional earth whereby uplift, subsidence, erosion, and deposition were all balanced. Thereby, Darwin coupled in his mind this dramatic evidence of elevation with accompanying subsidence and deposition. Thus he hypothesized that coral reefs of the Pacific developed on the margins of subsiding land masses, in the three stages of fringing reef, barrier reef, and atoll.*TIS

1913 It was on, or around, this day that the Three Sisters Radio towers near Arlington, Va went into service. In an area called Radio, near the Columbia Pike and Courthouse Road. Virginia. It was a neighborhood named for the old U.S. Navy Wireless Station. The tallest of the three towers was 45 feet taller than the Washington Monument, and second only to the Eiffel Tower in the world.
The Navy opened Radio Arlington, call sign NAA, in 1913, launching the U.S. military’s global communications system on Fort Myers. A streetcar stop was even named “Radio.’’ Old Radio Arlington marked the first time the term “radio’’ was used in communications, according to Nan and Ross Netherton’s book “Arlington County in Virginia: A Pictorial History,” which was published in 1987. In the days of Marconi and other radio pioneers, the new communications mode was called “wireless telegraphy.’’
*The 625 Sentinal

At Tenwatts Blog I found that there is a marker outside the present Dept. of Defense facility there:
"Three radio towers similar to the Eiffel tower were erected here in 1913. One stood 600 feet, and the other two 450 feet above the 200-foot elevation of the site. The word "radio" was first used instead of "wireless" in the name of this naval communications facility. The first trans-Atlantic voice communication was made between this station and the Eiffel tower in 1915. The nation set its clocks by the Arlington Radio time signal and listened for its broadcast weather reports. The towers were dismantled in 1941, as a menace to aircraft approaching the new Washington National Airport."
I also found the nice postcard showing the three sisters (and some additions) taken from Arlington National Cemetery. His post suggests that the towers were eventually dismantled.

1947 Computer pioneer Alan Turing suggests testing artificial intelligence with the game of chess in a lecture to the London Mathematical Society. Computers, he argued, must like humans be given training before their IQ is tested. A human mathematician has always undergone an extensive training. This training may be regarded as not unlike putting instruction tables into a machine, he said. One must therefore not expect a machine to do a very great deal of building up of instruction tables on its own.*CHM

1966 The only verified example of a family producing five single children with coincidental birthdays is that of Catherine (1952), Coral (1953), Charles (1956), Claudia (1961), and Cecelia (1966), born to Ralph and Carolyn Cummins of Clintwood, VA. All on Feb 20th.  What is the probability of this happening? *VFR (RALPH? He should have changed his name.)

1979 The German Democratic Republic issued a stamp commemorating the centenary of Einstein’s birth. It shows the Einstein tower in Potsdam and his famous formula E = mc2. [Scott #1990]*VFR

In 1996, a bright "new" star was discovered in Sagittarius by Japanese amateur astronomer Yukio Sakurai. It was found not to be a usual nova, but instead was a star going through a dramatic evolutionary state, re-igniting its nuclear furnace for one final blast of energy called the "final helium flash." It was only the second to be identified in the twentieth century. A star like the Sun ends its active life as a white dwarf star gradually cooling down into visual oblivion. Sakurai's Object had a mass a few times that of the Sun. Its collapse after fusing most of its hydrogen fuel to helium raised its temperature so much higher it began nuclear fusion of its helium remains. This was confirmed using its light spectrum to identify the elements present.*TIS

2013 In celebration of the 100th anniversary of the publication of the three-volume version of Bertrand Russell and Alfred North Whitehead's Principia Mathematica, a London theater company staged the world premiere of a musical based on the epic mathematics text.
Performed by the Conway Collective based out of London's historic Conway Hall and written by Tyrone Landau, the play was described as "fascinating and unusual." *MAA DL


1844 Ludwig Eduard Boltzmann (February 20, 1844 – September 5, 1906) was an Austrian physicist famous for his founding contributions in the fields of statistical mechanics and statistical thermodynamics. He was one of the most important advocates for atomic theory at a time when that scientific model was still highly controversial. *Wik Trivia: Boltzmann's famous equation S = K log W (where S = entropy, K = Boltzmann's constant, and W = probability of a particular state) was inscribed as an epitaph on Boltzmann's tombstone. *Wik After obtaining his doctorate, he became an assistant to his teacher Josef Stefan. Boltzmann's fame is based on his invention of statistical mechanics, independently of Willard Gibbs. Their theories connected the properties and behaviour of atoms and molecules with the large scale properties and behaviour of the substances of which they were the building blocks. He also worked out a kinetic theory of gases, and the Stefan-Boltzmann law concerning a relationship between the temperature of a body and the radiation it emits. His firm belief and defense of atomism (that all matter is made of atoms) against hostile opposition to this new idea, may have contributed to his suicide in 1906. *TIS

1860 Mathias Lerch​ (20 February 1860, Milínov - 3 August 1922, Schüttenhofen) was an eminent Czech mathematician who published about 250 papers, largely on mathematical analysis and number theory. He studied in Prague and Berlin, and held teaching positions at the Czech Technical Institute in Prague, the University of Fribourg in Switzerland, the Czech Technical Institute in Brno, and Masaryk University in Brno; he was the first mathematics professor at Masaryk University when it was founded in 1920. In 1900, he was awarded the Grand Prize of the French Academy of Sciences for his number-theoretic work. The Lerch zeta-function is named after him as is the Appell–Lerch sum.*Wik

1926 Kenneth Harry Olsen (February 20, 1926 – February 6, 2011) was an American engineer who co-founded Digital Equipment Corporation (DEC) in 1957 with colleague Harlan Anderson *Wik

1929 Madan Lal Puri ( Sialkot in Pakistan , 20 February 1929 ) is a statistical Indian important in the context of nonparametric statistics and also occupied the fuzzy sets .*Wik

1931 John Willard Milnor (20 Feb 1931, )American mathematician who was awarded the Fields Medal in 1962 for his his proof that a 7-dimensional sphere can have 28 different differential structures. This work opened up the new field of differential topology. Milnor's theorem shows that the total curvature of a knot is at least 4. In the 1950's, Milnor did a substantial amount of work on algebraic topology in which he constructed the classifying space of a topological group and gave a geometric realisation of a semi-simplicial complex. Since the 1970's his interest is in dynamics, especially holomorphic dynamics. Milnor served the American Mathematical Society as vice president (1975-76) and was awarded the Wolf Prize in 1989. *TIS

1948 Andrew Christopher Fabian, OBE, FRS (20 February 1948 - ) is a British astronomer and astrophysicist. He is a Royal Society Research Professor at the Institute of Astronomy, Cambridge, and Vice-Master of Darwin College, Cambridge. He was the President of the Royal Astronomical Society from May 2008 through to 2010. He is an Emeritus Professor of Astronomy at Gresham College, a position in which he delivered free public lectures within the City of London between 1982 and 1984. He was also editor-in-chief of the astronomy journal Monthly Notices of the Royal Astronomical Society. He was educated at King's College London (BSc, Physics) and University College London (PhD).
His current areas of research include galaxy clusters, active galactic nuclei, strong gravity, black holes and the X-ray background. He has also worked on X-ray binaries, neutron stars and supernova remnants in the past. Much of his research involves X-ray astronomy and high energy astrophysics. His notable achievements include his involvement in the discovery of broad iron lines emitted from active galactic nuclei, for which he was jointly awarded the Bruno Rossi Prize. He is author of over 800 refereed articles and head of the X-ray astronomy group at the Institute of Astronomy. Fabian was awarded the Dannie Heineman Prize for Astrophysics by the American Astronomical Society in 2008 and the Gold Medal of the Royal Astronomical Society in 2012 *Wik


1762 Tobias Meyer (17 Feb 1723; 20 Feb 1762 at age 38) German astronomer who developed lunar tables that greatly assisted navigators in determining longitude at sea. Mayer also discovered the libration (or apparent wobbling) of the Moon. Mayer began calculating lunar and solar tables in 1753 and in 1755 he sent them to the British government. These tables were good enough to determine longitude at sea with an accuracy of half a degree. Mayer's method of determining longitude by lunar distances and a formula for correcting errors in longitude due to atmospheric refraction were published in 1770 after his death. The Board of Longitude sent Mayer's widow a payment of 3000 pounds as an award for the tables. *TIS Leonhard Euler described him as 'undoubtedly the greatest astronomer in Europe'. More notes on Meyer can be found on this blog at the Board of Longitude Project from the Royal Museums at Greenwich. Another nice blog by Thony Christie, The Renaissance Mathematicus tells of Meyer's measurement of the Moon's distance, and the importance of that measurement.

1778 Laura Maria Catarina Bassi (31 Oct 1711 in Bologna, Papal States, 20 Feb 1778 in Bologna, Papal States) was an Italian physicist and one of the earliest women to gain a position in an Italian university. *SAU She was the first woman in the world to earn a university chair in a scientific field of studies. She received a doctoral degree from the University of Bologna in May 1732, only the third academic qualification ever bestowed on a woman by a European university, and the first woman to earn a professorship in physics at a university in Europe. She was the first woman to be offered an official teaching position at a university in Europe.
In 1738, she married Giuseppe Veratti, a fellow academic with whom she had twelve children. After this, she was able to lecture from home on a regular basis and successfully petitioned the University for more responsibility and a higher salary to allow her to purchase her own equipment.
One of her principal patrons was Pope Benedict XIV. He supported less censorship of scholarly work, such as happened with Galileo, and he supported women figures in learning, including Agnesi.
She was mainly interested in Newtonian physics and taught courses on the subject for 28 years. She was one of the key figures in introducing Newton's ideas of physics and natural philosophy to Italy. She also carried out experiments of her own in all aspects of physics. In order to teach Newtonian physics and Franklinian electricity, topics that were not focused in the university curriculum, Bassi gave private lessons.[6] In her lifetime, she authored 28 papers, the vast majority of these on physics and hydraulics, though she did not write any books. She published only four of her papers.[2] Although only a limited number of her scientific works were left behind, much of her scientific impact is evident through her many correspondents including Voltaire, Francesco Algarotti, Roger Boscovich, Charles Bonnet, Jean Antoine Nollet, Giambattista Beccaria, Paolo Frisi, Alessandro Volta. Voltaire once wrote to her saying "There is no Bassi in London, and I would be much happier to be added to your Academy of Bologna than that of the English, even though it has produced a Newton". *Wik

1928 Antonio Abetti (19 Jun 1846, 20 Feb 1928 at age 81) Italian astronomer who was an authority on minor planets. At first a civil engineer, he became an astronomer at the University of Padua (1868-93), with an interest in positional astronomy and made many observations of small planets, comets and star occultations. In 1874, Abetti went to Muddapur, Bengal, to observe the transit of Venus across the sun's disk where his use of a spectroscope was the first use of this kind. Later, he became director at the Arcetri Observatory and Professor of astronomy at the University of Florence (1894-1921). The observatory had been founded by G. B. Donati in 1872, and Abetti equipped it with a new telescope that he had built in the workshops at Padua. He was active after retirement, until his death, and was followed by his son Giorgio.*TIS

1955 Arthur Lee Dixon FRS (27 November 1867 — 20 February 1955) was a British mathematician and holder of the Waynflete Professorship of Pure Mathematics at the University of Oxford. The younger brother of Alfred Cardew Dixon, he was educated at Kingswood School and Worcester College, Oxford, becoming a Tutorial Fellow at Merton College in 1898 and the Waynflete Professor in 1922. Dixon was the last mathematical professor at Oxford to hold a life tenure, and although he was not particularly noted for his mathematical innovations he did publish many papers on analytic number theory and the application of algebra to geometry, elliptic functions and hyperelliptic functions. Elected a Fellow of the Royal Society in 1912 and serving as President of the London Mathematical Society from 1924 to 1926, *Wik

1972 Maria Goeppert-Mayer (28 Jun 1906, 20 Feb 1972 at age 65) German physicist who shared one-half of the 1963 Nobel Prize for Physics with J. Hans D. Jensen of West Germany for their proposal of the shell nuclear model. (The other half of the prize was awarded to Eugene P. Wigner of the United States for unrelated work.) In 1939 she worked at Columbia University on the separation of uranium isotopes for the atomic bomb project. In 1949, she devised the shell nuclear model, which explained the detailed properties of atomic nuclei in terms of a structure of shells occupied by the protons and neutrons. This explained the great stability and abundance of nuclei that have a particular number of neutrons (such as 50, 82, or 126) and the same special number of protons. *TIS

2005 Esther (Klein) Szekeres (20 February 1910 – 28 August 2005) was a Hungarian–Australian mathematician with an Erdős number of 1. She was born to Ignaz Klein in a Jewish family in Budapest, Kingdom of Hungary in 1910. As a young woman in Budapest, Klein was a member of a group of Hungarians including Paul Erdős, George Szekeres and Paul Turán that convened over interesting mathematical problems.
In 1933, Klein proposed to the group a combinatorial problem that Erdős named as the Happy Ending problem as it led to her marriage to George Szekeres in 1937, with whom she had two children.
Following the outbreak of World War II, Esther and George Szekeres emigrated to Australia after spending several years in Hongkew, a community of refugees located in Shanghai, China. In Australia, they originally settled in Adelaide before moving to Sydney in the 1960s.
In Sydney, Esther lectured at Macquarie University and was actively involved in mathematics enrichment for high-school students. In 1984, she jointly founded a weekly mathematics enrichment meeting that has since expanded into a program of about 30 groups that continue to meet weekly and inspire high school students throughout Australia and New Zealand.
In 2004, she and George moved back to Adelaide, where, on 28 August 2005, she and her husband passed away within an hour of each other *Wik

2005 Edward Maitland Wright (13 Feb 1906 in Farnley, near Leeds, England - 2 Feb 2005 in Reading, England) was initially self-taught in Mathematics but was able to go and study at Oxford. He spent a year at Göttingen and returned to Oxford. He was appointed to the Char at Aberdeen where he stayed for the rest of his career, eventually becoming Principal and Vice-Chancellor of the University. He is best known for the standard work on Number Theory he wrote with G H Hardy. One of Wright's first papers, published in 1930, was on Bernstein polynomials. Also among his early work was a series of three papers titled Asymptotic partition formulae. The third in the series Asymptotic partition formulae, III. Partitions into kth powers was published by Acta Mathematica in 1934. *SAU

Credits :
*CHM=Computer History Museum
*FFF=Kane, Famous First Facts
*NSEC= NASA Solar Eclipse Calendar
*RMAT= The Renaissance Mathematicus, Thony Christie
*SAU=St Andrews Univ. Math History
*TIA = Today in Astronomy
*TIS= Today in Science History
*VFR = V Frederick Rickey, USMA
*Wik = Wikipedia
*WM = Women of Mathematics, Grinstein & Campbell

Tuesday, 19 February 2019

On This Day in Math - February 19

Copernicus statue at Olsztyn Castle

It is true that a mathematician who is not somewhat of a poet, will never be a perfect mathematician.
~Karl Weierstrass

The 50th day of the year; 50 is the smallest number that can be written as the sum of two squares in two distinct ways 50 = 49 + 1 = 25 + 25. *Tanya Khovanova, Number Gossip (What is the next, or what is the smallest number that can be written as the sum of two squares in three distinct ways? For solution from Ben Vitale, see bottom of post)

50 is also expressible as the sum of distinct primes in two ways so that all consecutive primes 2-23 are used :50 = 2 + 5 + 7 + 17 + 19 = 3 + 11 + 13 + 23.
The number 50 is somewhat responsible for the area of number theory about partitions. In 1740 Philip Naudé the younger (1684-1747) wrote Euler from Berlin to ask “how many ways can the number 50 be written as a sum of seven different positive integers?” Euler would give the answer, 522, within a few days but would return to the problem of various types of partitions throughout the rest of his life.

1512 The French invaded Brescia, in Northern Italy, during the War of the League of Cambrai. The militia of Brescia defended their city for seven days. When the French finally broke through, they took their revenge by massacring the inhabitants of Brescia. By the end of battle, over 45,000 residents were killed. During the massacre, a French soldier sliced Niccolò's jaw and palate with a saber. This made it impossible for Niccolò to speak normally, prompting the nickname "Tartaglia" Tartaglia is perhaps best known today for his conflicts with Gerolamo Cardano over the solution of cubics. (see this blog for the unfortunate common mistake about Tartaglia's family name.)

1549 Osiander wrote of Michael Stifel: “He has devised new numbers for the alphabet, namely the triangular numbers, and his fantasies are more absurd than before.” *VFR

1600 The Inquisition brought Giordano Bruno to the Campo dei Fiori in Rome’s center where they chained him to an iron stake and burned him alive for his beliefs that the earth rotated on its axis. *Amir Aczel, Pendulum, pg 9 (This date seems wrong. Thony Christie noted that " Bruno was executed on 17th Feb and not for his cosmology but for his heretical theology." Thanks... several other sources agree with Feb 17th date))

1616 On February 19, 1616, the Inquisition asked a commission of theologians, known as qualifiers, about the propositions of the heliocentric view of the universe after Nicollo Lorin had accused Galileo of Heretical remarks in a letter to his former student, Benedetto Castelli. On February 24 the Qualifiers delivered their unanimous report: the idea that the Sun is stationary is "foolish and absurd in philosophy, and formally heretical since it explicitly contradicts in many places the sense of Holy Scripture..."; while the Earth's movement "receives the same judgement in philosophy and ... in regard to theological truth it is at least erroneous in faith."At a meeting of the cardinals of the Inquisition on the following day, Pope Paul V instructed Bellarmine to deliver this result to Galileo, and to order him to abandon the Copernican opinions; should Galileo resist the decree, stronger action would be taken. On February 26, Galileo was called to Bellarmine's residence, and accepted the orders.*Wik

1671/72 Newton’s first publication appears as a letter in the Philosophical Transactions. It deals with his new theory of light, showing that a prism separates white light into its component colors. Huygens, Hooke and others objected so strongly that he vowed not to publish again. Fortunately that vow was not kept. *VFR The full text of that publication is here.

In 1855, M. Le Verrier presented the first weather map at the French Academy of Sciences.*TIS A storm on November 14, 1854 destroyed the French warship Henri IV and damaged other British and French vessels on the Black Sea involved in the Crimean War. A report from the state-supported Paris Observatory indicated that barometric readings showed that the storm had passed across Europe in about four days. Urban Leverrier, director of the Paris Observatory, concluded that had there been a telegraph line between Vienna and the Crimea, the British and French fleets could have received warnings. An earlier map is mentioned, but not shown in a letter dated Dec 1, 1816 in Gilbert's Annalen der Physik from Heinrich Wilhelm Brandes *Report of The International Meterological Congress, 1893

1876 Sylvester began his duties at the newly founded Johns Hopkins, *TIS

1901 Messages from Mars reported in Collier's Magazine. While conducting experiments on high-frequency electrical transmission in 1899 in his Colorado Springs, Colorado laboratory, Nikola Tesla picked up cosmic radio waves on his instruments. Announcing this development, he publicly opined that the messages came from outer space, possibly from inhabitants of Mars. In a Collier’s Weekly article dated February 19, 1901, Tesla wrote, “At the present stage of progress, there would be no insurmountable obstacle in constructing a machine capable of conveying a message to Mars … What a tremendous stir this would make in the world! How soon will it come?” Later discoveries revealed that Tesla had actually picked up common radio waves emitted by interstellar gas clouds. *History. Com

1940Edwin Hubble wrote in a letter to Harlow Shapley that he had determined the distance to the "Andromeda nebula". He included this graph. HT Massimo

1946 Alan Turing Presents the “Proposal for the Development in the Mathematics Division of an Automatic Computing Engine (ACE).”
This research proposal was presented to a meeting of the Executive Committee of the National Physical Laboratory (NPL) in Teddington, England, and approved at a second meeting held a month later.
Turing based this research on von Neumann’s First Draft of a Report on the EDVAC. He had studied it in summer 1945 when he was recruited by J.R. Womersley to join the staff of the NPL. *CHM

1971 The first warrant is issued to search a computer storage. Although the requirements for obtaining such a warrant were similar to those for searching a home, they ushered in a new era that would lead to increasingly sophisticated methods of encryption to hide computer files from law enforcement agents.*CHM

1972 The New Yorker published an article by A. Adler on “Mathematics and Creativity” that was not well received by the mathematical community. See The [old] Mathematical Intelligencer, no. 2. *VFR An abstract is here

1473 Nicolaus Copernicus Polish astronomer who proposed that the planets have the Sun as the fixed point to which their motions are to be referred; that the Earth is a planet which, besides orbiting the Sun annually, also turns once daily on its own axis; and that very slow, long-term changes in the direction of this axis account for the precession of the equinoxes *TIS
An advance copy of his work De revolutionibus orbium coelestium was presented to Copernicus. On the same day he died. *VFR
Over 450 years after his death, Copernicus was reburied in the cathedral at Frombork on Poland’s Baltic coast. The astronomer whose ideas were once declared heresy by the Vatican—was reburied with full religious honors.

1837 Aleksandr Nikolayevich Korkin (3 March [O.S. 19 February] 1837–September 1, 1908, all New Style) was a Russian mathematician. He made contribution to the development of partial differential equations. After Chebyshev, Korkin was the most important initiator of the formation of the Saint Petersburg Mathematical School*Wik

1863 Axel Thue(19 Feb 1863 in Tönsberg, Norway - 7 March 1922 in Oslo, Norway) Thue studied Diophantine equations, showing that, for example, y3 - 2x2 = 1 cannot be satisfied by infinitely many pairs of integers. Edmund Landau, in 1922, described Thue's work as, ".. the most important discovery in elementary number theory that I know. "
Thue's Theorem states, " If f (x, y) is a homogeneous polynomial with integer coefficients, irreducible in the rationals and of degree > 2 and c is a non-zero integer then f (x, y) = c has only a finite number of integer solutions." *SAU

1866 Thomas Jefferson Jackson See (19 Feb 1866 in Montgomery City, Missouri - 4 July 1962 in Oakland, California, USA) was an U S astronomer who studied in the University of Missouri and in Berlin. He fell out with his astronomical colleagues and was eventually banned from publishing. He spend the last part of his life arguing against Einstein's Theory of Relativity. *SAU

1889 Sir Ernest Marsden (19 Feb 1889, 15 Dec 1970) British-born New Zealand nuclear physicist who worked under Ernest Rutherford investigating atomic structure with Hans Geiger. Marsden visually counted scintillations from alpha particles after passing through gold foil and striking a phosphorescent screen. That some of these were observed scattered at surprisingly large angles led to Rutherford's theory of the nucleus as the massive, tiny centre of the atom. Later, Marsden's own experiments, working in New Zealand, hinted suggested transmutation of elements was possible when alpha particles bombarding nitrogen nuclei produced scattered particles of greater speed than the original radiation. *TIS

1553 Erasmus Reinhold (October 22, 1511 – February 19, 1553) was a German astronomer and mathematician, considered to be the most influential astronomical pedagogue of his generation. He was born and died in Saalfeld, Saxony.
He was educated, under Jacob Milich, at the University of Wittenberg, where he was first elected dean and later became rector. In 1536 he was appointed professor of higher mathematics by Philipp Melanchthon. In contrast to the limited modern definition, "mathematics" at the time also included applied mathematics, especially astronomy. His colleague, Georg Joachim Rheticus, also studied at Wittenberg and was appointed professor of lower mathematics in 1536.
Reinhold catalogued a large number of stars. His publications on astronomy include a commentary (1542, 1553) on Georg Purbach's Theoricae novae planetarum. Reinhold knew about Copernicus and his heliocentric ideas prior to the publication of De revolutionibis and made a favourable reference to him in his commentary on Purbach. However, Reinhold (like other astronomers before Kepler and Galileo) translated Copernicus' mathematical methods back into a geocentric system, rejecting heliocentric cosmology on physical and theological grounds.
It was Reinhold's heavily annotated copy of De revolutionibus in the Royal Observatory, Edinburgh that started Owen Gingerich on his search for copies of the first and second editions which he describes in The Book Nobody Read.[5] In Reinhold's unpublished commentary on De revolutionibus, he calculated the distance from the Earth to the sun. He "massaged" his calculation method in order to arrive at an answer close to that of Ptolemy.*Wik

1622 Sir Henry Savile (30 Nov 1549 in Bradley (near Halifax), Yorkshire, England - 19 Feb 1622 in Eton, Berkshire, England) Savile was an English mathematician who founded professorships of geometry and astronomy at Oxford. It is interesting to read Savile's comments in these lectures on why he felt that mathematics at that time was not flourishing. Students did not understand the importance of the subject, Savile wrote, there were no teachers to explain the difficult points, the texts written by the leading mathematicians of the day were not studied, and no overall approach to the teaching of mathematics had been formulated. Of course, as we shall see below, fifty years later Savile tried to rectify these shortcomings by setting up two chairs at the University of Oxford. *SAU

1799 Jean-Charles Borda, (4 May 1733 in Dax, France - 19 Feb 1799 in Paris, France) a major figure in the French navy who participated in sev­eral scientific voyages and the American revolution. Besides his contributions to navigational instruments he did important work on fluid mechanics, even showing that Newton’s theory of fluid resistance was untenable. He is best known for the voting system he created in 1770.*VFR (The Borda count is a single-winner election method in which voters rank candidates in order of preference. The Borda count determines the winner of an election by giving each candidate a certain number of points corresponding to the position in which he or she is ranked by each voter. Once all votes have been counted the candidate with the most points is the winner. Because it sometimes elects broadly acceptable candidates, rather than those preferred by the majority, the Borda count is often described as a consensus-based electoral system, rather than a majoritarian one.The Borda count is a popular method for granting awards for sports in the United States, and is used in determining the Most Valuable Player in Major League Baseball, and by the Associated Press and United Press International to rank teams in NCAA sports, to determine the winner of the Heisman Trophy.) [He was one of the main driving forces in the introduction of the decimal system. Borda made good use of calculus and experiment to unify areas of physics. For his surveying, he also developed a series of trigonometric tables. In 1782, while in command of a flotilla of six French ships, he was captured by the British. Borda's health declined after his release. He is one of 72 scientists commemorated by plaques on the Eiffel tower.]*TIS

1897 Karl (Theodor Wilhelm) Weierstrass (31 Oct 1815, 19 Feb 1897 at age 81) was a German mathematician who is known as the "father of modern analysis" for his rigour in analysis led to the modern theory of functions, and considered one of the greatest mathematics teachers of all-time. He was doing mathematical research while a secondary school teacher, when in 1854, he published a paper on Abelian functions in the famous Crelle Journal. The paper so impressed the mathematical community that he shortly received an honorary doctorate and by 1856, he had a University appointment in Berlin. In 1871, he demonstrated that there exist continuous functions in an interval which have no derivatives nowhere in the interval. He also did outstanding work on complex variables.*TIS Weierstrass died peacefully at the age of 82 at his home in Berlin after a long illness culminating in influenz. It is reported that his last wish was that the priest say nothing in his praise at the funeral, but to restrict the services to the customary prayers. *VFR

1908 Paul Matthieu Hermann Laurent (2 Sept 1841 in Echternach, Luxembourg - 19 Feb 1908 in Paris, France) He developed statistical formulas for the calculation of actuarial tables and studied heat conduction. *VFR

1916 Ernst Mach (18 Feb 1838; 19 Feb 1916 at age 77) Austrian physicist and philosopher who established important principles of optics, mechanics, and wave dynamics. His early physical works were devoted to electric discharge and induction. Between 1860 and 1862 he studied in depth the Doppler Effect by optical and acoustic experiments. He introduced the "Mach number" for the ratio of speed of object to speed of sound is named for him. When supersonic planes travel today, their speed is measured in terms that keep Mach's name alive. His lifetime interest, however, was in psychology and human perception. He supported the view that all knowledge is a conceptual organization of the data of sensory experience (or observation). *TIS

1929 Joseph Valentin Boussinesq (13 March 1842 – 19 February 1929) was a French mathematician and physicist who made significant contributions to the theory of hydrodynamics, vibration, light, and heat.
In 1897 he published Théorie de l' écoulement tourbillonnant et tumultueux des liquides, a work that greatly contributed to the study of turbulence and hydrodynamics.*Wik

1938 Edmund Georg Hermann Landau (14 Feb 1877 in Berlin, Germany - 19 Feb 1938 in Berlin, Germany) Although famous as a number theorist, he is best known for his textbooks which are written in an austere definition-theorem-proof style. His Grundlagen der Analysis is an excellent treatment of the development of our number systems from the Peano postualates. Reading this book is a good way to learn mathematical German. But if you are lazy, it has been translated into English. *VFR Landau gave the first systematic presentation of analytic number theory and wrote important works on the theory of analytic functions of a single variable.*SAU Legend has it that at the age of three, when is mother forgot her umbrella in a carriage, he replied, "It was number 354," and the umbrella was quickly re-acquired.

1940 Otto Toeplitz died in Jerusalem, after having left Germany in the Spring of 1939. He made lasting contributions to the theory of integral equations and the theory of functions of infinitely many variables. Today he is best remembered for two popular works which have been translated into English: The Enjoyment of Mathematics (original 1930, 1957), and The Calculus: A Genetic Approach (first published 1949; English 1963). These are some of the most successful attempts to bring higher mathematics to the general public. The later shows his deep interest in the history of mathematics; every calculus teacher could profit from reading it. *VFR

1990 Otto Neugebauer, historian of ancient and medieval mathematics and astronomy. *VFR
(May 26, 1899 – February 19, 1990) He was an Austrian-American mathematician and historian of science who became known for his research on the history of astronomy and the other exact sciences in antiquity and into the Middle Ages. By studying clay tablets he discovered that the ancient Babylonians knew much more about mathematics and astronomy than had been previously realized. The National Academy of Sciences has called Neugebauer "the most original and productive scholar of the history of the exact sciences, perhaps of the history of science, of our age." *Wik

@BenVitale: smallest number w/ 3 representations: \( 325 = 1^2 + 18^2 = 6^2 + 17^2 = 10^2+ 15^2\)

Credits :
*CHM=Computer History Museum
*FFF=Kane, Famous First Facts
*NSEC= NASA Solar Eclipse Calendar
*RMAT= The Renaissance Mathematicus, Thony Christie
*SAU=St Andrews Univ. Math History
*TIA = Today in Astronomy
*TIS= Today in Science History
*VFR = V Frederick Rickey, USMA
*Wik = Wikipedia
*WM = Women of Mathematics, Grinstein & Campbell