Sunday 23 February 2020

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

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