Monday, 16 July 2018

On This Day in Math - July 16

Pure mathematics is the world's best game. 
It is more absorbing than chess, more of a gamble than poker, 
and lasts longer than Monopoly. 
It's free. It can be played anywhere 
- Archimedes did it in a bathtub.

-Richard J. Trudeau

The 197th day of this year; 197 is the sum of all digits of all two-digit prime numbers: 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97.  It is simple to show that the sum of one-digit primes is 17. Do the sum of the digits of n-digit primes always end in seven? ( Or perhaps we ask, are there any others that do?

197 is the smallest prime number that is the sum of 7 consecutive primes: 17 + 19 + 23 + 29 + 31 + 37 + 41 (student challenge: can there be a prime that is the sum of eight consecutive primes?)

197 is the seventh, and last, year-day that will be a Keith number   created in 1987 by Michael Keith.  (they are also repfigit numbers, the term he originally used for them. )

197 is the sum of the first twelve prime numbers: 2 + 3 + 5 + 7 + 11 + 13 + 17 + 19 + 23 + 29 + 31 + 37

433 B.C. The Metonic 19-year cycle of the moon enacted. This masterpiece of approximation (19 solar years = 235 lunations) is still used today in the computation of the date of Easter. [See A. Philip, The Calendar: Its History, Structure and Improvement, p. 8]*VFR  (I have also seen June 27, 432 BC given for this event.  Purist may choose up sides and argue for their choice)

1661 Europe’s earliest modern-style banknotes, available to all and sundry with each note worth a fixed sum, were introduced by the Bank of Stockholm. The bank had been started in 1657 by Johan Palmstruch in close collaboration with the royal government which pocketed half the profits. It was Palmstruch who suggested the kreditivsedlar (credit notes) and they provided a welcome alternative to Sweden’s massive copper coins, which were dismayingly heavy and clumsy. Colloquially known as Palmstruchers the notes were printed on thick, white watermarked paper with the word banco as the watermark and carried the date, the bank’s seal and eight signatures, headed by Palmstruch’s, as an assurance of reliability. They were in stated denominations and payable to the bearer and anybody who had one was promised payment by the bank.  (*History Today )

1669  Wallis writes to Oldenburg complaining about the public perception of the Royal Society after Doctor Robert Smith's dedication of the New Theater consisted of only, "Satyrical invectives against Cromwell, Fanaticks, the Royal Society and Philosophy." *The mathematical work of John Wallis, D.D., F.R.S., (1616-1703) By Joseph Frederick Scott, pg 11

1730 The famous lines of Alexander Pope (1688–1744) which were intended as an epitaph for Newton:
Nature and Nature’s Laws lay hid in night: God said, Let Newton be! and all was light.
were published in the Grub-Street Journal, the first time they appeared in print. *VFR

1828 James Ryan recorded his copyright for The Differential and Integral Calculus, the first calculus book written by a U.S. citizen.*VFR

1848 Exactly 50 years earlier, Gauss received his doctorate. As part of the show at the golden jubilee Gauss was to light his pipe with a manuscript page from his Disquisitiones Arithmeticae. His student Dirichlet was outraged by this sacrilege and boldly snatched the paper as a treasured memento. [Eves, History of Mathematics, p. 370]*VFR

1945 The first atomic bomb explosion was carried out in a test at Alamogordo Air Base in New Mexico, at 12:29:15 G.C.T.  *VFR The atomic bomb was invented by two refugee German scientists in Britain, Professor Rudolph Peierls and Otto Frisch, of Birmingham University. They designed a "blue-print" for making an atom bomb in 1940. It actually began when the Italian-born physicist Enrico Fermi, working in the United States, invented an apparatus which produced the first atomic chain reactions. In 1940 both the Americans and British were researching the atom bomb and when the United States entered WW2, the British joined the American "Manhattan Project" and production of the bomb went on ahead in the US.*TIS

1969  Apollo 11 lifts off.  Launched by a Saturn V rocket from Kennedy Space Center in Merritt Island, Florida on July 16, Apollo 11 was the fifth manned mission of NASA's Apollo program. It would result in the first astronauts to land on the Moon on July 20, 1969. *Wik

In 1994, the first of 21 asteroids, major fragments of the comet Shoemaker-Levy 9 broken-up 2 years earlier, hit Jupiter, creating a 1200-mile wide fireball 600 miles high to the joy of astronomers awaiting the celestial fireworks, giving scientists their first chance to observe such a collision as it happened, and others through July 22. Jupiter is a gas giant, made up mostly of hydrogen and helium in gas and liquid form.When we observe Jupiter, we are looking not at a solid surface, but a banded atmosphere with swirling clouds and huge storms.*TIS

1995, incorporated a year earlier by Jeff Bezos in Washington (state) as an online bookstore, sells its first book, Douglas Hofstadter's Fluid Concepts and Creative Analogies: Computer Models of the Fundamental Mechanisms of Thought. *Wik

2186 (In case you live a really long time) will be the Closest approach to maximum possible duration of totality with 7 min 29 sec in the Atlantic Ocean. Maximum theoretical
duration is 7 min 31 sec. During the 4th millennium there are only 2 solar eclipses with maximum duration of totality longer than 7 min. In the years 3973 and 3991. There are none in 21st century. *NSEC

1678 Jakob Hermann (16 July 1678, Basel – 11 July 1733, Basel) was a Swiss mathematician who made contributions to dynamics.*SAU In 1729, he proclaimed that it was as easy to graph a locus on the polar coordinate system as it was to graph it on the Cartesian coordinate system. However, no one listened. He was a distant relative of Leonhard Euler. *Wik

1746 Giuseppe Piazzi (July 16, 1746 – July 22, 1826) Italian astronomer and author, born in Valtellina, discovered the first asteroid - Ceres. He established an observatory at Palermo and mapped the positions of 7,646 stars. He also discovered that the star 61 Cygni had a large Proper Motion, which led Bessel to chose it as the object of his parallax studies. He discovered Ceres on 1 Jan 1801, but was able to make only three observations. The term "asteroid," meaning "star-like" was coined (1803) by Herschel. Fortuitously, Gauss had recently developed mathematical techniques that allowed the orbit to be calculated. Within the next few years, astronomers discovered three more asteroids: Pallas, Juno, and Vesta. The thousandth Asteroid discovered was named Piazzi in his honor.*TIS

1819 Siegfried Heinrich Aronhold (16 July 1819 Angerburg, East Prussia – 13 March 1884, Berlin, Germany) was a German mathematician who worked on invariant theory and introduced the symbolic method.*Wik

1866 Edwin Brant Frost II (July 16, 1866 – May 14, 1935) American astronomer, born in Brattleboro, Vermont. His father, Carlton Pennington Frost, was dean of Dartmouth Medical School.
Frost joined the staff of Yerkes Observatory in 1898 and became its director in 1905 when George Hale resigned. Frost kept the position until his retirement in 1932. He was the editor of the Astrophysical Journal from 1902 to 1932, known for his careful attention to details. In 1915 he lost the use of his right eye and in 1921, his left. Despite his blindness he continued working for eleven more years until his retirement in 1932.
Frost's research focused on the determination of radial velocity using stellar spectroscopy and spectroscopic binaries. In 1902, he discovered the strange behavior of Beta Cephei, which later became the prototype for Beta Cephei variable stars. *TIA

1902 Gheorghe Calugareanu (16 July 1902 - 15 November 1976)As a lecturer, Calugareanu gave simple, clear explanations. He spoke quietly and he would start every lecture by spending ten minutes going over the material from the previous lecture. At the end of the lecture he would explain what was coming in the next lecture. This makes it sound as if he would make little progress, but on the contrary, he was able to go steadily though the material. Students really understood the lectures as he gave them and his lectures were models for the highest quality of teaching. His research was elegant and his personality shone through his mathematical papers as it did in his teaching. Some of his results had applications in molecular biology or fluid mechanics. In fact Calugareanu spoke of about the tension between pure and applied mathematics in his autobiographical paper . He remarks there that, in Communist Romania, the party and the state stress the importance of research which leads to improvements in the conditions of life. However, they also recognize the importance of fundamental research as a foundation for and preliminary to applications. The paper allows us to glimpse other aspects of Calugareanu's approach to mathematics. He addresses younger mathematicians explaining that because of the rapid expansion in mathematics there is great importance in having a guiding thread or theme in one's research. This, he explains, is especially true if one's work spans several fields. His own work did indeed span several fields, and he recognises that his thread was the idea of invariance which ran through his work in complex variables, differential topology, and modern algebra.*SAU

1903 Irmgard Flugge-Lotz (6 July 1903 - 22 May 1974)born in Hameln, Germany. Her father encouraged her in mathematics, but she chose engineering because “I wanted a life which would never be boring—a life in which new things would always occur.” She studied applied mathematics at the Technical University of Hanover and in 1929 she became a Doktor-Ingenieur, the equivalent of an American Ph.D. in Engineering. She made contributions to aerodynamics, control theory, and fluid mechanics. In 1960 she became full professor at Stanford. *WM

1951 Dan Bricklin (born 16 July 1951- ) American computer scientist who,with Bob Frankston, created VisiCalc, the first spreadsheet computer program (1979) which created a market beyond hobbyists for the emerging personal computers. Businesses found the program very useful because of the speed and accuracy of its calculations. Originally written in 6502 assembly language to run on a 32K-byte Apple II, it was soon ported to virtually all major 6502- and Z80-based personal computers then available. They did not reap huge financial profits from the spreadsheet program, despite eventually selling over a half-million copies by 1983, because at the time, copyright protection was not generally sought for software, and it was subsequently surpassed by Lotus 1-2-3 *TIS

1739 Charles François de Cisternay Du Fay (14 September 1698 – 16 July 1739) was a French chemist who made early experiments in electricity. In 1733, he distinguished electrical fluid in two types he named "vitreous electricity" and "resinous electricity" depending on the objects that produced the charge (subsequently called "positive" and "negative" by Benjamin Franklin). Du Fay discovered that objects with like charges repel each other, but oppositely charged objects repel. He also noted the effect of electricity shock on his body, and visible spark when making contact with a highly charged object. He observed that electricity may be conducted in the gaseous matter (now called plasma) adjacent to a red-hot body. Du Fay was also a pioneer in crystal optics.*TIS

1981 Jacob Wolfowitz (March 19, 1910 – July 16, 1981) was a Polish-born American statistician and Shannon Award-winning information theorist. He was the father of former Deputy Secretary of Defense and World Bank Group President Paul Wolfowitz.
While a part-time graduate student, Wolfowitz met Abraham Wald, with whom he collaborated in numerous joint papers in the field of mathematical statistics. This collaboration continued until Wald's death in an airplane crash in 1950. In 1951, Wolfowitz became a professor of mathematics at Cornell University, where he stayed until 1970. He died of a heart attack in Tampa, Florida, where he was a professor at the University of South Florida.
Wolfowitz's main contributions were in the fields of statistical decision theory, non-parametric statistics, sequential analysis, and information theory.*Wik

1983 Edouard Zeckendorf (2 May 1901 - 16 May 1983) was a Belgian doctor, army officer and mathematician. In mathematics, he is best known for his work on Fibonacci numbers and in particular for proving Zeckendorf's theorem. Zeckendorf's theorem states that every positive integer can be represented uniquely as the sum of one or more distinct Fibonacci numbers in such a way that the sum does not include any two consecutive Fibonacci numbers.
Zeckendorf was born in Liège in 1901. He was the son of a Dutch dentist. In 1925, Zeckendorf graduated as a medical doctor from the University of Liège and joined the Belgian Army medical corps. When Germany invaded Belgium in 1940, Zeckendorf was taken prisoner and remained a prisoner of war until 1945. During this period, he provided medical care to other allied POWs. *Wik

1994 Julian Seymour Schwinger (February 12, 1918 – July 16, 1994) American physicist who shared the 1965 Nobel Prize in Physics for his contributions to quantum electrodynamics (with Richard Feynman and Shin-Itiro Tomonaga). Schwinger worked on reconciling quantum mechanics with Albert Einstein's special theory of relativity. He published his first physics paper at the age of sixteen. During WW II, he developed important methods in electromagnetic field theory, which advanced the theory of wave guides. His variational techniques were applied in several fields of mathematical physics. In the 1940's he was one of the inventors of the "renormalization" technique. In 1957, he proposed that theoretically there were two different neutrinos: one associated with the electron and one with the muon. Later experimental work provided verification. He invented source theory. *TIS  Schwinger was Oppenheimer's most brilliant student. Oppenheimer once said of him, "When ordinary people give a talk, they tell you how to do it.  When Julian gives a talk, it is to tell you that only he can do it." *Freeman Dyson, Infinities in all Directions.

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

Sunday, 15 July 2018

On This Day in Math - July 15

Mathematics is as much an aspect of culture as it is a collection of algorithms.

-Carl Boyer

The 196th day of the year, A Lychrel number is a natural number which cannot form a palindromic number through the iterative process of repeatedly reversing its base 10 digits and adding the resulting numbers. 196 is the lowest number conjectured to be a Lychrel number; the process has been carried out for one billion iterations without finding a palindrome, but no one has ever proven that it will never produce one. The number produced on the one billionth iteration had 413,930,770 digits. The name "Lychrel" was coined by Wade VanLandingham—a rough anagram of his girlfriend's name Cheryl. No Lychrel numbers are known, though many numbers are suspected Lychrels, the smallest being 196. (Students might try finding the number of iterations of the process to find a palindrome for various n. 195, for example, takes four iterations :
195 + 591 = 786
786 + 687 = 1473
1473 + 3741 = 5214
5214 + 4125 = 9339)
DO not try the numbers 89 or 98. Harry J Saal used a computer to repeatedly iterate this process and finally did come up with a palindrome, the number 8,813,200,023,188 on the 24th iteration.

Jim Wilder noticed that 142 =196 and 132=169... are there other squares of consecutive numbers that share the same digits?

A number is said to be square-full if for every prime, p, that divides it, p2 also divides it. 196 is such a number. Are there cube-full numbers? (of course there are, but what are they?)


622 Mohammed’s flight, the Hegira, from Mecca to Medina began. Traditionally, the Islamic calendar began at sunset on this day.*VFR

1662 The Royal Society of London received its charter. *VFR Its official foundation date is 28 November 1660, when a group of 12 met at Gresham College after a lecture by Christopher Wren, then the Gresham Professor of Astronomy, and decided to found 'a Colledge for the Promoting of Physico-Mathematicall Experimentall Learning'. This group included Wren himself, Robert Boyle, John Wilkins, Sir Robert Moray, and William, Viscount Brouncker.  n 1662 the Society was permitted by Royal Charter to publish and the first two books it produced were John Evelyn's Sylva and Micrographia by Robert Hooke. *Royal Society Web page

1808 Thomas Jefferson writes to Augustin-François Silvestre French inventor and popularizer of science to thank him for sharing copies of " volumes of the Memoirs of the Agricultural Society of the Seine" and shares his ideas about the importance of the plough, including details of a mould board of his own design. "I shall with great pleasure attend to the construction and transmission to the Society of a plough with my mould board. This is the only part of that useful instrument to which I have paid any particular attention. But knowing how much the perfection of the plough must depend, 1st, on the line of traction; 2d, on the direction of the share; 3d, on the angle of the wing; 4th, on the form of the mould-board; " *Letters of Thomas Jefferson,

1828 The Board of Longitude is dissolved by act of Parliament. In the Parliamentary discussions prior to the act, John Crocker, First Secretary of the Admiralty,  argued that the Board was :
"wholly occupied in reading the wild ravings of mad men, who fancied they had discovered perpetual motion and such like chimeras.

1913 A window at Westminster Abbey, in memory of Lord Kelvin, was unveiled.*VFR (If someone has a better image of this window to offer, please send me a copy and I will replace this very small image.)

1928 The first message for transmission by the Enigma was encoded.*VFR The first Enigma was invented by German engineer Arthur Scherbius at the end of World War I. This model and its variants were used commercially from the early 1920s, and adopted by military and government services of several countries — most notably by Nazi Germany before and during World War II. Several different Enigma models were produced, but the German military models are the ones most commonly discussed. *Wik


1808 Sir Henry Cole (15 July 1808 – 18 April 1882) British industrial designer, museum director and writer who produced the first commercial Christmas card.* Cole played a pivotal role in the introduction of the Penny Post, the English postal system (assistant to Rowland Hill, 1837-40), influenced the expansion of railways, helped establish the Victoria and Albert Museum, contributed greatly to the success of London’s Great Exhibition of 1851, and promoted art and science education. In 1843, wishing to save much handwriting of seasonal correspondance, Cole introduced the world's first commercial Christmas card. He commissioned artist John Callcott Horsley to make the artwork for 1000 hand-coloured lithographs. (Individuals' homemade Christmas cards had existed earlier.)

1848 Vilfredo Federico Damaso Pareto (15 July 1848 – 19 August 1923) born Wilfried Fritz Pareto, was an Italian engineer, sociologist, economist, and philosopher. He made several important contributions to economics, particularly in the study of income distribution and in the analysis of individuals' choices. "His legacy as an economist was profound. Partly because of him, the field evolved from a branch of moral philosophy as practiced by Adam Smith into a data intensive field of scientific research and mathematical equations. His books look more like modern economics than most other texts of that day: tables of statistics from across the world and ages, rows of integral signs and equations, intricate charts and graphs."[1] He introduced the concept of Pareto efficiency and helped develop the field of microeconomics. He also was the first to discover that income follows a Pareto distribution, which is a power law probability distribution. The Pareto principle was named after him and built on observations of his such as that 80% of the land in Italy was owned by 20% of the population. He also contributed to the fields of sociology and mathematics.*Wik

1865 Wilhelm Wirtinger (15 July 1865 – 15 January 1945) was an Austrian mathematician, working in complex analysis, geometry, algebra, number theory, Lie groups and knot theory.Wirtinger was greatly influenced by Felix Klein with whom he studied at the University of Berlin and the University of Göttingen. In 1907 the Royal Society of London awarded him the Sylvester Medal, for his contributions to the general theory of functions. *Wik

1895 Rudolf Diesel applies for patent for an internal combustion engine in the US (patented Aug 9, 1898.) "My invention has reference to improvements in apparatus for regulating the fuel supply in slow-combustion motors" *

1906 Adolph Andrei Pavlovich Yushkevich (15 July, 1906 – 17 July, 1993) was one of the leading historians of mathematics in the world. His doctorate was on Russian mathematics during the 18th century and he began publishing in 1929 the first of over 300 works on the history of mathematics. He contributed 21 articles to the Dictionary of Scientific Biography which are referenced in this Archive. This Archive also references over 50 articles by Yushkevich about a wide range of mathematicians from the earliest to modern times. Yushkevich was arguably the leading world authority on Euler and he was one of the leading authorities on medieval mathematics. *SAU

1909 William Gemmell Cochran (15 July 1909, Rutherglen – 29 March 1980, Orleans, Massachusetts) Statistician. In 1934 R A Fisher left Rothamsted Experimental Station to accept the Galton chair at University College, London and Frank Yates became head at Rothamsted. Cochran was offered the vacant post but he had not finished his doctoral course at Cambridge. Yates later wrote:-
... it was a measure of good sense that he accepted my argument that a PhD, even from Cambridge, was little evidence of research ability, and that Cambridge had at that time little to teach him in statistics that could not be much better learnt from practical work in a research institute.
Cochran accepted the post at Rothamsted where he worked for 5 years on experimental designs and sample survey techniques. During this time he worked closely with Yates. At this time he also had the chance to work with Fisher who was a frequent visitor at Rothamsted.
Cochran visited Iowa Statistical Laboratory in 1938, then he accepted a statistics post there in 1939. His task was to develop the graduate programme in statistics within the Mathematics Department. In 1943 he joined Wilks research team at Princeton.
At Princeton he was involved in war work examining probabilities of hits in naval warfare. By 1945 he was working on bombing raid strategies.
He joined the newly created North Carolina Institute of Statistics in 1946, again to develop the graduate programme in statistics. From 1949 until 1957 he was at Johns Hopkins University in the chair of biostatistics. Here he was more involved in medical applications of statistics rather than the agricultural application he had studied earlier.
From 1957 until he retired in 1976 Cochran was at Harvard. His initial task was to help set up a statistics department, something which he had a great deal of experience with by this time. He had almost become a professional at starting statistics within universities in the USA. *SAU

1922 Leon Max Lederman (July 15, 1922 - ) American physicist who, along with Melvin Schwartz and Jack Steinberger, received the Nobel Prize for Physics in1988 for their joint research and discovery (1960-62) of a new subatomic particle, the muon neutrino. Neutrinos are subatomic particles having no detectable mass and no electric charge, which travel at nearly the speed of light. The discovery of muon neutrinos, a new type of neutrino, was followed by discoveries by other scientists of a number of different "families" of subatomic particle. Together, they now form a standard model, a scheme that has been used to classify all known elementary particles. He was director of the Fermi National Accelerator Laboratory in Batavia, Ill.*TIS

1930 Steven Smale (July 15, 1930 - ) born in Flint, Michigan. He earned three degrees at the University of Michigan and now teaches at Berkeley. He has made significant contributions to topology (Fields Medal, 1966), dynamical systems, economics, and numerical analysis. This still leaves time for chess, go, sailing, collecting minerals, and lots of political activism. For an interview with this fa­cinating mathematician, see More Mathematical People (1990), edited by Donald J. Albers, G. L. Alexanderson and Constance Reid.*VFR

1943 Jocelyn Bell Burnel(15 July 1943- ) British astronomer who discovered the first four pulsars. She was a Cambridge University graduate student, age 24, searching for quasars in 1967, when she noticed an unusual stellar radio signal - a rapid series of pulses repeating every 1.337 sec. This interstellar beacon was not man-made, so it was nicknamed in fun as LGM, for Little Green Men. In the next few months, Bell (her maiden name) found three more sources of radio pulses by careful scrutiny of hundreds of feet of pen-recorder paper. These represented a new class of celestial objects - pulsars - which astronomers eventually associated with superdense matter in the final stage of the evolution of massive stars. To date, hundreds more pulsars have been identified. *TIS


998 Abu'l-Wafa (10 June 940 – 15 July 998) was an Islamic astronomer and mathematician who wrote commentaries on the works of earlier mathematicians. He made astronomical observations and constructed accurate trigonometric tables.*SAU
He made important innovations in spherical trigonometry, and his work on arithmetics for businessmen contains the first instance of using negative numbers in a medieval Islamic text.
He is also credited of compiling tables of sines and tangents at 15' intervals. He also introduced the sec and cosec and studied the interrelations between the six trigonometric lines associated with an arc. His Almagest was widely read by medieval Arabic astronomers in the centuries after his death. He is known to have written several other books that have not survived. *Wik

1841 Félix Savary (October 4, 1797, Paris - July 15, 1841 in Estagel) was a student at the École Polytechnique completing his studies in 1815. He then taught at the École, becoming a professor of astronomy and geodesy there in 1831. There he became a founder of studies into surveying and machines.
Savary also served as librarian at the Bureau des Longitudes from 1823 to 1829. Then on 24 December 1832, in recognition of his achievements, he was elected to the Académie des Sciences.
He worked on electromagnetism and electrodynamics, some work being done jointly with Ampère. In particular, on this topic, he wrote Mémoire sur l'application du calcul aux phenomènes élecro-dynamique (1823).
Savary also developed a theorem (named after him) on the curvature of a roulette, the curve traced out by a point on a fixed curve which rolls on a second curve.
He wrote on the rotation of magnets, studied the intensity of magnetism through an electrical discharge (1827), and applied the laws of gravity to determine the orbits of double stars in close orbit round each other (1827). In fact, on the topic of double stars, he published Mémoire sur les orbites des étoiles doubles (1827), and Sur la détermination des orbites que décrivent autour de leur centre de gravité deux étoiles très rapprochées l'une de l'autre (1827) in Connaissance des Temps. The star x Ursae Majoris is a double star and Savary demonstrated that the two stars move in elliptical orbits with the centre of gravity at the focus of the ellipses. Although this might appear to be a fairly simple consequence of Newton's law of gravitation, nevertheless it was important for it was the first verification of the laws for objects outside the solar system. This was the first verification of the universal nature of Newton's laws.*SAU

1931 Ladislaus Josephowitsch Bortkiewic studied law at St Petersburg, graduating in 1890 and then went on to study political economy and statistics for a year of postgraduate work. He studied at Strasbourg from 1891 to 1892, then at Göttingen under Lexis in 1892, going on to also study at Vienna and Leipzig. After submitting a dissertation, he was awarded a doctorate in 1893 from Göttingen.
After lecturing in statistics and actuarial science from 1895 to 1897 as a privatdozent in Strasbourg he went to St Petersburg where he was a clerk in the Railway Office from 1897 until 1901. However, during this time he returned to academic life, teaching statistics from 1899 until December 1900 at the Alexandrowskii Lyceum. Then in 1901 he was appointed as an extraordinary professor of statistics at the University of Berlin. Bortkiewicz became an ordinary professor of statistics and political economy at the University of Berlin in 1920 and he spent the rest of his life there. An unfortunate argument with an Italian statistician Gini, who accused Bortkiewicz of plagiarism, led to an unhappy episode near the end of Bortkiewicz's life.
Bortkiewicz worked on mathematical statistics and applications to actuarial science and political economy. His work on actuarial science was largely concerned with mortality tables. He examined life expectancy in an increasing population and showed in 1893, contrary to what had previously been believed, that life expectancy in such a population could only be computed from mortality tables and was not a function of the observed birth rate and death rate. He published on mortality rates again in publication of 1904 and 1911 where he examined methods to compare mortality rates.
Good argues that the Poisson distribution should have been named the von Bortkiewicz distribution. Bortkiewicz was interested in the law of small numbers and he used the divergence coefficient Q, deducing its expectation and standard deviation. He published a work The Law of Small Numbers in 1898. In this he was the first to note that events with low frequency in a large population followed a Poisson distribution even when the probabilities of the events varied.Other areas to which Bortkiewicz applied his statistical methods include radioactivity (1913), order statistics, and applications to legal studies. *SAU

1961 Nina Karlova Bari (November 19, 1901, Moscow – July 15, 1961, Moscow) was hit by a train in Moscow Metro. It is unclear whether it was an accident or a suicide brought on by despondency over the death of Nikolai Nikolaevich Luzin (1883–1950), her teacher and reported lover.*VFR

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

Saturday, 14 July 2018

On This Day in Math - July 14

Antoine Caron: Astronomers Studying an Eclipse *TIA

Nature is not embarrassed by difficulties of analysis.
~Augustin Fresnel

The 195th day of the year..195 is the sum of eleven consecutive primes: 3 + 5 + 7 + 11 + 13 + 17 + 19 + 23 + 29 + 31 + 37 Students might wonder which numbers can (and cannot) be expressed as the sum of one or more consecutive Primes.

195 is also the third integer that is the sum of the squares of three consecutive primes.*Prime Curios

also, 1*95 = 19*5 Derek Orr tells me there are only four non-trivial 3-digit numbers with this property *@Derektionary

a Heronian triangle is a triangle that has side lengths and area that are all integers. There is an almost-equilateral, scalene triangle with one side of 195. The other sides are 194, and 193. Students can find the area using Heron's formula.


1686 On June 20th Halley Wrote to Newton that Hooke has protested his "discovery" of the inverse square law should be noted in Principia. Newton responded On July 14, 1686, with a peace offering; "And now having sincerely told you the case between Mr Hooke and me, I hope I shall be free for the future from the prejudice of his letters. I have considered how best to compose the present dispute, and I think it may be done by the inclosed scholium to the fourth proposition." This scholium was "The inverse law of gravity holds in all the celestial motions, as was discovered also independently by my countrymen Wren, Hooke and Halley."

1696  Construction of the Eddystone lighthouse began today by Henry Winstanley.  Winstanley ...investing some of the money he had made from his work and commercial enterprises in five ships. Two of them were wrecked on the Eddystone Rocks near Plymouth, and he demanded to know why nothing was done to protect vessels from this hazard. Told that the reef was too treacherous to mark, he declared that he would build a lighthouse there himself, and the Admiralty agreed to support him with ships and men.
In the 1690s he opened a Mathematical Water Theatre known as "Winstanley's Water-works" in London's Piccadilly. This was a commercial visitor attraction which combined fireworks, perpetual fountains, automata and ingenious mechanisms of all kinds, including "The Wonderful Barrel" of 1696 which served visitors with hot and cold drinks from the same piece of equipment. It was a successful and profitable venture and continued to operate for some years after its creator’s death.(*Today in History)

1776 The beginning of Cook's third and last voyage made with the Resolution and the Discovery, which cleared the channel on 14 July 1776. This voyage, in which Cook was killed, came to an end in 1780.*Wik

1791 A mob in Birmingham, England, rioted during festivities marking the anniversary of the fall of the Bastille on this date in 1789. The mob, which ran wild for three days, destroyed the house, laboratory and library of Joseph Priestley, discoverer of oxygen, because of his anti religious views and espousal of revolutionary causes.*VFR Within a few years, on 7 Apr 1794, he forever left England and traveled to the United States. Priestley discovered oxygen nearly 20 years earlier, on 1 Aug 1774.*TIS

1831 Evariste Galois again arrested, as a precautionary measure. He received a six months sentence. *VFR

In 1867, Alfred Nobel demonstrated dynamite for the first time at a quarry in Redhill, Surrey. In 1866 Nobel produced what he believed was a safe and manageable form of nitroglycerin called dynamite. He established his own factory to produce it but in 1864 an explosion at the plant killed Nobel's younger brother and four other workers. Deeply shocked by this event, he now worked on a safer explosive and in 1875 came up with gelignite. Other inventions followed including ballistite, a form of smokeless power, artificial gutta-percha and a mild steel for armour-plating.*TIS

1868 Alvin J. Fellows of New Haven, Connecticut, received patent #79,965 for the first tape measure. It was enclosed in a circular case with a spring lock to hold the tape at any desired point. *VFR (for my son Robin, who seems to collect them as icons of his trade) Earlier, a machine to print ribbon for the supple sewing tape measures had already been patented on 3 Sep 1847, after four years of research by the French fashion designer, Lavigne. Further, however, Sheffield, England claims to be not just the home of stainless steel, but also where the spring tape measure was invented. *TIS  (This was for the spring type tapes common today. Earlier tapes were produced with a brass fold-out clip to rewind them... One my grand-daughter just found for her dad at a boot-sale for 50 pence was an old Chesterman that was marked in links (.01 chains) and rods (1/4 of a chain) on one side. .... "James Chesterman moved to Sheffield from London in 1820. Nine years later he patented the spring tape measure. He also invented the self-winding window blind, produced the first long steel Measuring tape and the first Woven metallic tape. His business adopted the bow as its trademark, and he named his factory the bow works which moved to this site in 1864.  James Chesterman & Co became synonymous with high quality measuring instruments, especially tapes, callipers and squares. In 1963 amalgamation with John Rabone & Sons created Rabone Chesterman, who were subsequently bought by Stanley Tools and transferred to Stanley's Woodside Plant.  Bow Works was refurbished and extended for its new occupants, Norwich Union in 1993."

1887 The first textbook about the international language, Esperanto, was published by its inventor, Dr. Ludwig Zamenhof, a Pole. Esperanto means “one who hopes.” The Italian mathemati¬cian, Giuseppi Peano, created an international language of his own, Latina sina flexione (Latin without inflections), but it was even less successful than Esperanto. *VFR

1897 The Dorabella Cipher is an enciphered letter written by composer Edward Elgar to Dora Penny, which was included with a "thank you" note from his wife dated July 14, 1897. Penny never deciphered it and its meaning remains unknown.
Elgar also named Variation 10 of his 1899 Variations on an Original Theme (Enigma) Dorabella as a dedication to Dora Penny. *Wik

1943 George Washington Carver was honored by U.S. President Franklin Delano Roosevelt dedicating $30,000 for a National Monument to his accomplishments. The area of Carver's childhood near Diamond Grove, in southwest Missouri has been preserved as a park, with a bust of the agricultural researcher, instructor, and chemical investigator. This park was the first designated national monument to an African American in the United States. In 1850-65, Diamond was a typical "crossroads village" near a diamond-shaped grove of trees not far from the Carver farm in Newton County. Also called Diamond Grove, it consisted of a general store, a combination blacksmith shop and post office, and a church that served as a schoolhouse during the week.*TIS

1954 At a Conference for California Teachers of Mathematics, a Los Angeles dentist named Leon Bankoff presented a talk proving that the 2000 year old proof of Archimedes that there were a pair of congruent "Archimedean Twin Circles" in the Arbelos was in fact false. He produced a third identical circle, now usually called the "Bankoff triplet circle".
Later (1979) Thomas Schoch discovered a dozen new Archimedean circles; and then in 1998, Peter Y. Woo of Biola University, generalized two of Schoch's circles, to discover an infinite family of Archimedean circles named the Woo circles in 1999 *Wik *Mathematics Magazine For more on the Archimedean Circles, see my blog on  The Shoemaker's Knife Cuts Beautiful Math Across the Centuries

1977 Minor planet (2509) Chukotka 1977 NG. Discovered by N. S. Chernykh at Nauchnyj. Named for a National Area of the R.S.F.S.R., situated in the northeastern part of the U.S.S.R. The discoverer participated in an expedition there to observe the 1972 total solar eclipse. *NSEC

2004 A patent application by John St. Clair was filed for a training program to teach people to walk through walls:Publication number US20060014125 A1   (Ok, just think about it a minute.  Someone had to say,  "Yeah, we'll give them a patent for that.")


2015 The New Horizons probe, launched on Jan. 19, 2006, with Clyde Tombaugh's ashes on board,  arrived at Pluto on July 14, 2015. *The Las Cruces Sun-New
Also on board was a 1991 US postage stamp which was a motivator for people in the project.


1610 Ferdinand II (9 July 1578 – 15 February 1637) Fifth grand duke (granduca) of Tuscany, a patron of sciences, whose rule was subservient to Rome. Ferdinand II de' Medici was Grand Duke from 1621. He encouraged scientific studies, and he protected Galileo and the Accademia del Cimento (1657 - 1667). He also devised a sealed thermometer which, unlike Galileo's open one, was not affected by changes in air pressure. It was to him that Galileo dedicated the lens with which he had discovered the satellites of Jupiter and he also made him a gift of the armed lodestone. J. W. Blaeu dedicated to him one of his globes of the fifth type. Ferdinand II was also a patron of Robert Dudley.*TIS

1671 Jacques Eugène d'Allonville, Chevalier de Louville par Fontenelle (July 14, 1671 – September, 1732) French astronomer and mathematician.
He was born in the Château de Louville, and studied mathematics before joining the navy. He achieved the rank of colonel before retiring from military service in 1713, following the peace of Utrecht. He thereafter took up the study of astronomy.
He is noted for determining a method for precisely calculating the occurrence of solar eclipses.
The crater Louville on the Moon is named in his honor. *TIA

1793 George Green baptized in Nottingham, England. The date of his birth is unknown. His most famous work, An Essay on the Application of Mathematical Analysis to the Theory of Electricity and Magnetism was published, by subscription, in March 1828. Most of the fifty-two subscribers were friends and patrons. The work lay unnoticed until William Thomson rediscovered it and showed it to Liouville and Sturm in Paris in 1845. The Theory of Potential it developed led to the modern mathematical theory of electicity. *VFR
George Green was an English mathematician, born near Nottingham, who was first to attempt to formulate a mathematical theory of electricity and magnetism. He was a baker while, remarkably, he became a self-taught mathematician. In March 1828 he published An Essay on the Application of Mathematical Analysis to the Theories of Electricity and Magnetism. He became an undergraduate at Cambridge in October 1833 at the age of 40. Lord Kelvin (William Thomson) subsequently saw, was excited by the Essay. Through Thomson, Maxwell, and others, the general mathematical theory of potential developed by an obscure, self-taught miller's son heralded the beginning of modern mathematical theories of electricity.*TIS

1905 Laurence Chisholm Young (14 July 1905 – 24 December 2000) was a mathematician known for his contributions to measure theory, the calculus of variations, optimal control theory, and potential theory. He is the son of William Henry Young and Grace Chisholm Young, both prominent mathematicians. The concept of Young measure is named after him. *Wik

1918 Jay W(right) Forrester (born July 14, 1918- ) is a U.S. electrical engineer and management expert. In 1944-51 he supervised the building of the Whirlwind computer at the Massachusetts Institute of Technology, for which he invented the random-access magnetic core memory, the information-storage device employed in most digital computers. He also studied the application of computers to management problems, developing methods for computer simulation.*TIS


1800 Lorenzo Mascheroni (May 13, 1750 – July 14, 1800) was a geometer who proved in 1797 that all Euclidean constructions can be made with compasses alone, so a straight edge in not needed. In fact this had been (unknown to Mascheroni) proved in 1672 by a little known Danish mathematician Georg Mohr. *SAU In his Adnotationes ad calculum integrale Euleri (1790) he published a calculation of what is now known as the Euler–Mascheroni constant, usually denoted as γ (gamma).*Wik

1827 Augustin Jean Fresnel (10 May 1788, Broglie (Eure)- 14 July 1827 (aged 39)
Ville-d'Avray (Hauts-de-Seine)) French physicist who first investigated the effect of interference of light, with results known as Fresnel fringes. This decisively work, together with further experiments with polarized light supported Thomas Young's wave theory of light Fresnel advanced the wave theory by identifying light as transverse waves rather than the longitudinal waves previously assumed by Young and Huygens. His pioneering work in optics included showing that white light is composed of a spectrum of innumerable wavelengths ranging from red to shorter violet wavelenths. In 1819, he improved the optical system of lighthouses by replacing metal reflectors with revolutionary stepped lenses of his design.*TIS

1865 Benjamin Gompertz (March 5, 1779 – July 14, 1865), was a self educated mathematician, denied admission to university because he was Jewish.[citation needed] Nevertheless he was made Fellow of the Royal Society in 1819. Gompertz is today mostly known for his Gompertz law (of mortality), a demographic model published in 1825. The model can be written in this way:

N(t) = N(0) e^{-c (e^{at}-1)},

where N(t) represents the number of individuals at time t, and c and a are constants.

This model is a refinement of the demographic model of Malthus. It was used by insurance companies to calculate the cost of life insurance. The equation, known as a Gompertz curve, is now used in many areas to model a time series where growth is slowest at the start and end of a period. The model has been extended to the Gompertz–Makeham law of mortality.

1899 Sir Arthur Thomas Cotton (15 May 1803 – 24 July 1899) British engineer whose life-work was constructing irrigation, navigation canals and dams for water storage in Southern India, saving thousands from famine and promoting local economy. He joined the Madras engineers in 1819, fought in the first Burmese war (1824-26) and began his ambitious irrigation project (1826-62). He built dams on several rivers, transforming the drought-stricken Tanjore district into the richest part of the state of Madras. His ambitious masterplan was not completed in his lifetime, but his ideas anticipated projects that were subsequently taken up. In the present time, India's goal of a National Water Grid confronts the problem of increasingly scarce water. Cotton founded the Indian school of hydraulic engineering.*TIS

1953 Richard von Mises (19 April 1883, Lviv – 14 July 1953, Boston, Massachusetts) Austrian-American mathematician and aerodynamicist who notably advanced statistics and the theory of probability. Von Mises' contributions range widely, also including fluid mechanics, aerodynamics, and aeronautics. His early work centred on aerodynamics. He investigated turbulence, making fundamental advances in boundary-layer-flow theory and airfoil design. Much of his work involved numerical methods and this led him to develop new techniques in numerical analysis. He introduced a stress tensor which was used in the study of the strength of materials.Von Mises' primary work in statistics concerned the theory of measure and applied mathematics. His most famous, yet controversial, work was in probability theory. *TIS He is often credited with the creation of the "Birthday Problem", but in this blog I suggest otherwise.

1956 John Miller studied at Glasgow and Göttingen. He returned to Glasgow to the Royal College of Science and Technology (the precursor to Strathclyde University). He became President of the EMS in 1913. *SAU

1960 Maurice de Broglie (27 April 1875–14 July 1960)(6th duke) (Louis-César-Victor-) Maurice de Broglie was a French physicist who made many contributions to the study of X rays. While in the navy (1895-1908), he first distinguished himself by installing the first French shipboard wireless. From 1912, his chief interest was X-ray spectroscopy. His "method of the rotating crystal" was an application of Bragg's "focussing effect" to eliminate spurious spectral lines. De Broglie discovered the third L absorption edge (1916), which led to the exploration of "corpuscular spectra." During 1921-22, he worked with his brother Louis to refine Bohr's specification of the substructure of the various atomic shells. He also did pioneer work in nuclear physics and cosmic radiation. *TIS

2016  Maryam Mirzakhani, the first woman and first Iranian to win the Fields Medal,died of metastatic breast cancer  at the age of 40. She had been a professor at Stanford University since 2008. *Sci Am

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, 13 July 2018

On This Day in Math - July 13

There is (gentle reader) nothing (the works of God only set apart) which so much beautifies and adorns the soul and mind of man as does knowledge of the good arts and sciences. ... Many ... arts there are which beautify the mind of man; but of all none do more garnish and beautify it than those arts which are called mathematical, unto the knowledge of which no man can attain, without perfect knowledge and instruction of the principles, grounds, and Elements of Geometry.

~John Dee, The Mathematical Preface

This is the 194th day of the year, 1944+1 = 1,416,468,497 is prime *Prime Curios

194 is also the smallest number that can be written as the sum of 3 squares (not all unique) in five ways. (There is a slightly larger number that is expressible as the sum of 3 unique squares in five ways. )

194 is the product of the largest and smallest prime less than 100.

194 is the sum of three consecutive squares, \( 194 = 7^2 + 8^2 + 9^2 \)


Newton writes to John Collins, "...about the infinite series I am not yet resolved, not knowing when I shall proceed to finish it."   *Correspondence of Scientific Men of the Seventeenth Century ..., Volume 2

1773 Gerolamo Saccheri, a Jesuit priest, received the imprimatur of the Inquisition for his Euclides ab Omni Naevo Vindicatus (Euclid Cleansed of Every Blemish), an important forerunner of non-Euclidean geometry. [George E. Martin, The Foundations of Geometry and the Non-Euclidean Plane, p. 304]*VFR

1783 Astronomer William Bayly is paid 200 pounds by the Board of Longitude for "as a recompense for his troubles in reducing, compiling, and printing the astronomical observations of Captain Cooks last voyage, intended to be published with the historical account thereof."  *Derek Howse, Britain's Board of Longitude, The Finances
In 1772 Bayly accompanied William Wales as an astronomer on Cook's second voyage of discovery to the southern hemisphere. The two ships employed in the expedition, the Resolution and the Adventure sailed on 13 June. He also sailed in Cook's third and last voyage made with the Resolution and the Discovery, which cleared the channel on 14 July 1776. This voyage, in which Cook was killed, came to an end in 1780.

2012 the third Friday-the-thirteenth of the year. Each Gregorian 400-year cycle contains 146,097 days (365 × 400 = 146,000 normal days, plus 97 leap days) and they equal 146,097 days, total. 146,097 ÷ 7 = 20,871 weeks. Thus, each cycle contains the same pattern of days of the week (and thus the same pattern of Fridays that are on the 13th).
The 13th day of the month is slightly more likely to be a Friday than any other day of the week. On average, there is a Friday the 13th once every 212.35 days (compared to Thursday the 13th, which occurs only once every 213.59 days).
2012 has had Friday-the-13ths in January, April and July . pointed out that these three Fri-13ths occur in intervals of 13 weeks.
According to the Stress Management Center and Phobia Institute in Asheville, North Carolina, an estimated 17 to 21 million people in the United States are affected by a fear of this day. Some people are so paralyzed by fear that they avoid their normal routines in doing business, taking flights or even getting out of bed. "It's been estimated that \([US]$800 or $900\) million is lost in business on this day". Despite this, representatives for both Delta and Continental Airlines say that their airlines do not suffer from any noticeable drop in travel on those Fridays.
According to folklorists, there is no written evidence for a "Friday the 13th" superstition before the 19th century. The earliest known documented reference in English occurs in Henry Sutherland Edwards' 1869 biography of Gioachino Rossini. *Wik

2016 Jaime Escalante commemorative stamp was officially unveiled at the 87th conference of the League of United Latin American Citizens (LULAC) today in Washington, D.C. Escalante, a teacher in his native Bolivia who arrived in the states in 1963, became known for using innovative methods to teach inner-city students in East Los Angeles that some considered "unteachable," and many of whom went on to master calculus under his tutelage.
His story was the subject of the seminal 1988 movie "Stand and Deliver," which is one of the most viewed movies in U.S. film history. *NBC

2018 Next solar eclipse on a Friday the 13th. The last solar eclipse on a Friday 13th was in December 1974. Both are partial solar eclipses. There are 24 solar eclipses on a Friday the 13th between the years 0 and 3000; Of which 13 partial, 9 annular and 2
total solar eclipses. *NSEC


1527 John Dee born in London, England (13 July 1527–1608 or 1609). In 1570 he wrote a “fruitfull Praeface” to the Billingsley translation of Euclid, which he edited. This was the first English Euclid.
Dee was a noted English mathematician, astronomer, astrologer, occultist, navigator, imperialist and consultant to Queen Elizabeth I. He devoted much of his life to the study of alchemy, divination and Hermetic philosophy.
Dee straddled the worlds of science and magic just as they were becoming distinguishable. One of the most learned men of his age, he had been invited to lecture on advanced algebra at the University of Paris while still in his early twenties. Dee was an ardent promoter of mathematics and a respected astronomer, as well as a leading expert in navigation, having trained many of those who would conduct England's voyages of discovery.*Wik Aubrey's Brief Lives gives Dee credit for inventing the phrase, "The British Empire."

Thony Christie, The Renaissance Mathematicus has written a really interesting blog post on Dee.

1741 Carl Friedrich Hindenburg (13 July 1741– 17 March 1808) published a series of works on combinatorial mathematics.*SAU
Hindenburg co-founded the first German mathematical journals. He also influenced Christian Kramp's work in combinatorics. In 1796, he edited Sammlung combinatorisch-analytischer Abhandlungen, which contained a claim that de Moivre's multinomial theorem was "the most important proposition in all of mathematical analysis"*Wik

1822 Heinrich Louis d'Arrest13 July 1822 – 14 June 1875) German astronomer who, while a student at the Berlin Observatory, hastened the discovery of Neptune by suggesting comparison of the sky, in the region indicated by Urbain Le Verrier's calculations, with a recently prepared star chart. The planet was found the same night. His father-in-law was A. F. Moebius (1790 - 1868). d'Arrest found several comets, the one of 1851 with a period of 6.6 years bears his name. One work he published was on the Asteroids between Mars and Jupiter, another work titled Siderum nebulosorum observationes Hafniensis contained 1942 nebula, 340 described for the first time.*TIS The crater D'Arrest on the Moon is named after him, as well as a crater on the Martian satellite Phobos and the asteroid 9133 d'Arrest.

1924 Donald Edward Osterbrock (July 13, 1924 - January 11, 2007) was an American astronomer who was a leading authority on the history of astronomy, and director of the University of California's Lick Observatory. He applied physics to produce accurate models of stars. For example, treating the outer part of the sun as turbulent and convective, he explained the seemingly anomalous fact that the sun's corona is hotter than its surface. He investigated the nature of ionized gas around hot stars, and was a pioneer in the use of spectroscopic methods for the study of gaseous nebulae. He discovered new types of active galactic nuclei, which are powered by black holes in the centers of galaxies. He fostered the construction of the 10-meter Keck Telescopes in Hawaii. *TIS

1932 Hubert Reeves, CC OQ (born July 13, 1932) is a Canadian astrophysicist and popularizer of science. He attended Collège Jean-de-Brébeuf, a prestigious French-language college in Montreal. He has been a Director of Research at the Centre national de la recherche scientifique since 1965 and currently lives in Paris, France where he often speaks on television promoting science. *Wik

1944 Erno Rubik (July 13, 1944, ) Hungarian mathematician, educator and inventor of Rubik's Cube (1974), which became a popular toy of the 1980s. Rubik's Cube consists of 26 small cubes that rotate on a central axis; nine coloured cube faces, in three rows of three each, form each side of the cube. When the cube arrangement is randomized, the player must then return it to the original condition of faces with matching colours, which is one among 43 quintillion possible configurations.*TIS


1762 James Bradley (March 1693 – 13 July 1762) English astronomer, the third Astronomer Royal, who in 1728 announced his discovery of the aberration of starlight, an apparent slight change in the positions of stars caused by the the motion of the person looking at them with the yearly motion of the Earth. That finding provided the first direct evidence for the revolution of the Earth around the Sun. Bradley was one of the first post-Newtonian observational astronomers who led the quest for precision. From the aberration of starlight, Bradley was also able to make calculations giving the speed of light to be about 283,000 km/s. Further, Bradley discovered that the earth nods a little on its axis, which he named as nutation.*TIS

1794 James Lind FRSE FRCPE (4 October 1716 – 13 July 1794) was a Scottish physician. He was a pioneer of naval hygiene in the Royal Navy. He is of matheamtical interest because he conducted the first modern clinical trial. He developed the theory that citrus fruits cured scurvy. He argued for the health benefits of better ventilation aboard naval ships, the improved cleanliness of sailors' bodies, clothing and bedding, and below-deck fumigation with sulphur and arsenic. He also proposed that fresh water could be obtained by distilling sea water. His work advanced the practice of preventive medicine and improved nutrition.
The concepts behind clinical trials are ancient. The Book of Daniel chapter 1, verses 12 through 15, for instance, describes a planned experiment with both baseline and follow-up observations of two groups who either partook of, or did not partake of, "the King's meat" over a trial period of ten days. Persian physician Avicenna, in The Canon of Medicine (1025) gave similar advice for determining the efficacy of medical drugs and substances. In spite of this history, there seems to have been no clinical trials actually practiced in Western Europe. He blocked a group of twelve men suffering form the effects of scurvy after two months at sea into six different treatment groups of two each. He applied six different treatments, one group getting an issue of cider, one getting citrus, and four other possible alternatives. (The word placebo would not be used until 1772.) Both men in the citrus group showed considerable improvement, and one of the Cider subjects showed mild improvement after the study was stopped in six days. *Wik

1807 Johann(III) Bernoulli (4 Nov 1744 in Basel, Switzerland - 13 July 1807 in Berlin, Germany) wrote a number of works on astronomy and probability theory. Bernoulli wrote a number of works on astronomy, reporting on astronomical observations and calculations, but these are of little importance. Strangely his most important contributions were the accounts of his travels in Germany which were to have a historical impact.
In the field of mathematics he worked on probability, recurring decimals and the theory of equations. As in his astronomical work there was little of lasting importance. He did, however, publish the Leipzig Journal for Pure and Applied Mathematics between 1776 and 1789.
He was well aware of the famous mathematical line from which he was descended and he looked after the wealth of mathematical writings that had passed between members of the family. He sold the letters to the Stockholm Academy where they remained forgotten about until 1877. At that time when these treasures were examined, 2800 letters written by Johann(III) Bernoulli himself were found in the collection. *SAU (See "A Confusion of Bernoulli's" by the Renaissance Mathematicus.)

1896 Friedrich August Kekulé von Stradonitz (7 September 1829–13 July 1896) Kekulé was a German theoretical chemist who figured out how carbon atoms could have a valence of four and join together to make long isomers or even rings. He was the first to discover the ring structure of benzene and greatly advanced the understanding of organic chemistry and aromatic compounds of the time.
Kekulé wrote about the method of his discovery where he was sitting by the fireplace and started to nod off. He dreamed of atoms arranging themselves in groups of ever increasing size until they became long chains. The chains started to wind and turn like snakes until one snake grabbed its own tail. He woke up suddenly and spent the rest of the nightworking out the structure.*This Day in Science History

1921 Gabriel Lippmann (16 August 1845 – 13 July 1921) French physicist, born Hollerich, Luxembourg, who received the Nobel Prize for Physics in 1908 for producing the first colour photographic plate. Lippmann was a giant of his day in classical physics research, especially in optics and electricity. He worked in Berlin with the famed Hermann von Helmholtz before settling in Paris to head (in 1886) the Sorbonne's Laboratories of Physical Research until his death. His inventions include an instrument for precisely measuring minute differences in electrical power and the "coleostat" for steady, long-exposure sky photography.*TIS

1941 Ivan Ivanovich Privalov (13 Feb 1891 in Nizhny Lomov, Penza guberniya (now oblast), Russia - 13 July 1941 in Moscow, USSR) Privalov, often in collaboration with Luzin, studied analytic functions in the vicinity of singular points by means of measure theory and Lebesgue integrals. He also obtained important results on conformal mappings showing that angles were preserved on the boundary almost everywhere. In 1934 he studied subharmonic functions, building on the work of Riesz. He published the monograph Subharmonic Functions in 1937 which gave the general theory of these functions and contained many results from his papers published between 1934 and 1937. *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