Thursday, 13 May 2021

On This Day in Math - May 13

In mathematics you don't understand things.
You just get used to them.

~ John von Neumann

The 133rd day of the year; 133 is a "happy number".  If you sum the squares of the digits and then repeat the process and the sum will eventually come to one. (12 + 32+32= 19 ... ===  82 === 68 === 100 ====1) Some numbers, "unhappy ones", never reach one. (Student's might explore happy numbers to find how many times the process must be iterated for different numbers to reach one, for example I (33) = 5  Alternatively, curious students may wonder what happens to the "unhappy" numbers if they never reach one.)

133 is a repdigitin base 11 (111) and base 18 (77),

133 is the sum of the squares of the first three semi-primes, and is a semi-prime itself. it is the smallest number with this property.  133= 42 + 62 +92 =7*19

And Jim Wilder @wilderlab posted this interesting observation about 133 and it's reversal, 331.


1637 The table knife was created by Cardinal Richelieu in France. Until this time, daggers were used to cut meat, as well as to pick one's teeth. Richelieu had the points rounded off all of the knives to be used at his table *TIS

1673 Scottish mathematician, physicist and optician James Gregory in a letter to John Collins, remarks on diffraction:
If ye think fit, ye may signify to Mr. Newton a small experiment, which (if he know it not already) may be worthy of his consideration. Let in the sun’s light by a small hole to a darkened house, and at the hole place a feather, (the more delicate and white the better for this purpose,) and it shall direct to a white wall or paper opposite to it a number of small circles and ovals, (if I mistake them not) whereof one is somewhat white, (to wit, the middle, which is opposite to the sun,) and all the rest severally coloured. I would gladly hear his thoughts of it.
*Thony Christie, The Renaissance Mathematicus

1733 Swedish Astronomer Birger Wassenius reports on the Eclipse and attributes solar prominences to the Moon:
I can tell you is this, that I soon after the sun's total extinction became aware of some small lighter spots UTI the bright ring, or the atmosphere, about 3 or 4, of different temperament and size, which set in towards the moon's periphery , but at no point next to it. As is now not the moon altogether at one time could fall into my eyes through a long tube, so I had particularly esteem of the largest of these spots, which in the tube appeared on the northeast side of the moon. Being that as composed of three reddish cloud drops placed adjacent to one side, with darker colors or stripes in between, such as the figure below shows fairly. "
*Astronomer Guide

In 1769 Britain's Board of Longitude awarded 10 Pounds to Israel Lyons, Mathematician for, "Reward for his solution to a problem proposed by the late Dr Halley which the Commissioners of Longitude think will be useful to Navigation."  The problem seemed to be related to "traverse sailing."  In June of 1775 his widow would receive an additional 31.50 Pounds for "some of her husband's Problems & Solutions which have been given up by her..." *Derek Howse, Britain's Board of Longitude: The Finances, 1714-1828

1829 Charles-Francois Sturm presented his theorem for finding the number of real roots of a polynomial equation to the French Academy. *VFR  For counting and isolating the real roots, other methods, such as Descartes' rule of signs, are usually preferred, because they are computationally more efficient.

1861 Australian astronomer John Tebbutt discovered C/1861 J1, the Great Comet of 1861.

In 1890, Nikola Tesla was issued a patent for an electric generator (No. 428,057). *TIS

1940 aviation pioneer Igor Sikorsky made the maiden flight with his newly developed helicopter VS-300 *@yovisto

2010 The Times reported on 13 May 2010 that Foucault's original Pendulum is damaged, "Historic instrument is irreparably damaged in an accident at a Paris museum. The original pendulum, which was used by French scientist Leon Foucault to demonstrate the rotation of the Earth and which forms an integral part of Eco's novel's labyrinthine plot, has been irreparably damaged in an accident in Paris. The pendulum's cable snapped last month and its sphere crashed to the marble floor of the Musee des Arts et Metiers. In 1851, Foucault used the pendulum to perform a sensational demonstration in the Paris Pantheon, proving to Napoleon III and the Parisian elite that the Earth revolved around its axis. Such was its success that the experiment was replicated throughout Europe.
Thierry Lalande, the museum's ancient scientific instruments curator, said that the pendulum's brass bob had been badly damaged in three places and could not be restored.
"It's not a loss, because the pendulum is still there, but it's a failure because we were unable to protect it," he said. The circumstances surrounding the accident have raised eyebrows in France.
The museum regularly hosts cocktail parties in the chapel that houses the pendulum, and Mr Lalande admitted that several alarming incidents had occurred over the past year. In May 2009, for example, a partygoer grabbed the 28kg instrument and swung it into a security barrier. *Times Higher Education

2013 Peruvian mathematician Harald Andrés Helfgott releases pre-print claiming a completed proof of the weak Goldbach Conjecture. The weak, or ternary, Goldbach conjecture states that every odd integer greater than 5 can be written as the sum of three primes; *The Value of the Variable at

2016 Friday the 13th.  The thirteenth of the month is more likely to occur on Friday than on any other day of the week. 
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).
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.

In both Greek and Spanish populations, Tuesday the 13th is considered an "unlucky" day, and Italians have a similar tradition for Friday the 17th.

Don't worry, if something terrible doesn't happen to you today, you have another chance for disaster next January. *PB

1750 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.*SAU He is also known for the Euler–Mascheroni constant which gives the limit of the difference between ln(n) and the sum of the harmonic series for the first n terms. The constant first appeared in a 1735 paper by the Swiss mathematician Leonhard Euler, titled De Progressionibus harmonicis observationes (Eneström Index 43). Euler used the notations C and O for the constant. In 1790, Italian mathematician Lorenzo Mascheroni used the notations A and a for the constant. The notation γ appears nowhere in the writings of either Euler or Mascheroni, and was chosen at a later time because of the constant's connection to the gamma function. For example, the German mathematician Carl Anton Bretschneider used the notation γ in 1835. *Wikipedia, with editing He was also a founder of the science of mechanics, asserting that the velocity of a falling body was independent of its weight.

1753 Lazare-Nicolas-Marguerite Carnot,  (13 May 1753 – 2 August 1823)  who published his "Reflections on the Metaphysics of the Infinitesimal Calculus" in 1797. It was written in 1784 for a competition of the Berlin academy seeking a “clear and precise” foundation for the calculus. *VFR  His son Sadi Carnot was a founder of the field of thermodynamics and the theory of heat engines .  He is better known outside of mathematics as a military tactician and politician.

1857 Frederick William Sanderson (13 May 1857 – 15 June 1922) was headmaster of Oundle School from 1892 until his death. He was an education reformer, and both at Oundle, and previously at Dulwich College where he had started as assistant master, he introduced innovative programs of education in engineering. Under his headmastership, Oundle saw a reversal of a decline from which it had been suffering in the middle of the 19th century, with school enrolment rising from 92 at the time of his appointment to 500 when he died.
Sanderson was the inspiration for the progressive headmaster character in H. G. Wells' novel Joan and Peter. Wells had sent his own sons to Oundle, and was friendly with Sanderson. After Sanderson's death, which occurred shortly after delivering an address to Wells and others, Wells initially worked on his official biography, entitled Sanderson of Oundle, but later abandoned it in favour of an unofficial biography, The Story of a Great Schoolmaster. *Wik

1931 András Hajnal (May 13, 1931 - ) is an emeritus professor of mathematics at Rutgers University and a member of the Hungarian Academy of Sciences known for his work in set theory and combinatorics. Hajnal is the author of over 150 publications. Among the many co-authors of Paul Erdős, he has the second largest number of joint papers, 56. With Peter Hamburger, he wrote a textbook, Set Theory*Wik

1826 Christian Kramp, (July 8, 1760 – May 13, 1826) As Bessel, Legendre and Gauss did, Kramp worked on the generalised factorial function which applied to non-integers. His work on factorials is independent of that of Stirling and Vandermonde. The word factorial is reported to be the creation of Louis François Antoine Arbogast (1759-1803). The symbol now commonly used for factorial seems to have been created by Christian Kramp in 1808. It is referred to as "Kramp's notation" in Chrystal's famous Algebra.

1878 Joseph Henry (17 Dec 1797, 13 May 1878 at age 80) One of the first great American scientists after Benjamin Franklin. Although Henry at an early age appeared to be headed for a career in the theater, a chance encounter with a book of lectures on scientific topics turned his interest to science. He aided Samuel F.B. Morse in the development of the telegraph and discovered several important principles of electricity, including self-induction, a phenomenon of primary importance in electronic circuitry. He was the first Secretary (director) of the Smithsonian Institution (1846-1878), where he established the foundation of a national weather service. For more than thirty years, Henry insisted that basic research was of fundamental importance. *TIS

1939 Stanisław Leśniewski (March 30, 1886, Serpukhov – May 13, 1939, Warsaw) was a Polish mathematician, philosopher and logician. Leśniewski belonged to the first generation of the Lwów-Warsaw School of logic founded by Kazimierz Twardowski. Together with Alfred Tarski and Jan Łukasiewicz, he formed the troika which made the University of Warsaw, during the Interbellum, perhaps the most important research center in the world for formal logic. *Wik

1944 William Edward Hodgson Berwick (11 March 1888 in Dudley Hill, Bradford – 13 May 1944 in Bangor, Gwynedd) was a British mathematician, specializing in algebra, who worked on the problem of computing an integral basis for the algebraic integers in a simple algebraic extension of the rationals.*Wik

1983 Otto (Hermann Leopold) Heckmann (23 Jun 1901, 13 May 1983 at age 81) was a German astronomer noted for measuring stellar positions and his studies of relativity and cosmology. He also made notable contributions to statistical mechanics. In 1931, He proved that, under the assumptions that matter is homogeneously distributed throughout the universe and is isotropic (having identical properties in every direction), the theory of general relativity could result in an open, or Euclidean, universe as readily as a closed one. Heckmann organized an international program to photograph and chart the positions of the stars in the Northern Hemisphere, which led to the publication in 1975 of the third German Astronomical Society catalog, Astronomische Gesellschaft Katalog (AGK3). *TIS

1984 Stanislaw Marcin Ulam (13 April 1909 – 13 May 1984)  Polish-American mathematician who played a major role in the development of the hydrogen bomb at Los Alamos. He solved the problem of how to initiate fusion in the hydrogen bomb by suggesting that compression was essential to explosion and that shock waves from a fission bomb could produce the compression needed. He further suggested that careful design could focus mechanical shock waves in such a way that they would promote rapid burning of the fusion fuel. Ulam, with J.C. Everett, also proposed the "Orion" plan for nuclear propulsion of space vehicles. While Ulam was at Los Alamos, he developed "Monte-Carlo method" which searched for solutions to mathematical problems using a statistical sampling method with random numbers. *TIS He is buried in Santa Fe National Cemetery in Santa Fe, New Mexico, USA

“While chatting at the Scottish Caf´e with Borsuk, an outstanding Warsaw topologist, he [Ulam] saw in a flash the truth of what is now called the Borsuk-Ulam theorem. Borsuk had to commandeer all his technical resources to prove it.” For n = 2, this theorem can be interpreted as asserting that some point on the globe has precisely the same weather as its antipodal point. The ‘weather’ has to mean two variables (R2) that vary continuously (f) on the surface (S 2) of the earth. Perhaps temperature and humidity will do? *

2005 George Bernard Dantzig (November 8, 1914 – May 13, 2005) was an American mathematical scientist who made important contributions to operations research, computer science, economics, and statistics.
Dantzig is known for his development of the simplex algorithm, an algorithm for solving linear programming problems, and his work with linear programming, some years after it was invented by the Soviet mathematician & economist Leonid Kantorovich. In statistics, Dantzig solved two open problems in statistical theory, which he had mistaken for homework after arriving late to a lecture of Jerzy Neyman.
Dantzig was the Professor Emeritus of Transportation Sciences and Professor of Operations Research and of Computer Science at Stanford. *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, 12 May 2021

On This Day in Math - May 12

One of the endlessly alluring aspects of mathematics
is that its thorniest paradoxes
have a way of blooming
into beautiful theories.

~Philip J. Davis

The 132nd day of the year; 132 and its reversal (231) are both divisible by the prime 11 (132/11 = 12, 231/11 = 21). Note that the resulting quotients are also reversals. *Prime Curios

132 is the last year day which will be a Catalan Number. The Catalan sequence was described in the 18th century by Leonhard Euler, who was interested in the number of different ways of dividing a polygon into triangles (the octagon can be divided into 6 triangles 142 ways. The sequence is named after Eugène Charles Catalan, who discovered the connection to parenthesized expressions during his exploration of the Towers of Hanoi puzzle.

If you take the sum of all 2-digit numbers you can make from 132, you get 132: 12 + 13 + 21 + 23 + 31 + 32 = 132. 132 is the smallest number with this property,


1364 Founding of the Uniwersytet Jagiellonski in Krakow,
Poland and re-established in 1400 by a member of the Jagiello family)
King Casimir III of Poland received permission to found an institution of higher learning (first called Krakow Academy)in Poland from Pope Urban V. A royal charter of foundation was issued on 12 May 1364, and a simultaneous document was issued by the City Council granting privileges to the Studium Generale. The King provided funding for one chair in liberal arts, two in Medicine, three in Canon Law and five in Roman Law, funded by a quarterly payment taken from the proceeds of the royal monopoly on the salt mines at Wieliczka.
Copernicus (1473-1543) was a student in 1491‑1496 (or 1495) and there is a statue in the library courtyard.

1732 Laura Maria Caterina Bassi awarded Doctorate of science from University of Bologna:
The University of Bologna is the oldest university in Europe and at the beginning of the eighteenth century students were still examined by public disputation, i.e. the candidate was expected to orally defend a series of academic theses. At the beginning of 1732 Bassi took part in a private disputation in her home with members of the university faculty in the presence of many leading members of Bolognese intellectual society. As a result of her performance during this disputation she was elected a member of the prestigious Bologna Academy of Science on 20th March. Rumours of this extraordinary young lady quickly spread and on 17th April she defended forty-nine theses in a highly spectacular public disputation. On 12th May following a public outcry she was awarded a doctorate from the university in a grand ceremony in the city hall of Bologna. Following a further public disputation the City Senate appointed her professor of philosophy at the university, making her the first ever female professor at a European university.
See more at *Thony Christie, The Renaissance Mathematicus

1796 A paper on “Newton's Binomial Theorem Legally Demonstrated by Algebra” read to the Royal Society by the Rev. William Sewell, A. M. Communicated by Sir Joseph Banks, Bart. K. B. P. R. S.

1819 Sophie Germain penned a letter from her Parisian home to Gauss in which she gave a strategy for a general proof of Fermat’s last theorem. Germain's letter to Gauss contained the first substantial progress toward a proof in 200 years. *WIK

1930, the Adler Planetarium and Astronomical Museum was opened to the public in Chicago, Illinois. A program using the Zeiss II star projector was presented by Prof. Philip Fox, who resigned from the staff of Northwestern Observatory to take charge of the new $1 million facility. Housed in a granite building, it was donated to the city by Max Adler, retired vice president of Sears, Roebuck & Co. He had been so impressed when he previously visited the world’s first planetarium at the Deutsches Museum, Munich, Germany, that he resolved to construct America's first modern planetarium open to the public in his home city. Its site was within the fairgrounds of the Century of Progress Exposition in 1933-34, and was an outstanding attraction. *TIS

1941 Zuse Completes Z3 Machine:
Konrad Zuse completes his Z3 computer, the first program-controlled electromechanical digital computer. It followed in the footsteps of the Z1 - the world’s first binary digital computer - which Zuse had developed in 1938. Much of Zuse’s work was destroyed in World War II, although the Z4, the most sophisticated of his creations, survives. *CHM  For a little more information and perspective on Zuse and his creations, see this Renaissance Mathematicus blog.

1984 The Hindu newspaper from Madras, India, reported the unveiling of a statue of Srinivasa Ramanujan. [Mathematics Magazine 57 (1984), p 244]. *VFR

2004 discovery of what was believed to be the world's oldest seat of learning, the Library of Alexandria, was announced by Zahi Hawass, president of Egypt's Supreme Council of Antiquities during a conference at the University of California. A Polish-Egyptian team had uncovered 13 lecture halls featuring an elevated podium for the lecturer. Such a complex of lecture halls had never before been found on any Mediterranean Greco-Roman site. Alexandria may be regarded as the birthplace of western science, where Euclid discovered the rules of geometry, Eratosthenes measured the diameter of the Earth and Ptolemy wrote the Almagest, the most influential scientific book about the nature of the Universe for 1,500 years*TIS

2013, This is the third "Pythagorean Day" of the 21st Century, 5/12/13. The first was on March 4, 2005 (3/4/05) and the second on June 8, 2010. How many more will there be in the 21st Century, and when is the next one?


1820 Florence Nightingale (12 May 1820 – 13 August 1910) is remembered as the mother of modern nursing. But few realize that her place in history is at least partly
linked to her use, following William Farr, Playfair and others, of graphical methods to convey complex statistical information dramatically to a broad audience. An example of "Stigler's Law of Eponomy" (Stigler, 1980), Nightingale's Coxcomb chart did not orignate with her, though this should not detract from her credit. She likely got the idea from William Farr, a close friend and frequent correspondent, who used the same graphic principles in 1852. The earliest known inventor of polar area charts is Andre-Michel Guerry (1829). [gallery of data visualization]
Pearson wrote of here, "Her statistics were more than a study, they were indeed her religion. For her Quetelet was the hero as scientist, and the presentation copy of his Physique sociale is annotated by her on every page. ... she held that the universe -- including human communities -- was evolving in accordance with a divine plan; that it was man's business to endeavor to understand this plan and guide his actions in sympathy with it. But to understand God's thoughts, she held we must study statistics, for these are the measure of His purpose. Thus the study of statistics was for her a religious duty.
K Pearson, The Life, Letters and Labours for Francis Galton (1924). *SAU

1845 Henri Brocard (12 May 1845 – 16 January 1922) who published (1897–99) a two volume catalog of plane curves and their properties. *VFR
His best-known achievement is the invention and discovery of the properties of the Brocard points, the Brocard circle, and the Brocard triangle, all bearing his name.  Contemporary mathematician Nathan Court wrote that he, along with Émile Lemoine and Joseph Neuberg , was one of the three co-founders of modern triangle geometry. 
In a triangle ABC with sides a, b, and c, where the vertices are labeled A, B and C in counterclockwise order, there is exactly one point P such that the line segments AP, BP, and CP form the same angle, ω, with the respective sides c, a, and b, namely that
\angle PAB = \angle PBC = \angle PCA.\,

1857 Oskar Bolza (12 May 1857–5 July 1942) After studying with Weierstrass and Klein, and realizing the diffi­culties of obtaining a suitable position in Germany, he came to the U.S. where he played an important role in the development of mathematics at Hopkins, Clark and Chicago. *VFR He published "The elliptic s-functions considered as a special case of the hyperelliptic s-functions" in 1900. From 1910, he worked on the calculus of variations. Bolza wrote a classic textbook on the subject, "Lectures on the Calculus of Variations" (1904). He returned to Germany in 1910, where he researched function theory, integral equations and the calculus of variations. In 1913, he published a paper presenting a new type of variational problem now called "the problem of Bolza." The next year, he wrote about variations for an integral problem involving inequalities, which later become important in control theory. Bolza ceased his mathematical research work at the outbreak of WW I in 1914.*TIS

1902 Frank Yates FRS (May 12, 1902 – June 17, 1994) was one of the pioneers of 20th century statistics. In 1931 Yates was appointed assistant statistician at Rothamsted Experimental Station by R.A. Fisher. In 1933 he became head of statistics when Fisher went to University College London. At Rothamsted he worked on the design of experiments, including contributions to the theory of analysis of variance and originating Yates' algorithm and the balanced incomplete block design. During World War II he worked on what would later be called operational research. *Wikipedia

1910 Dorothy Mary Hodgkin OM FRS (12 May 1910 – 29 July 1994), known professionally as Dorothy Crowfoot Hodgkin or simply Dorothy Hodgkin, was a British biochemist who developed protein crystallography, for which she won the Nobel Prize in Chemistry in 1964.
She advanced the technique of X-ray crystallography, a method used to determine the three-dimensional structures of biomolecules. Among her most influential discoveries are the confirmation of the structure of penicillin that Ernst Boris Chain and Edward Abraham had previously surmised, and then the structure of vitamin B12, for which she became the third woman to win the Nobel Prize in Chemistry.
In 1969, after 35 years of work and five years after winning the Nobel Prize, Hodgkin was able to decipher the structure of insulin. X-ray crystallography became a widely used tool and was critical in later determining the structures of many biological molecules where knowledge of structure is critical to an understanding of function. She is regarded as one of the pioneer scientists in the field of X-ray crystallography studies of biomolecules. *Wik

1926 James Samuel Coleman (May 12, 1926 – March 25, 1995) was a U.S. sociologist, a pioneer in mathematical sociology whose studies strongly influenced education policy. In the early 1950s, he was as a chemical engineer with Eastman-Kodak Co. in Rochester, N.Y. He then changed direction, fascinated with sociology and social problems. In 1966, he presented a report to the U.S. Congress which concluded that poor black children did better academically in integrated, middle-class schools. His findings provided the sociological underpinnings for widespread busing of students to achieve racial balance in schools. In 1975, Coleman rescinded his support of busing, concluding that it had encouraged the deterioration of public schools by encouraging white flight to avoid integration.*TIS

1919 Wu Wenjun or Wu Wen-Tsün (May 12, 1919- ) is a Chinese mathematician and academician at the Chinese Academy of Sciences (CAS).The research of Wu includes the following fields: algebraic topology, algebraic geometry, game theory, history of mathematics, automated theorem proving. His most important contributions are to algebraic topology. The Wu class and the Wu formula are named after him. In the field of automated theorem proving, he is known for Wu's method.
He is also active in the field of history of Chinese mathematics, he was the chief editor of the ten volume Grand Series of Chinese Mathematics, covering from antiquity to late Qin dynasty. *Wik


1003 Gerbert d'Aurillac (Pope Sylvester II)  (c. 946 – 12 May 1003)  French scholar who reintroduced the use of the abacus in mathematical calculations. He may have adopted the use of Arabic numerals (without the zero) from Khwarizmi. He built clocks, organs and astronomical instruments based on translations of Arabic works(One of his mechanical instruments was an oracular metal cast head that answered questions yes or no, sort of a tenth century magic 8-ball with speaking ability). (He was often accused after his death of being in league with demons )
He made no original contribution to mathematics or astronomy . However, he served in the all-important role of popularizer, communicating the value and importance of science to the uninitiated public. With the inspiration of Gerbert, Europe began its slow crawl out of the Dark Ages.*TIS

1682 Michelangelo Ricci ( 30 Jan., 1619; Rome, -  12 May,  1682; Rome) was a friend of Torricelli; in fact both were taught by Benedetti Castelli. He studied theology and law in Rome and at this time he became friends with René de Sluze. It is clear that Sluze, Torricelli and Ricci had a considerable influence on each other in the mathematics which they studied.
Ricci made his career in the Church. His income came from the Church, certainly from 1650 he received such funds, but perhaps surprisingly he was never ordained. Ricci served the Pope in several different roles before being made a cardinal by Pope Innocent XI in 1681.
Ricci's main work was Exercitatio geometrica, De maximis et minimis (1666) which was later reprinted as an appendix to Nicolaus Mercator's Logarithmo-technia (1668). It only consisted of 19 pages and it is remarkable that his high reputation rests solely on such a short publication.
In this work Ricci finds the maximum of xm(a - x)n and the tangents to ym = kxn. The methods are early examples of induction. He also studied spirals (1644), generalised cycloids (1674) and states explicitly that finding tangents and finding areas are inverse operations (1668). *SAU

In his own time Ricci's fame as a mathematician rested more on the many letters he wrote on mathematical topics, rather than on his published work. He corresponded with many mathematicians across Europe including Clavius, Viviani and de Sluze.

1684 Edme Mariotte(1620 ? – 12 May 1684) Little is known about his early life in the Cote d'Or region of eastern France, but in  1660 he discovered the eye's blind spot.and supposedly amazed the French Royal Court.  At this time he may have been working at a Parish Church, but that is not known.  In 1668 Colbert invited Mariotte to participate in the "l'Académie des Sciences", and in 1670 he moved to Paris. He published regularly right from his appointment. He is actually pictured in the portrait of the Establishment of the Academy, just to the left of Huygens and Cassini (he is sixth from the right in the picture).
The first volume of the Academies papers was released in 1673, and he had many of the articles.  His scope reached across the natural sciences including papers on fluid motion, heat, sound and acoustics, air pressure, and freezing water.  When he is known at all, it is usually as confirming what we now call Boyle's Law, but in fact his work went well beyond what Hooke and Boyle had shown, and he demonstrated that the pressure decreased in arithmetic progression as the altitude changed in geometric progression.  He also was the first to explain how the altitude at a high place could be calculated with a barometer.  He did not give a formula, but described a procedure assuming that a rise of  63 "Paris feet" resulted in the drop in the barometric reading of 1 line or 1/144th of an inch.  And I choose to call the desk toy called Newton's cradle by so many, Mariotte's cradle, since he was the first to describe this law of impact between bodies.  Edme quit the Academy in 1681 and died on 12 May 1684 in Paris.

1742 Joseph Privat de Molières (1677 in Tarascon, Bouches-du-Rhône, France - 12 May 1742 in Paris, France) In 1723 he was appointed to a chair at the Collège Royal to succeed Varignon.
He argued against Newton and for Descartes' view of physics although he knew Newton's to be the more precise. Of course, although we now accept Newton's ideas of gravitation without much thought, it is clear if one thinks about it for a while that the idea of action at a distance through a vacuum is absurd. Many around this time voiced such an opinion (Newton himself realised this was a weakness in his theories) but where Privat de Molières differed from other critics of Newton's theory of gravitation is that he attempted to make a mathematically sound theory based on the idea of vortices. Understanding the accuracy of the theory of gravitation, Privat attempted to bring Newton's calculations into the vortex theory of matter of Malebranche. The problem was Kepler's laws, easily explained by Newton, but the cause of real problems for Descartes' vortex theory of planetary motion. In fact in a memoir written in 1733 Privat criticised Newton's theories for being too accurate saying that physical phenomena did not have geometrical precision *SAU

1753 Nicolas Fatio de Duillier (alternative names are Facio or Faccio;) (26 February 1664 – 12 May 1753) was a Swiss mathematician known for his work on the zodiacal light problem, for his very close (some have suggested "romantic" ) relationship with Isaac Newton, for his role in the Newton v. Leibniz calculus controversy , and for originating the "push" or "shadow" theory of gravitation.
[Le Sage's theory of gravitation is a kinetic theory of gravity originally proposed by Nicolas Fatio de Duillier in 1690 and later by Georges-Louis Le Sage in 1748. The theory proposed a mechanical explanation for Newton's gravitational force in terms of streams of tiny unseen particles (which Le Sage called ultra-mundane corpuscles) impacting all material objects from all directions. According to this model, any two material bodies partially shield each other from the impinging corpuscles, resulting in a net imbalance in the pressure exerted by the impact of corpuscles on the bodies, tending to drive the bodies together.]
He also developed and patented a method of perforating jewels for use in clocks.

When Leibniz sent a set of problems for solution to England he mentioned Newton and failed to mention Faccio among those probably capable of solving them. Faccio retorted by sneering at Leibniz as the ‘second inventor’ of the calculus in a tract entitled ‘Lineæ brevissimæ descensus investigatio geometrica duplex, cui addita est investigatio geometrica solidi rotundi in quo minima fiat resistentia,’ 4to, London, 1699. Finally he stirred up the whole Royal Society to take a part in the dispute (Brewster, Memoirs of Sir I. Newton, 2nd edit. ii. 1–5).
In 1707, Fatio came under the influence of a fanatical religious sect, the Camisards, which ruined Fatio's reputation. He left England and took part in pilgrim journeys across Europe. After his return only a few scientific documents by him appeared. He died in 1753 in Maddersfield near Worcester, England. After his death his Geneva compatriot Georges-Louis Le Sage tried to purchase the scientific papers of Fatio. These papers together with Le Sage's are now in the Library of the University of Geneva.
Eventually he retired to Worcester, where he formed some congenial friendships, and busied himself with scientific pursuits, alchemy, and the mysteries of the cabbala. In 1732 he endeavoured, but it is thought unsuccessfully, to obtain through the influence of John Conduitt [q. v.], Newton's nephew, some reward for having saved the life of the Prince of Orange. He assisted Conduitt in planning the design, and writing the inscription for Newton's monument in Westminster Abbey. *Wik

1856 Jacques Philippe Marie Binet (February 2, 1786 – May 12, 1856) was a French mathematician, physicist and astronomer born in Rennes; he died in Paris, France, in 1856. He made significant contributions to number theory, and the mathematical foundations of matrix algebra which would later lead to important contributions by Cayley and others. In his memoir on the theory of the conjugate axis and of the moment of inertia of bodies he enumerated the principle now known as Binet's theorem. He is also recognized as the first to describe the rule for multiplying matrices in 1812, and Binet's formula expressing Fibonacci numbers in closed form is named in his honour, although the same result was known to Abraham de Moivre a century earlier.
u_n = \frac{(1 + \sqrt{5})^n - (1 - \sqrt{5})^n}{2^n \sqrt{5}}
Cauchy wrote his obituary, the only one he ever wrote. Apparently Cauchy was motivated by their common Bourbon fervour. [Ivor Grattan-Guiness, Convolutions in French Mathematics, 1800–1840, p. 192] *VFR

1910 Sir William Huggins (7 Feb 1824; 12 May 1910 at age 86) English astronomer who explored the spectra of stars, nebulae and comets to interpret their chemical composition, assisted by his wife Margaret Lindsay Murray. He was the first to demonstrate (1864) that whereas some nebulae are clusters of stars (with stellar spectral characteristics, ex. Andromeda), certain other nebulae are uniformly gaseous as shown by their pure emission spectra (ex. the great nebula in Orion). He made spectral observations of a nova (1866). He also was first to attempt to measure a star's radial velocity. He was one of the wealthy 19th century private astronomers that supported their own passion while making significant contributions. At age only 30, Huggins built his own observatory at Tulse Hill, outside London *TIS

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, 11 May 2021

On This Day in Math - May 11

A mind which has a taste for scientific inquiry,
and has learned the habit of applying its principles readily to the cases which occur,
has within itself an inexhaustible source of pure and exciting contemplations.

~John Herschel

The 131st day of the year; 131 is the sum of three two-digit primes (31 + 41 + 59) whose concatenation is the decimal expansion of pi (3.14159...).

Any ordering of the digits of 131 is still prime. This is called an "absolute" prime.

131 is the sum of three prime numbers that all begin with the same digit. *Prime Curios

bonus: 131 is the 32nd prime and the sum of the digits of both numbers is 5. 32 & 131 is the smallest n, P(n) pair with this property. Such numbers are often called Honaker Primes after G. L. Honaker, Jr, from Prime Curios.  There is only one more such prime that is a  year day.

The reciprocal of 131 repeats with a period of 130 digits, 1/131 =0.007633587786259


1892 Edgeworth’s first Newmarch lecture. In May and June of 1892 Edgeworth, newly appointed to the Oxford chair and editor of The Economic Journal, gave six Newmarch lectures, "On the Uses and Methods of Statistics."

1894 The Mississipi Weather Almanac lists this date as the date of the "most unusual weather event in the states history." In the little town of Bovina, just a short run from Vicksburg (Grant had his Army made Bovina a field hospital during the siege of Vicksburg) during a hail storm a 6" by 8" gopher turtle fell from the sky encased in ice. (admit it, you just don't find that kind of fascinating science information on your typical blog) * "Queen of the Turtle Derby" by Julia Reed

1897 black American inventor, William U. Moody was issued a U.S. design patent for a “game board design.” . It shows a rectangular board with a particular arrangement of partitions in the form of arcs of concentric circles and some other shorter partitions causing a complex route for a ball to travel from one corner to the diagonal corner, presumably, by tilting the board. *TIS
This was one of a number of variants of the most popular maze game of the period. Charles Martin Crandall produced many popular toys from his plant in Pennsylvania, and his "Pigs in Clover", release in 1889, captured the nation in a frenzy. The New York Tribune's March 13, 1889 issue reported Senator William M. Evarts purchased one from a street fakir in order to get rid of him. He took the puzzle home and worked it for hours. The following morning he brought it with him into senate chambers where Senator George Graham Vest stopped by Evarts' desk, borrowed the puzzle and took it to a cloak room. Soon thereafter he was joined by Senators James L. Pugh, James B. Eustis, Edward C. Walthall and John E. Kenna. A page was sent out to buy five of the puzzles and upon his return, the group engaged in a "pig driving contest". About 30 minutes later, Senator Vest announced his accomplishment of driving the last pig in the pen. A few days later a political cartoon in the New York World's March 17, 1889 issue lampooned President Benjamin Harrison's advisors and cabinet members showing the group sitting around playing the game. The caption read "Will Mr. Harrison be able to get all these hungry pigs in the official pen?"

1905 Albert Einstein's paper, "On the motion of small particles suspended in liquids at rest required by the molecular-kinetic theory of heat." (Brownian motion paper) is received by Annalen der Physik, .
"In this paper Einstein reports that the kinetic theory of heat predicts that small particles suspended in water must execute a random motion visible under the microscope. He suspects this motion is Brownian motion but has insufficient datato affirm it. The prediction is a powerful test of the truth of the kinetic theory of heat. A failure to observe the effect would refute the theory. If it is seen and measured, it provides a way to estimate Avogadro's number. The domain in which the effect is observed is one in which the second law of thermodynamics no longer holds, a disturbing result for the energeticists of the time. "  * John D. Norton, Einstein, 1905

1920 Oxford University passed a statute admitting women to degrees. *VFR

1928 radio station WGY, in Schenectady, NY, began America’s first regularly scheduled TV broadcasts. The programs lasted from 1:30 to 2:00 p.m. on Tuesdays, Thursdays, and Fridays. Most of the viewers were on the technical staff at nearby General Electric, which had designed the system and was using the broadcasts to refine its equipment. A handful of hobbyists who had built their own sets were also able to watch. Those who tuned in had to make constant adjustments, turning two knobs at once to keep the blurry picture discernible on their three-inch-square screens. By the end of 1928, 17 more stations around the country began scheduled broadcasts, designed to test the apparatus rather than attract viewers. *TIS

1951, Jay Forrester patented computer core memory.

1957 Howard F. Fehr, of Columbia University Teachers College, in an address at Syracuse: “A mathematics professor who talks at length affects both ends of the listener—he makes one end feel numb and the other feel dumb.” [Eves, Revisited, p. 151] . *VFR

1959 Eugene P. Wigner delivered a penetrating Courant Lecture at NYU on “The Unreasonable Effectiveness of Mathematics in the Natural Sciences,” which is well worth reading. *VFR

1979 VisiCalc Introduced. It was the first program operable by inexperienced computer users. As it ran only on the Apple, the company soon was on top of the market. *VFR

1986 A specially designed bicycle set the human powered land speed record of 105.37 km per hour (65.48 miles per hour). *VFR

1997 Garry Kasparov loses in the rematch with IBM's Deep Blue in the first match of what many considered a test of artificial intelligence. The world's best chess player, Kasparov lost the match and $1.1 million purse to the IBM supercomputer, which he had claimed could never surpass human chess ability. After losing the sixth and final game of the match, Kasparov accused IBM of building a machine specifically to beat him. Observers said he was frustrated by Deep Blue's quickness although they expected him to win with unconventional moves. *CHM On February 10, 1996, Deep Blue became the first machine to win a chess game against a reigning world champion under regular time controls. However, Kasparov won three and drew two of the following five games, beating Deep Blue by a score of 4–2 (wins count 1 point, draws count ½ point). The match concluded on February 17, 1996.
Deep Blue was then heavily upgraded (unofficially nicknamed "Deeper Blue") and played Kasparov again in May 1997, winning the six-game rematch 3½–2½, ending on May 11. *Wik


1702 Isaac Greenwood. (11 May 1702 Boston, Massachusetts – 22 October 1745 Charleston, South Carolina ) In 1727 he was installed at Harvard as the first Hollis professor of mathematics and natural and experimental philosophy. He strengthened and modernized the science program at Harvard. *VFR
During his tenure, he wrote anonymously the first natively-published American book on mathematics – the Greenwood Book, published in 1729. This book made the first published statement of the short scale value for billion in the United States, which eventually became the value used in most English-speaking countries.
He was removed from the Chair for intemperance (drunkenness) in 1737.
Unable to support his family, he joined the Royal Navy as a chaplain – HMS Rose in 1742, and later HMS Aldborough in 1744. He was released from service in Charleston, South Carolina, on 22 May 1745.
He drank himself to death a few months later on 22 October 1745.*Wik

1871 Frank Schlesinger (May 11, 1871 New York City – July 10, 1943 Old Lyme, Connecticut) American astronomer who pioneered in the use of photography to map stellar positions and to measure stellar parallaxes, which could give more precise determinations of distance than visual ones, and with less than one hundredth as much time at the telescope. He designed instruments and mathematical and numerical techniques to improve parallax measurements. He published ten volumes of zone catalogs, including some 150,000 stars. He compiled positions, magnitudes, proper motions, radial velocities, and other data to produce the first edition and, with Louise Jenkins, the second, of the widely-used Bright Star Catalogues, making Yale a leading institution in astrometry. He established a second Yale observatory in South Africa. *VFR

1881 Theodore von Karman (May 11, 1881 – May 7, 1963) Hungarian-American aerospace engineer and physicist who was active primarily in the fields of aeronautics and astronautics. He is responsible for many key advances in aerodynamics, notably his work on supersonic and hypersonic airflow characterization.*Wik; He was director of the Institute for Aerodynamics at the Rheinisch-Westfälische Technische Hochschule (RWTH) in AACHEN, Nordrhein-Westfalen, in 1913-1934. The main lecture theatre complex is named the Kármán Auditorium and there is a photo and a bust of him in the foyer.

1924 Eugene Borisovich Dynkin ( May 11, 1924 — 14 November 2014) was a Soviet and American mathematician. He has made contributions to the fields of probability and algebra, especially semisimple Lie groups, Lie algebras, and Markov processes. The Dynkin diagram, the Dynkin system, and Dynkin's lemma are named for him.
In 1968, Dynkin was forced to transfer from the Moscow University to the Central Economic Mathematical Institute of the USSR Academy of Sciences. He worked there on the theory of economic growth and economic equilibrium. He remained at the Institute until 1976, when he emigrated to the United States. In 1977, he became a professor at Cornell University, where he died in 2014. *Wik

1918 Richard Phillips Feynman (11 May, 1918 – 15 February, 1988) was an American theoretical physicist who was probably the most brilliant, influential, and iconoclastic figure in his field in the post-WW II era. By age 15, he had mastered calculus. He took every physics course at MIT. His lifelong interest was in subatomic physics. In 1942, he went to Los Alamos where Hans Bethe made the 24 year old Feynman a group leader in the theoretical division, to work on estimating how much uranium would be needed to achieve critical mass for the Manhattan (atomic bomb) Project. After the war, he developed Feynman Diagrams, a simple notation to describe the complex behavior of subatomic particles. In 1965, he shared the Nobel Prize in Physics for work in quantum electrodynamics. *TIS

1930 Edsger Wybe Dijkstra (May 11, 1930 – August 6, 2002) was a Dutch computer scientist. He received the 1972 Turing Award for fundamental contributions to developing programming languages, and was the Schlumberger Centennial Chair of Computer Sciences at The University of Texas at Austin from 1984 until 2000. Among his contributions to computer science are the shortest path-algorithm, also known as Dijkstra's algorithm; Reverse Polish Notation and related Shunting yard algorithm; the THE multiprogramming system, an important early example of structuring a system as a set of layers; Banker's algorithm; and the semaphore construct for coordinating multiple processors and programs. Another concept due to Dijkstra in the field of distributed computing is that of self-stabilization – an alternative way to ensure the reliability of the system. Dijkstra's algorithm is used in SPF, Shortest Path First, which is used in the routing protocols OSPF and IS-IS. *Wik


1610 Matteo Ricci (October 6, 1552; Macerata – May 11, 1610;Beijing )was an Italian Jesuit who went to China as a missionary and introduced the Chinese to Western mathematics.*SAU
There is now a memorial plaque in Zhaoqing to commemorate Ricci's six-year stay there, as well as a "Ricci Memorial Centre", in a building dating from the 1860's. *Wik

1686 Otto von Guericke (originally spelled Gericke) (November 20, 1602 – May 11, 1686 (Julian calendar); November 30, 1602 – May 21, 1686 (Gregorian calendar)) was a German scientist, inventor, and politician. He is best remembered for his invention of the Magdeburg hemispheres, popularized in the writings of Caspar Schott. His major scientific achievements were the establishment of the physics of vacuums, the discovery of an experimental method for clearly demonstrating electrostatic repulsion, and his advocacy of the reality of "action at a distance" and of "absolute space". *Wik

1871 1st Baronet) Sir John (Frederick William) Herschel (7 March 1792 – 11 May 1871) was an English astronomer. As successor to his father, Sir William Herschel, he discovered another 525 nebulae and clusters. John Herschel was a pioneer in celestial photography, and as a chemist contributed to the development of sensitized photographic paper (independently of Talbot). In 1819, he discovered that sodium thiosulphate dissolved silver salts, as used in developing photographs. He introduced the terms positive image and negative image. Being diverse in his research, he also studied physical and geometrical optics, birefringence of crystals, spectrum analysis, and the interference of light and sound waves. To compare the brightness of stars, he invented the astrometer.*TIS [He was buried in Westminster Abbey.]

1957 Théophile Ernest de Donder (19 August 1872 – 11 May 1957) was a Belgian mathematician and physicist famous for his 1923 work in developing correlations between the Newtonian concept of chemical affinity and the Gibbsian concept of free energy.
He received his doctorate in physics and mathematics from the Université Libre de Bruxelles in 1899, for a thesis entitled Sur la Théorie des Invariants Intégraux (On the Theory of Integral Invariants).
He was professor between 1911 and 1942, at the Université Libre de Bruxelles. Initially he continued the work of Henri Poincaré and Élie Cartan. As from 1914 he was influenced by the work of Albert Einstein and was an enthusiastic proponent of the theory of relativity. He gained significant reputation in 1923, when he developed his definition of chemical affinity. He pointed out a connection between the chemical affinity and the Gibbs free energy.
He is considered the father of thermodynamics of irreversible processes. De Donder’s work was later developed further by Ilya Prigogine. De Donder was an associate and friend of Albert Einstein. *Wik

1965 Jason John Nassau (29 March 1893 in Smyrna, (now Izmir) Turkey - 11 May 1965 in Cleveland, Ohio, USA) was an American astronomer.
He performed his doctoral studies at Syracuse, and gained his Ph.D. mathematics in 1920. (His thesis was Some Theorems in Alternants.) He then became an assistant professor at the Case Institute of Technology in 1921, teaching astronomy. He continued to instruct at that institution, becoming the University's first chair of astronomy from 1924 until 1959 and chairman of the graduate division from 1936 until 1940. After 1959 he was professor emeritus.
From 1924 until 1959 he was also the director of the Case Western Reserve University (CWRU) Warner and Swasey Observatory in Cleveland, Ohio. He was a pioneer in the study of galactic structure. He also discovered a new star cluster, co-discovered 2 novae in 1961, and developed a technique of studying the distribution of red (M-class or cooler) stars.*Wik

2012 Fritz Joseph Ursell FRS (28 April 1923 – 11 May 2012) was a British mathematician noted for his contributions to fluid mechanics, especially in the area of wave-structure interactions. He held the Beyer Chair of Applied Mathematics at the University of Manchester from 1961–1990, was elected Fellow of the Royal Society in 1972 and retired in 1990.
Ursell came to England as a refugee in 1937 from Germany. From 1941 to 1943 he studied at Trinity College, Cambridge, graduating with a bachelor degree in mathematics. *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

Monday, 10 May 2021

On this Day in Math - May 10

Nature is not embarrassed by difficulties of analysis.

~Augustin Fresnel 

The 130th day of the year; 130 is the sum of the factorials of the first five terms of the Fibonacci sequence.
Did you know that any four terms of the Fibonacci sequence will give you a Pythagorean triangle? If we use 3, 5, 8, 13 you can get 3+13 = 39, 2*5*8 = 80, and 3*8 + 5 * 13 = 89, and {39, 80, 89} is a Pythagorean Right triangle with an area of 1560 (which is 3 * 5 * 8 * 13) Which makes it a Heronian triangle. First observed by Charles W. Raine in 1948. For more on this Pythagonacci connection

130 is the sum of the squares of the divisors of 10, ( \( 1^2 + 2^2 + 5^2 + 10^2 = 130 \)
130 is also the only number equal to the sum of the squares of its first 4 divisors: 130 = 1^2 + 2^2 + 5^2 + 10^2.*Prime Curios

This is the 46th day of the year that is the sum of two squares.It is the sum of two squares in two different ways. 130 = 11² + 3² = 9² + 7².


1741 d'Alembert is (finally) accepted to the French Academy of Sciences.  He had applied five times since March 1 of the  same year.  He was accepted as an adjunct associate astronomer at the age of 24. *Thomas L. Hankins, Jean d'Alembert: science and the Englightenment; pg 25

1752 Thomas-François Dalibard of France conducted Franklin's experiment using a 40-foot (some say 50 ft) (12 m)-tall iron rod instead of a kite, and he extracted electrical sparks from a cloud. Based on his observations, Franklin had proposed an experiment with an elevated rod or wire to "draw down the electric fire" from a cloud, with the experimenter standing in the protection of an enclosure similar to a soldier's sentry box.
Before Franklin could put his proposal into practice, D'Alibard performed his experiment in Paris. One week later, M. Delor repeated the experiment in Paris, followed in July by an Englishman, John Canton. But one unfortunate physicist did not fare so well. Georg Wilhelm Reichmann attempted to reproduce the experiment, according to Franklin's instructions, standing inside a room. A glowing ball of charge traveled down the string, jumped to his forehead and killed him instantly - providing history with the first documented example of ball lightning in the process.
As for Franklin, he was apparently unaware of these other experiments when he undertook his own version during a thunderstorm in June 1752, on the outskirts of Philadelphia. Unlike Reichmann, he quite sensibly stood under a shed roof to ensure he was holding a dry, non-conducting portion of the kite string.*AMERICAN PHYSICAL SOCIETY News

1760 Euler writes the tenth of his Letters to a German Princess.  This one on the "Compression of the air. " .  "The explanation of sound, which I have had the honor of presenting to you Highness, leads me forward to..." (The Euler Archive)

1810 Friedrich Wilhelm Bessel was summoned by the King of Prussia to be Professor of Astronomy at the University at Konigsburg and to supervise the construction of an Observatory, becoming its first Director. In 1819 he developed and published Fourier series, three years before Fourier! In 1824, he first systematically studied the Bessel functions. In 1838, he made the first observation of a stellar parallax, hence of a stellar distance, of 61 Cygni, about 11 light-years away. Its parallax is less than .3" (or .3' ??) of arc – the aberration due to the Earth's motion is about 40'. He had started working on this about thirty years previously. Henderson, 1839, and Struve, 1840, made independent measurements of a stellar parallax.

1831 Everiste Galois was arrested, following a banquet, of about 200 young republicans, that he actively attended.*VFR (SEE MAY 9)

1869 the first transcontinental railroad to run West out of Chicago was completed, running to Promontory, Utah. Amidst a crowd of dignitaries and workers, with the engines No. 119 and Jupiter practically touching noses, the Central Pacific and Union Pacific railroads were joined together. Telegraph operators transmitting to both coasts transmit the blows of the hammer as they fall on a golden spike. The nation listened as west and east came together in undivided union. *TIS

1898 Dewar becomes the first person to liquefy Hydrogen, working in the basement laboratory of the Ri with only a few assistants. *Royal Institution web page

1910 Florence Nightingale was presented with the badge of honour of the Norwegian Red Cross Society. *VictorianWeb

1925 John T. Scopes was given a preliminary hearing before three judges. He had been arrested and charged under a new Tennessee's state law, the Butler act, which prohibited the teaching of Darwin's theory of evolution in public schools. Scopes had agreed to participate in a challenge to that law, with the support of local leaders in Dayton, Tennessee, and the American Civil Liberties Union. A few weeks later, at what became known as the Scope's Monkey Trial, he was found guilty and fined $100. Although upon appeal the fine was ruled excessive and over-ruled, the state law itself was not found unconstitutional. Thereafter, the law was not enforced, but it was not repealed until 1967.*TIS (The state of Tennessee still seems to be struggling with this issue, 2011)

1933 Kurt Schutte, the last of Hilbert’s sixty-nine doctoral students, defends his dissertation on logic. For the full list see Hilbert’s Gesammelte Abhandlungen, vol. 3, pp. 431–433. *VFR

In 1949, the first planetarium in the U.S. owned by a university opened at the University of Chapel Hill, North Carolina. The Morehead Planetarium, one of the largest in the U.S., was the gift of John Motley Morehead III (1870-1965), class of 1891. The Morehead Building, erected at the north end of the campus, included the 68-ft dome, 300-seat Star Theater with a Zeiss Model II Star Projector. Morehead was an industrialist and chemist who commercially developed production of calcium carbide, basic to manufacturing acetylene gas, which led to the founding of Union Carbide Corporation. As the U.S. space program began, the planetarium provided important celestial navigation training for U.S. astronauts in the Mercury program.*TIS

1960 Triton ended her 84 day, 36,014 mile circumnavigation of the globe, the first by a submerged submarine. The ship generally followed the path of the first round the world voyager, Magellan. [Navy Facts, 181, 204] *VFR (Magellan's circumnavigation took three years, On August 10, 1519 to September 6, 1522. Of the 237 men who set out on five ships, only 18 completed the circumnavigation and managed to return to Spain in 1522.  As far as I know the Triton had no casualties.)

2012 National Abacus Day in Japan. Today is National Abacus Day in Japan. By manipulating beads, the user of an abacus can perform simple addition, subtraction, multiplication, and division. *CHM

2013 An annular solar eclipse will take place on May 10, 2013, with a magnitude of 0.9544. A solar eclipse occurs when the Moon passes between Earth and the Sun, thereby totally or partially obscuring the image of the Sun for a viewer on Earth. An annular solar eclipse occurs when the Moon's apparent diameter is smaller than the Sun, causing the Sun to look like an annulus (ring), blocking most of the Sun's light. An annular eclipse appears as a partial eclipse over a region thousands of kilometres wide.
Annularity will be visible from northern Australia and the southern Pacific Ocean, with the maximum of 6 minutes 3 seconds visible from the Pacific Ocean east of French Polynesia. *Wik

1788 Augustin Jean Fresnel (10 May 1788 - 14 July 1827, aged 39)did important work on optics where he was one of the founders of the wave theory of light.  In 1817, Young had proposed a small transverse component to light, while yet retaining a far larger longitudinal component. Fresnel, by the year 1821, was able to show via mathematical methods that polarization could be explained only if light was entirely transverse, with no longitudinal vibration whatsoever.  In the early 19th century, Poisson declared that since Fresnel’s ideas on the wave nature of light implied that the shadow cast by a disk would contain a bright spot at its center, Fresnel’s ideas were obviously flawed. The spot was later detected, proving Fresnel right!   He is perhaps best known to the general public as the inventor of the Fresnel lens, first adopted in lighthouses while he was a French commissioner of lighthouses, and found in many applications today.*Wikipedia

1821 Baldassarre Boncompagni, (10 May 1821 – 13 April 1894),  noted historian of mathematics. He set up his own publishing house and published his own journal dealing with the history of mathematics from 1868 to 1887. He was responsible for making known the importance of Leonardo Fibonacci to the history of mathematics. *VFR Boncompagni edited Bullettino di bibliografia e di storia delle scienze matematiche e fisiche ("The bulletin of bibliography and history of mathematical and physical sciences") (1868-1887), the first Italian periodical entirely dedicated to the history of mathematics. He edited every article that appeared in the journal. He also prepared and published the first modern edition of Fibonacci's Liber Abaci.*Wik

1847 Wilhelm Karl Joseph Killing (10 May 1847 in Burbach (near Siegen), Westphalia, Germany - 11 Feb 1923 in Münster, Germany)introduced Lie algebras independently of Lie in his study of non-euclidean geometry. The classification of the simple Lie algebras by Killing was one of the finest achievements in the whole of mathematical research.*SAU

1900 Cecilia Helena Payne-Gaposchkin (10 May 1900; 7 Dec 1979 at age 79) was an English-American astronomer who was the first to apply laws of atomic physics to the study of the temperature and density of stellar bodies, and the first to conclude that hydrogen and helium are the two most common elements in the universe. During the 1920s, the accepted explanation of the Sun's composition was a calculation of around 65% iron and 35% hydrogen. At Harvard University, in her doctoral thesis (1925), Payne claimed that the sun's spectrum was consistent with another solution: 99% hydrogen with helium, and just 1% iron. She had difficulty persuading her superiors to take her work seriously. It was another 20 years before Payne's original claim was confirmed, by Fred Hoyle. *TIS

1904 Edward James McShane is famous for his work in the calculus of variations, Moore-Smith theory of limits, the theory of the integral, stochastic differential equations, and ballistics. In the early 1950s United States senator Joseph R McCarthy whipped up strong feelings against communism. McShane had been asked to complete a questionnaire. One question asked:-
... whether he had ever been involved with organisations that had at any time advocated the violent overthrow of the U.S. government.
It was quite a brave move for McShane to reply "yes", because he was an employee of the State of Virginia! At the University of Virginia this sense of humour added to his popularity with both staff and graduate students.. *SAU

1926 Oliver Gordon Selfridge (May 10, 1926 – December 3, 2008), grandson of Harry Gordon Selfridge, the founder of Selfridges' department stores, was a pioneer of artificial intelligence. He has been called the "Father of Machine Perception."
Selfridge was born in England, educated at Malvern College and Middlesex School and then earned an S.B. from MIT in mathematics in 1945. He then became a graduate student of Norbert Wiener's at MIT, but did not write up his doctoral research and never earned a Ph.D. While at MIT, he acted as one of the earlier reviewers for Wiener's Cybernetics book in 1949. He was also technically a supervisor of Marvin Minsky, and helped organize the first ever public meeting on Artificial Intelligence (AI) with Minsky in 1955.
Selfridge wrote important early papers on neural networks and pattern recognition and machine learning, and his "Pandemonium" paper (1959) is generally recognized as a classic in artificial intelligence. In it, Selfridge introduced the notion of "demons" that record events as they occur, recognize patterns in those events, and may trigger subsequent events according to patterns they recognize. Over time, this idea gave rise to Aspect-oriented programming.
In 1968, in their formative paper "The Computer as a Communication Device", J. C. R. Licklider and Robert Taylor introduced a concept known as an OLIVER (Online Interactive Expediter and Responder) which was named in honor of Selfridge.
Selfridge spent his career at Lincoln Laboratory, MIT (where he was Associate Director of Project MAC), Bolt, Beranek and Newman, and GTE Laboratories where he became Chief Scientist. He served on the NSA Advisory Board for 20 years, chairing the Data Processing Panel. Selfridge retired in 1993.
Selfridge also authored four children's books, "Sticks", "Fingers Come In Fives", "All About Mud", and "Trouble With Dragons". *Wik


IPaolo Ruffini (September 22, 1765 – May 10, 1822) Italian mathematician and physician who made studies of equations that anticipated the algebraic theory of groups. He is regarded as the first to make a significant attempt to show that there is no algebraic solution of the general quintic equation (an equation with the variable in one term raised to the fifth power). In 1799 Ruffini published a book on the theory of equations with his claim that quintics could not be solved by radicals, General theory of equations in which it is shown that the algebraic solution of the general equation of degree greater than four is impossible. Ruffini used group theory in his work but he had to invent the subject for himself. He also wrote on probability and the application of probability to evidence in court cases. *TIS

1829 Thomas Young  (13 June 1773 – 10 May 1829) English physician and physicist who reinforced the wave theory of light with his study of interference of light. As a medical student, he had discovered the how the shape of the eye's lens changes to focus. In 1801, he recognized the cause of astigmatism. Young demonstrated the wave nature of light, polarization of light, interference fringes, and explained the colours seen in thin films such as soap bubbles. He associated wavelength with colour of light, and the eye's perception of any colour as a mixture of red, blue and green. Young's modulus is named after his work with elasticity. He also worked measuring the size of molecules, liquid surface tension. He was also an Egyptologist who helped decipher the Rosetta Stone. The museum in Cairo has another "roseta", the Decree of Canopus, in Hieroglyphic, Demotic and Greek, issued by Ptolemy III Euergetes in -238. It decrees leap years to be included in the calendar. It was not discovered until 1866, too late to assist Young and Champollion in deciphering, but which confirmed their work.

1924 August Gutzmer (2 Feb 1860 in Neu-Roddahn, near Neustadt an der Dosse, Germany -10 May 1924 in Halle, Germany) was a German mathematician who worked on differential equations. *SAU

1941 Diederik Korteweg (31 March 1848 – 10 May 1941) was a Dutch mathematician with wide interests, now best-known as the joint discoverer of the Korteweg-de Vries equation for solitary waves.

1989 Hassler Whitney (March 23, 1907 – May 10, 1989) was an American mathematician. He was one of the founders of singularity theory, and did foundational work in manifolds, embeddings, immersions, and characteristic classes. *SAU

2009 Carol Jo Crannell (November 15, 1938 – May 10, 2009) was a solar physicist known for her work on solar flares and on the astrophysical observation of x-rays and gamma rays. She worked for thirty years at the NASA Goddard Space Flight Center.
Crannell was born in Columbus, Ohio. She graduated from Miami University in 1960, and completed her Ph.D. in physics at Stanford University in 1967, with Robert Hofstadter as her doctoral advisor. She worked at the Goddard Space Flight Center from 1974 until 2004, when she retired.
Crannell also held an adjunct faculty position at Catholic University of America, where her husband, Hall L. Crannell, is an emeritus professor. Her daughter, Annalisa Crannell, is a mathematician at Franklin & Marshall College.
Crannell's doctoral research concerned particle showers. At Goddard, Crannell pushed for x-ray and gamma-ray observations of the sun, and led balloon-mounted experiments to make these observations.
Crannell played an active role in the struggle for equal opportunity for women in physics. She chaired the Committee on the Status of Women in Physics of the American Physical Society, and helped found the CSWP Gazette, the newsletter of the Committee. Through her position at the Catholic University she also helped bring underrepresented students to summer internships at Goddard.
Crannell became a Fellow of the American Physical Society in 1992, and a Fellow of the American Association for the Advancement of Science in 1998. In 1990, Women in Aerospace gave her their Outstanding Achievement Award "for her dedication to expanding women’s opportunities for career advancement and for increasing their visibility through her activities as an aerospace professional".

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, 9 May 2021

On This Day in Math - May 9

Margarita philosophica of Gregor Reisch *MAA

If you ask a drunkard what number is larger, 2/3 or 3/5, he might not be able to tell you. But if you rephrase the question: What is better, 2 bottles of vodka for 3 people, or 3 bottles of vodka for 5 people, he will tell you right away.
Israel Gelfand (from Love and Math, by Edward Frenkel)

The 129th day of the year; 129 is the smallest number with four representations as a sum of three positive (but not necessarily distinct) squares: 129 = 12 + 82 + 82 = 22 + 22 + 112 = 22 + 52 + 102 = 42 + 72 + 82 .

129 is also the sum of the first ten primes.

129 is the smallest sum of distinct seventh powers (17 + 27).

And if you've not spent some time in Western Ky, and perhaps even if you have, you might not guess where the official Banana Capital of the US is. It's in the little town of Fulton, Ky, along the train route from New Orleans to Chicago, and Fulton had the distinction of being the place where Union Fruit company chose to pause the trains bringing fresh bananas along the way to re-ice them for the rest of their journey.At one time over 70% of Bananas shipped into the US came through Fulton. About 13 miles away is the even smaller town of Wingo, formerly called Wingo Station ( because it set along the same New Orleans and Ohio rail line passing through Fulton. And what they have in common other than that, is the reason I mention them today, they are on the ends of Ky Route 129. They are just a pretty spring drive of 40 miles from here in Possum Trot.


1562 In the evening Don Carlos, son of Phillip II of Spain, and heir to the throne lay dying from a fall on a staircase a month earlier. In hopes of a miracle, the king prayed, and then caused, or allowed, the body of a 15th-Century priest from the village to be brought and laid by his son. Within days the young man recovered, and the grateful father commissioned the royal clockmaker, Juanelo Turriano, to create one of the first human form automatons in Europe, the praying monk. The incredible wind up device would walk lifelike in a square, nodding his head as his mouth moves in prayer, sometimes beating his chest, and kissing his cross and rosary. The device is now in the Smithsonian, and it still works.
For more about the story read here,  and more pictures of the automaton just search Praying Monk on your favorite search engine. 

1664 Hooke speaks to Royal Society on finding the Giant Red Spot on Jupiter OUHOS Collections@OUHOSCollection

1694 Johann Bernoulli, in a letter to Leibniz, introduced the term and the explicit process of “sepera­tio indeterminatarum” or separation of variables for solving differential equations. He published it in Acta eruditorum in November, 1694. [Ince, 531] *VFR In 1691 the inverse problem of tangents led Leibniz to the implicit discovery of the method of separation of variables.

1831 Galois party toast will lead to his arrest. Derbyshire describes the events in "Unknown Quantity, a real and imaginary history of Algebra."

1848 “Proficiency in Algebra, the elements of geometry, trigonometry, and surveying, will give you the art of developing truth by the skilful use of the reasoning powers, and, besides, store your mind with a species of knowledge of daily practical utility to a lawyer. ... It is the helm of the mind, stering it over the shortest route from the point of departure to the destination—from cause to effect.” So wrote the American soldier Albert Sindney Johnson (1803–1862) to his son. From William Preston Johnson (the son), The Life of General Albert Sindney Johnson (1878),p. 162, as quoted by Florian Cajori in Mathematics in Liberal Education (1928), p. 103. *VFR

1854  There is a "letter from Rankine to Thomson of 9 May 1854 in which he suggests more reasonably that the leading term in the departure from the perfect-gas laws is linear in the density, or (1/V). This turned out to be so .."  (JAMES JOULE, WILLIAM THOMSON AND THE CONCEPT OF A PERFECT GAS by J. S. ROWLINSON)

1914 Think of all the work that mothers do in raising their children. Mothers need to be celebrated! President Woodrow Wilson proclaimed May 9, 1914, the first Mother's Day. He asked Americans on that day to give a public "thank you" to their mothers and all mothers.
Anna Jarvis of Philadelphia wanted to remember her own mother along with all mothers. Anna’s mother had been very active in working to improve the health of people in her community. Jarvis’s mother also organized a Mother’s Friendship event in her community to bring confederate and union soldiers together for a peaceful celebration. Many other women such as Julia Ward Howe, Elizabeth Cady Stanton and Elizabeth Smith also fought for peace and encouraged mothers to speak out. Anna Jarvis convinced her mother’s church to celebrate Mother’s Day on the anniversary of her mother’s death, and campaigned for a national day honoring mothers. Because of Jarvis’s hard work, Woodrow Wilson chose that date for the national holiday. (Library of Congress web site) This year it's May 13... Happy Birthday to Mom's everywhere.

1926 Americans Richard Byrd and Floyd Bennett became the first men to fly over the North Pole. *TIS

1972 100 high school students took the first U.S.A. Mathematical Olympiad. The purpose was to discover secondary school students with superior mathematical talent. One of the five problems on the exam was: “A random number selector can only select one of the nine integers 1, 2,..., 9, and it makes these selections with equal probability. Determine the probability that after n selections (for n larger than 1), the product of the n numbers selected will be divisible by 10.” For the winners, the other problems, and the solutions, see AMM 80 (1973), pp 276–281. *VFR

2013 Surfs Up, Sun's Not, in Hawaii, at least for a moment. Solar Eclipse in Honolulu *Carey Johnson ‏@TheTelescopeGuy

2016 It happens only a little more than once a decade – and the next chance to see it is TODAY!. Throughout the U.S., sky watchers can watch Mercury pass between Earth and the sun in a rare astronomical event known as a planetary transit. Mercury will appear as a tiny black dot as it glides in front of the sun’s blazing disk over a period of seven and a half hours. Three NASA satellites will be providing images of the transit and one of them will have a near-live feed. *NASA


1746  Gaspard Monge, (9 May 1746 – 28 July 1818) noted geometer, son of a peddler and knife grinder   at Beaune, France. Today there is a statue of him in his home town. (I stumbled across it while visiting vineyards).*VFR One of the founders of descriptive geometry (the mathematics of projecting solid figures onto a plane, upon which modern engineering drawing is based) and the application of the techniques of analysis to the theory of curvature. The latter ultimately led to the revolutionary work of Georg Riemann on geometry and curvature. He became a close friend of Napoleon and was appointed minister for the navy (1792-93), but was stripped of all honours on the restoration of the Bourbons. He died in poverty. *TIS
As an active Jacobin, he was acting head of the government on the day Louis XVI was executed.  He was also Minister of the Navy. He was in official disfavor when he died and had been expelled from the Academy in 1816 (along with Lazare Carnot), but his students erected a monument with a bust. MONGE was buried in the cemetery of Père Lachaise (Mausoleum at right below) but in 1989, he was translated to the Panthéon.

1785 James Pollard Espy (9 May 1785, 24 Jan 1860) American meteorologist who was one of the first to collect meteorological observations by telegraph. He gave apparently the first essentially correct explanation of the thermodynamics of cloud formation and growth. Every great atmospheric disturbance begins with a rising mass of heated, thus less dense air. While rising, the air mass dilates and cools. Then, as water vapour precipitates as clouds, latent heat is liberated so the dilation and rising continues until the moisture of the air forming the upward current is practically exhausted. The heavier air flows in beneath, and, finding a diminished pressure above it, rushes upward with constantly increasing violence. Water vapour precipitated during this atmospheric disturbance results in heavy rains.*TIS

1876 Gilbert Ames Bliss (9 May 1876, Chicago – 8 May 1951, Harvey, Illinois) did important work in the calculus of variations. Through­out his career at Chicago he stressed the importance of a strong union between teaching and research. *VFR  This is another one who died within a week of their birthday (he died on May 8). 

1898 Arend Heyting
(May 9, 1898 – July 9, 1980) is important in the development of intuitionistic logic and algebra.He was a student of Luitzen Egbertus Jan Brouwer at the University of Amsterdam, and did much to put intuitionistic logic on a footing where it could become part of mathematical logic. Heyting gave the first formal development of intuitionistic logic in order to codify Brouwer's way of doing mathematics. The inclusion of Brouwer's name in the Brouwer–Heyting–Kolmogorov interpretation is largely honorific, as Brouwer was opposed in principle to any formalisation of intuitionistic logic (and went as far as calling Heyting's work a "sterile exercise").   *Wik

1936 Alexandre Aleksandrovich Kirillov (May 9,1936) is a Soviet and Russian mathematician, renowned for his works in the fields of representation theory, topological groups and Lie groups. In particular he introduced the orbit method into representation theory.
Kirillov studied at Moscow State University where he was a student of Israel Gelfand. His Ph.D. (kandidat) dissertation Unitary representations of nilpotent Lie groups 1962 was so successful that he was awarded the much higher degree of Doctor of Science instead. At the time he was the youngest Doctor of Science in the Soviet Union. He worked at the Moscow State University until 1994 when he became the Francis J. Carey Professor of Mathematics at the University of Pennsylvania.
During his school years, Kirillov was a winner of many mathematics competitions, and he is still an active organizer of Russian mathematical contests. Kirillov is an author of many popular school-oriented books and articles.
In 2012 he became a fellow of the American Mathematical Society.
Kirillov's son, Alexander Kirillov, Jr., is also a mathematician, working on the representation theory of Lie groups at the State University of New York at Stony Brook. *Wik

1950 Esteban Terrades i Illa (15 September 1883;Barcelona,- 9 May 1950,Madrid,) was a Spanish mathematician, scientist and engineer. He researched and taught widely in the fields of mathematics and the physical sciences, working not only in his native Catalonia, but also in the rest of Spain and in South America. He was also active as a consultant in the Spanish aeronautics, electric power, telephone and railway industries. *Wik


1525 Gregor Reisch (born at Balingen in Württemberg, about 1467; died at Freiburg, Baden, 9 May 1525) was a German Carthusian humanist writer. He is best known for his Margarita philosophica, which first appeared at Freiburg in 1503. It is an encyclopedia of knowledge intended as a text-book for youthful students, and contains in twelve books Latin grammar, dialectics, rhetoric, arithmetic, music, geometry, astronomy, physics, natural history, physiology, psychology, and ethics. The usefulness of the work was increased by numerous woodcuts and a full index. *Wik
Image of Calculating-Table by Gregor Reisch: Margarita Philosophica, 1503. The woodcut shows Arithmetica instructing an algorist and an abacist (inaccurately represented as Boethius and Pythagoras). There was keen competition between the two from the introduction of the Algebra into Europe in the 12th century until its triumph in the 16th.

1931 Albert Abraham Michelson (December 19, 1852 – May 9, 1931) German-born American physicist who accurately measured the speed of light and received the 1907 Nobel Prize for Physics "for his optical precision instruments and the spectroscopic and metrological investigations" he carried out with them. He designed the highly accurate Michelson interferometer and used it to establish the speed of light as a fundamental constant. With Edward Morley, he also used it in an attempt to measure the velocity of the earth through the ether (1887). The experiment yielded null results that eventually led Einstein to his theory of relativity. He measured the standard meter bar in Paris to be 1,553,163.5 wavelengths of the red cadmium line (1892-3). *TIS  There is a marker near the place where the experiment was done.  It says, "Near this spot, in July 1887, Dr. Albert A. Michelson of Case and Dr. Edward W. Morley of Western Reserve University conducted the world-famous Michelson-Morley experiment, one of the outstanding scientific achievements of the 19th century and a cornerstone of modern physics. In commemoration, this tablet has been set in stone by both colleges on December 19, 1952, the 100th anniversary of Dr. Michelson's birth.

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