## Friday 2 February 2024

### On This Day in Math - February 2

Smooth shapes are very rare in the wild
but extremely important in the ivory tower and the factory.

~Benoit Mandelbrot

The 33rd day of the year; among the infinity of integers, there are only six that can not be formed by the addition of distinct triangular numbers. The largest of these is 33. What are the other five?

33 = 1!+2!+3!+4! *jim wilder @wilderlab

33 is the smallest n such that n, n+1 and n+2 are all semi-primes, the products of two primes. *Bob S McDonald

The 33 letter Dutch word nepparterrestaalplaatserretrappen is the longest palindrome I know in any language. It means fake stairways from the ground floor to the sun lounge, made of steel plate. The shorter word "saippuakauppias" for a soap vendor is the longest single word palindrome in the world that is in everyday use. *Wiktionary

1033 is the largest known power of ten that can be expressed as the power of two factors neither of which contains a zero. 1033 = 233 533 = 8,589,934,592 x 116,415,321,826,934,814,453,125 *Cliff Pickover @pickover

A fun problem given to Fibonacci at the contest before Frederic II  Three men, A, B, and C possess a sum of money w with shares in the ratio 1:2:3.  A takes away x and deposits half of it with man D. B takes away y and deposits 1/3 of it with D.  C takes away the rest, z, and deposits 1/6 of it with D.  The ratio of each persons money in D's hands is now 3:2:1.   Fibonacci showed there were many solutions, but one of the solutions involves 33.  Please share your solutions.

EVENTS

 *Wik

1673
From Hooke's Diary: Sir Jonas More; Cox here: compleated arithmeticall engin in ye contrivance for a product of 20 places. He would present the "engin" to the Royal Society three days later.*‏@HookesLondon This "Cox" is most likely Christopher Cock, the designer of instruments who is believed to have made the microscope used by Hooke his observations for his beautiful Micrographia. These microscopes were compound lens instruments, which suffered greatly from spherical aberration.

1823 Gauss completes the “Gauss-Markov Theorem.” *VFR
In statistics, the Gauss–Markov theorem, named after Carl Friedrich Gauss and Andrey Markov, states that in a linear regression model in which the errors have expectation zero and are uncorrelated and have equal variances, the best linear unbiased estimator of the coefficients is given by the ordinary least squares (OLS) estimator. *Wik

1826 Mary Somerville’s work was first read by the Royal Society. In 1826 she presented her paper entitled "The Magnetic Properties of the Violet Rays of the Solar Spectrum" to the Royal Society. The paper attracted favorable notice and, aside from the astronomical observations of Caroline Herschel, was the first paper by a woman to be read to the Royal Society and published in its Philosophical Transactions. Caroline Herschel had a paper on comets read to the society in 1787.
The Royal Society’s bust of Somerville by Chantrey

1841 The earliest recorded observance of Groundhog day in America was on this day in the diary of Morgantown, Pa. storekeeper,James Morris:
"Last Tuesday, the 2nd, was Candlemas day, the day on which, according to the Germans, the Groundhog peeps out of his winter quarters and if he sees his shadow he pops back for another six weeks nap, but if the day be cloudy he remains out, as the weather is to be moderate."
entry for Feb 4th *Wik

1851 “You are invited to come to see the Earth turn, tomorrow from three to five, at Meridian Hall of the Paris Observatory.” Foucault sent these handwritten invitations to all the known scientists in Paris. *Amir D Aczel, Pendulum, pg 93

1883 Preliminary meeting of the Edinburgh Mathematical Society

*Proceedings of the Edinburgh Mathematical Society, Volumes 1-4

In 1947, Edwin H. Land gave the first demonstration his invention of instant photography at a meeting of the Optical Society of America. On 28 Nov 1948, his Polaroid Land Camera first went on sale, at a Boston department store. The 40 series, model 95 roll film camera went on sale for 89.75. This first model was sold through 1953, and was the first commercially successful self- developing camera system. A sepia-coloured photograph took about one minute to produce. His first commercial success came in 1939 with his invention of Polaroid filters for lenses in products such as ski goggles, sunglasses and slip-on sunglasses for optical glasses.TIS Polaroid Land Camera Model 95, the first commercially available instant camera. ============================================================= 1962, eight of the nine planets lined up for the first time in 400 years.*TIS On May 12,2011 six planets (Mercury, Venus, Jupiter, Mars, Uranus and Neptune, were essentially in a line. All the planets will not be aligned (at least as closely as they can get) until sometime in the 29th century. 1977 Radio Shack officially begins creating TRS-80 computer. It is one of the earliest mass-produced and mass-marketed retail home computers. By 1979, the TRS-80 had the largest selection of software in the microcomputer market. Until 1982, the TRS-80 was the best-selling PC line, outselling the Apple II series by a factor of five according to one analysis. *Wik 2004 Google does a doodle in honor of Gaston Julia's 111th birthday, but a day early by my calculation. My records show his birthday is Feb 3. (It's me vrs Google, choose sides people.) 2020 Google released a Somerville doodle (to celebrate when her 1826 paper was read to the Royal Society). BIRTHS 1522 Lodovico Ferrari (2 Feb 1522 in Bologna, Italy - 5 Oct 1565) Italian mathematician who was the first to find an algebraic solution to the biquadratic, or quartic, equation (an algebraic equation that contains the fourth power of the unknown quantity but no higher power).*TIS born in Bologna, Italy. In 1536 he was sent to live with Girolamo Cardano, who taught him Latin, Greek, and mathematics. He collaborated with Cardano in research on third and fourth degree equations. *VFR He began as the servant of Cardano but was extremely bright, so Cardano started teaching him mathematics. Ferrari aided Cardano on his solutions for quadratic equations and cubic equations, and was mainly responsible for the solution of quartic equations that Cardano published. While still in his teens, Ferrari was able to obtain a prestigious teaching post after Cardano resigned from it and recommended him. Ferrari eventually retired young (only 42) and quite rich. He then moved back to his home town of Bologna where he lived with his widowed sister Maddalena to take up a professorship of mathematics at the University of Bologna in 1565. Shortly thereafter, he died of white arsenic poisoning, allegedly murdered by his greedy sister.*Wik 1766 Timofei Fedorovic Osipovsky (February 2, 1766–June 24, 1832) was a Russian mathematician, physicist, astronomer, and philosopher. Timofei Osipovsky graduated from the St Petersburg Teachers Seminary. He was to became a teacher at Kharkov University. Kharkov University was founded in 1805. The city of Kharkov, thanks to its educational establishments, became one of the most important cultural and educational centers of Ukraine. Osipovsky was appointed to Kharkov University in 1805, the year of the foundation of the University. In 1813 he became rector of the University. However in 1820 Osipovsky was suspended from his post on religious grounds. His most famous work was the three volume book A Course of Mathematics (1801–1823). This soon became a standard university text and was used in universities for many years. *Wik 1786 Jacques Philippe Marie Binet (2 Feb 1786 in Rennes, Bretagne, France - 12 May 1856 in Paris, France) investigated the foundations of matrix theory which was to set the scene for later work by Cayley and others. He discovered the rule for multiplying matrices in 1812 and it is almost certainly for this that he will be remembered rather than his other work. He did, however, write a number of important papers which were influential in the development of mathematics, in particular he wrote Mémoire sur les intégrales définies eulériennes in 1840. The following year he wrote on number theory, making a contribution to the theory of the Euclidean algorithm. *SAU He is also remembered for Binet's formula expressing Fibonacci numbers in closed form, which is named in his honor, although the same result was known to Abraham de Moivre a century earlier. $F(n) = \frac{(1+\sqrt{5})^2-(1-\sqrt{5})^2}{2^n\sqrt{5}}$ 1793 William Hopkins FRS (2 February 1793 – 13 October 1866) was an English mathematician and geologist. He is famous as a private tutor of aspiring undergraduate Cambridge mathematicians, earning him the sobriquet the senior-wrangler maker. Before graduation, Hopkins had married Caroline Frances Boys (1799–1881) and was, therefore, ineligible for a fellowship. He instead maintained himself as a private tutor, coaching the young mathematicians who sought the prestigious distinction of Senior Wrangler. He was enormously successful in the role, earning the sobriquet senior wrangler maker and grossing £700-800 annually. By 1849, he had coached almost 200 wranglers, of whom 17 were senior wranglers including Arthur Cayley and G. G. Stokes. Among his more famous pupils were Lord Kelvin, James Clerk Maxwell and Isaac Todhunter. He also made important contributions in asserting a solid, rather than fluid, interior for the Earth and explaining many geological phenomena in terms of his model. However, though his conclusions proved to be correct, his mathematical and physical reasoning were subsequently seen as unsound.In 1833, Hopkins published Elements of Trigonometry and became distinguished for his mathematical knowledge. There was a famous story that the theory of George Green (1793–1841) was almost forgotten. In 1845, Lord Kelvin (William Thomson, a young man in 1845) got some copies of Green's 1828 short book from William Hopkins. Subsequently, Lord Kelvin helped to make Green's 1828 work famous according to the book "George Green" written by D.M. Cannell. *Wik It is known that he gave one copy of Green's book to Liouville, founder and editor of a popular French Mathematical Journal. 1849 Leopold Bernhard Gegenbauer (2 Feb 1849 - 3 June 1903) was an Austrian mathematician who gave his name to a sequence of orthogonal polynomials. He gave the well-known asymptotic estimate 6n/π2 for the number of square-free integers not exceeding n.*SAU 1881 Gustav Herglotz (2 February 1881 – 22 March 1953) was a German mathematician. He is best known for his works on the theory of relativity and seismology. From 1925 (until becoming Emeritus in 1947) he again was in Göttingen as the successor of Carl Runge on the chair of applied mathematics. One of his students was Emil Artin. Herglotz made contribution in many fields of applied and pure mathematics. The Theorem of Herglotz is known in differential geometry, and he also contributed to number theory. He worked in the fields of celestial mechanics, theory of electrons, special relativity (where he developed a theory of elasticity), general relativity, hydrodynamics, refraction theory. *Wik 1882 Joseph Henry Maclagen Wedderburn (2 Feb 1882 in Forfar, Angus, Scotland - 9 Oct 1948 in Princeton, New Jersey, USA) studied at Edinburgh, Leipzig, Berlin and Chicago. He returned to Scotland to work at Edinburgh but then moved to a post at Princeton where he spent the rest of his career except for a break for service in World War I. He made far-reaching discoveries in the theory of rings, algebras and matrices. He became an honorary member of the EMS in 1946. *SAU 1893 Cornelius Lanczos (2 Feb 1893 - 25 June 1974) worked on relativity and mathematical physics and invented what is now called the Fast Fourier Transform. *SAU 1896 Kazimierz Kuratowski (2 Feb 1896 in Warsaw, Russian Empire (now Poland) - 18 June 1980 in Warsaw, Poland) He worked in the area of topology and set theory. He is best known for his theorem giving a necessary and sufficient condition for a graph to be planar.*SAU Kuratowski's theorem: "A finite graph is planar if and only if it does not contain a subgraph that is a subdivision of K5 (the complete graph on five vertices) or K3,3 (complete bipartite graph on six vertices, three of which connect to each of the other three)." (in simpler, but less exact terms, it can't be drawn in such a way that no edges cross each other." Math Historian V F Rickey calls this "the most cited theorem in graph theory." The well-known recreational problem of connecting three houses to three utilities is not possible to draw because it is K3,3 (below). The utility problem posits three houses and three utility companies--say, gas, electric, and water--and asks if each utility can be connected to each house without having any of the gas/water/electric lines/pipes pass over any other.(1913 Dudeney: first publication of Gas, Water and Electricity Problem. according to David Singmaster, Gardner says 1917) (see June 21) I have a short blog with two other proofs that this is impossible that should be appropriate for high school students. 1897 Gertrude Blanch (2 Feb, 1897 (sometimes 1898) - 1 Jan,1996) was an American mathematician who did pioneering work in numerical analysis and computation. After the war, Blanch's career was hampered by FBI suspicions that she was secretly a communist. Their evidence for this seems scarce, and included, for example, the observation that she had never married or had children. In what must have been a remarkable showdown, the diminutive fifty-year-old mathematician demanded, and won, a hearing to clear her name. Subsequently, she worked for the Institute for Numerical Analysis at UCLA and the Aerospace Research Laboratory at Wright-Patterson Air Force Base in Dayton, Ohio. She was one of the founders of the ACM. She published over thirty papers on functional approximation, numerical analysis and Mathieu functions. In 1962, she was elected a Fellow in the American Association for the Advancement of Science. Blanch retired in 1967 at the age of 69, but continued working under a consulting contract for the Air Force for another year. Thereafter she moved to San Diego and continued to work on numerical solutions of Mathieu functions until her death in 1996, concentrating on the use of continued fractions to achieve highly accurate results in a small number of computational steps. This work has not been published. The Gertrude Blanch Papers, 1932-1996 are stored at the Charles Babbage Institute, University of Minnesota, Minneapolis. *Wik 1903 Bartel Leendert van der Waerden (2 Feb 1903 - 12 Jan 1996) This famous algebraist is best known for his book Moderne Algebra, but has, more recently, done interesting work on the history of ancient mathematics. *VFR DEATHS 1704 Guillaume François Antoine, Marquis de l'Hôpital (?, 1661, Paris – February 2, 1704, Paris) was a French mathematician. His name is firmly associated with l'Hôpital's rule for calculating limits involving indeterminate forms 0/0 and ∞/∞. Although the rule did not originate with l'Hôpital, it appeared in print for the first time in his treatise on the infinitesimal calculus, entitled Analyse des Infiniment Petits pour l'Intelligence des Lignes Courbes. This book was a first systematic exposition of differential calculus. Several editions and translations to other languages were published and it became a model for subsequent treatments of calculus. or a while, he was a member of Nicolas Malebranche's circle in Paris and it was there that in 1691 he met young Johann Bernoulli, who was visiting France and agreed to supplement his Paris talks on infinitesimal calculus with private lectures to l'Hôpital at his estate at Oucques. In 1693, l'Hôpital was elected to the French academy of sciences and even served twice as its vice-president. Among his accomplishments were the determination of the arc length of the logarithmic graph, one of the solutions to the brachistochrone problem, and the discovery of a turning point singularity on the involute of a plane curve near an inflection point. L'Hôpital exchanged ideas with Pierre Varignon and corresponded with Gottfried Leibniz, Christiaan Huygens, and Jacob and Johann Bernoulli. His Traité analytique des sections coniques et de leur usage pour la résolution des équations dans les problêmes tant déterminés qu'indéterminés ("Analytic treatise on conic sections") was published posthumously in Paris in 1707. *Wik 1769 Robert Smith (1689 – 2 February 1768) was an English mathematician and music theorist. In his will Smith left £3500 South Sea stock to the University of Cambridge. The net income on the fund is annually divided equally between the Smith's Prize and the stipend of the Plumian Professor. Smith was probably born at Lea near Gainsborough, the son of the rector of Gate Burton, Lincolnshire. After attending Queen Elizabeth's Grammar School, Gainsborough (now Queen Elizabeth's High School) he entered Trinity College, Cambridge, in 1708, and becoming minor fellow in 1714, major fellow in 1715 and senior fellow in 1739, was chosen Master in 1742, in succession to Richard Bentley. From 1716 to 1760 he was Plumian Professor of Astronomy, and he died in the Master's Lodge at Trinity. In February 1719 he was elected a Fellow of the Royal Society Besides editing two works by his cousin, Roger Cotes, who was his predecessor in the Plumian chair, he published A Compleat System of Opticks in 1738, which gained him the sobriquet of Old Focus, and Harmonics, or the Philosophy of Musical Sounds in 1749. Smith never married but lived with his unmarried sister Elzimar (1683–1758) in the lodge at Trinity College. Although he is often portrayed as a rather reclusive character, John Byrom's journal shows that in the 1720s and 1730s Smith could be quite sociable. Yet ill health, particularly gout, took its toll and severely inhibited his academic work and social activities. He died at the lodge on 2 February 1768, and on 8 February he was buried in Trinity College Chapel, the funeral oration being delivered by Thomas Zouch. According to the Oxford Dictionary of National Biography, Smith helped to spread Isaac Newton's ideas in Europe and "Newton's successes in optics and mechanics dominated Smith's scientific career". Bishop was a Christian that although did not publish theological works, wrote a Zachary Grey's response to the Examination of the Fourteenth Chapter of Newton's Observations on Daniel. *Wik 1950 Constantin Carathéodory (or Constantine Karatheodori) (13 September 1873 – 2 February 1950) was a Greek mathematician. He made significant contributions to the theory of functions of a real variable, the calculus of variations, and measure theory. His work also includes important results in conformal representations and in the theory of boundary correspondence. In 1909, Carathéodory pioneered the Axiomatic Formulation of Thermodynamics along a purely geometrical approach. *Wik He is the only modern Greek mathematician “who does not suﬀer by comparison with the famous names of Greek antiquity.” *VFR. 1911 Hugues Charles Robert Méray (November 12, 1835, Chalon-sur-Saône, Saône-et-Loire - February 2, 1911, Dijon) was a French mathematician. He is noted as the first to publish an arithmetical theory of irrational numbers. His work did not have much of a role in the history of mathematics because France, at that time, was less interested in such matters than Germany.*Wik 1965 George Neville Watson (31 Jan 1886 in Westward Ho!, Devon, England - 2 Feb 1965 in Leamington Spa, Warwickshire, England) studied at Cambridge, and then taught at Cambridge and University College London before becoming Professor at Birmingham. He is best known as the joint author with Whittaker of one of the standard text-books on Analysis. Titchmarsh wrote of Watson's books, "Here one felt was mathematics really happening before one's eyes. ... the older mathematical books were full of mystery and wonder. With Professor Watson we reached the period when the mystery is dispelled though the wonder remains." *SAU 1970 Bertrand Arthur William Russell (18 May 1872 - 2 Feb 1970) (3rd earl) was a Welsh mathematical logician, analytical philosopher and writer. He worked to establish foundations of mathematics and developed contemporary formal logic. He is known for Russell's paradox (concerning the set of all sets that are not members of themselves), his theory of types, and his contributions to the first-order predicate calculus. He believed in logicism, the theory that mathematics was in some important sense reducible to formal logic. With Alfred Whitehead, he co-authored Prinicpia Mathematica (1910). Russell is regarded as one of the most important logicians of the twentieth century. He was active in social and political campaigns, and advocated pacifism and nuclear disarmament. The Nobel Prize for Literature was awarded to Russell in 1950 *TIS 2005 Edward Maitland Wright (13 Feb 1906 in Farnley, near Leeds, England - 2 Feb 2005 in Reading, England) was initially self-taught in Mathematics but was able to go and study at Oxford. He spent a year at Göttingen and returned to Oxford. He was appointed to the Char at Aberdeen where he stayed for the rest of his career, eventually becoming Principal and Vice-Chancellor of the University. He is best known for the standard work on Number Theory he wrote with G H Hardy. One of Wright's first papers, published in 1930, was on Bernstein polynomials. Also among his early work was a series of three papers titled Asymptotic partition formulae. The third in the series Asymptotic partition formulae, III. Partitions into kth powers was published by Acta Mathematica in 1934. *SAU 2011 Rodney Hill FRS (11 June 1921 – 2 February 2011) was an applied mathematician and a former Professor of Mechanics of Solids at Gonville and Caius College, Cambridge. In 1953 he was appointed Professor of Applied Mathematics at Nottingham University. His 1950 The Mathematical Theory of Plasticity forms the foundation of plasticity theory. Hill is widely regarded as among the foremost contributors to the foundations of solid mechanics over the second half of the 20th century. His early work was central to founding the mathematical theory of plasticity. This deep interest led eventually to general studies of uniqueness and stability in nonlinear continuum mechanics, work which has had a profound influence on the field of solid mechanics—theoretical, computational and experimental alike—over the past decades. Hill was the founding editor of the Journal of the Mechanics and Physics of Solids, still among the principal journals in the field. His work is recognized worldwide for its concise style of presentation and exemplary standards of scholarship. Publisher Elsevier, in collaboration with IUTAM, established a quadrennial award in the field of solid mechanics, known as the Rodney Hill Prize, first presented at ICTAM in Adelaide in August 2008. The prize consists of a plaque and a cheque for US25,000. Its first recipient is Michael Ortiz, for his contribution to nonconvex plasticity and deformation microstructures (California Institute of Technology, USA).
He won the Royal Medal in 1993 for his contribution to the theoretical mechanics of soil and the plasticity of solids and was elected a Fellow of the Royal Society in 1961. He was awarded an Honorary Degree (Doctor of Science) by the University of Bath in 1978. *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