## Saturday 31 December 2022

### On This Day in Math - December 31

 The Difficult Problem, Bogdonay-Belsky

The problem for mental solution, appropriate for today is
(normally the last day of the year)

For other great mathematicians or philosophers, he [Gauss] used the epithets magnus, or clarus, or clarissimus; for Newton alone he kept the prefix summus.
~W.W.R. Ball

### The 365th (and usually last) day of the year; 365 is a centered square number, and thus the sum of two consecutive squares (132 + 142 ) and also one more than four times a triangular number.365 is the sum of two squares in two ways, 132 + 142 and  192 + 22 *Lord Karl VoldeviveThere are 10 days during the year that are the sum of three consecutive squares. This is the last one (proof left to the reader ;-} .365 = 10²+11²+12²; *jim wilder@wilderlab365 is the smallest number that can be written as a sum of consecutive squares in more than one way (and all the numbers squared are consecutive.): 365 =102 + 112 + 122 =132 + 142 .365 is a palindrome in base 2; 101101101and base 8; 555

EVENTS
1719 When the first Astronomer Royal, John Flamsteed died on this day (see below) he was serving as Rector of Burstow (just east of Gatwick), and had been for thirty-five years. For some reason, no marker was placed on the grave, and 170 years later, it was not clear where the famous astronomer was buried. Finally, in 1888, another astronomer from Greenwich Observatory, Edwin Dunkin searched, and found, the burial site mentioned in his wife's will. Today there are several markers in the church at Barstow, including the one below indicating his resting place in the Chancel.
Several other images of the church, and markers for Flamsteed, are at the site from which I obtained this note. *Blogs Greenwich http://blogs.greenwich.co.uk/rob-powell/the-grave-of-john-flamsteed/
 Stephen Craven - http://www.geograph.org.uk/photo/2786257

1831  Gauss writes to his close friend, Wilhelm Olbers regarding an essay published by Laplace"The essay...  is quite unworthy of this great geometer. I find two different, very gross blunders in it.  I had always imagined that among geometers of the first rank the calculation was always only the dress in which they present that which they created not by calculation, but by mediation about the subject itself. ". *Carl Friedrich Gauss: Titan of Science by Guy Waldo Dunnington, Jeremy Gray, Fritz-Egbert Dohse

1915 The Mathematical Association of America was founded in Columbus, Ohio. Starting with 1045 charter members, the Association now has some 34,000 members who are interested in the improvement of mathematical instruction at the collegiate level. *VFR

1935, a patent was issued for the game of Monopoly assigned to Parker Brothers, Inc., by Charles Darrow of Pennsylvania (No. 2,026,082). The patent titled it a "Board Game Apparatus" and described it as "intended primarily to provide a game of barter, thus involving trading and bargaining" in which "much of the interest in the game lies in trading and in striking shrewd bargains." Illustrations included with the patent showed not only the playing board and pieces, cards, and the scrip money. He had invented the game on 7 Mar 1933, though it was preceded by other real-estate board games. *TIS

1956 The earliest mention of the term "Big Bang" appeared in the New York Times in describing the efforts of Fred Hoyle, were working to disprove the idea.  Hoyle had created the term on March 28, 1949 on a BBC radio show as a term of contempt for the theory which he opposed.
1961 This was the last day of the year 1961, a Stobogrammatic number. If you rotate the number by 180o it still looks the same. Then name seems to have been created for the Jan 1961 issue of The Mathematics Magazine by J. M. Howell of Los Angeles City College. The last day of the year is a significant date since it is the last time someone will be living in such a year for a very long time. *Mathematics Magazine

1987 The last minute (UT) of the last hour of the last day of the year 1987 carried an extra second, a leap second. This was to coordinate the slowdown in rotation of the Earth on its axis, or Solar Time, with the more precise atomic time. The one-second insertion was made at 6:59:59 P.M. at the Naval Observatory in Washington D.C. Just exactly when the proverbial man-in-the¬street choose to insert this second was his own business, but in New York’s Times Square it was done with much hoopla at midnight. *U.S. Naval Observatory's “Stargazing Notes for December 1987.” *VFR

1999 Millenium memorial puzzle at Luppitt. It is made of fine grained granite, which is an exceptionally hard stone. It was unveiled on 31st December 2000 - Just in time for the true Millennium. The puzzles on the site, as described at the puzzle's website:

The puzzles include a wordsearch concealing over 30 local placenames, a three way anamorphic illusion, a completely new idea based on the Tinner's Rabbits, an ancient maze from a French church, a modern Railway Maze (specially designed by Professor Sir Roger Penrose), a Word Anagram, a Letter misplacement puzzle, a traditional Word square puzzle, cryptarithms, hidden mice, and other curiosities and puzzles.

1999 Professor Andrew Wiles is knighted. The Princeton mathematician found fame in October 1994 when he succeeded in proving Fermat's Last Theorem. This was an amazing achievement that had eluded some of the greatest minds since Pierre Fermat conjured up his theory in the 1630s. His work has received every major honour and he had the pleasure in 1999 of seeing some of his former pupils crack another of mathematics' great puzzles: The Shimura-Taniyama-Weil conjecture. *BBC

1999 Alan Sugar, the man who founded Amstrad some 30 years ago and now runs Tottenham Hotspur football club,(Sugar sold his interest in the Spurs in 2007 according to a comment from Luke Robinson, below) has been knighted.
So too has Maurice Wilkes, who developed the world's first practical stored-program computer in 1949.
"I'm tickled pink by the news," said Mr Sugar, whose company launched the world's first mass-market word processor built with low-cost components from the Far East.
At the height of its success, Amstrad was worth £1.5bn on the FTSE-100 index. Mr Sugar eventually broke Amstrad up, spinning off Viglen Technology, its personal computer business, of which he is now chairman.
Maurice Wilkes led the Cambridge University team that developed the Edsac - Electronic Delay Storage Automatic Calculator. It was a huge contraption that could carry out just 650 instructions per second. Nevertheless, it went down in history as the first truly programmable computer. *BBC

The last day of 2017, a prime year; to be followed by 2018, which is twice a prime (2 x 1009); and then 2019 which is three times a prime (3 x 673) ;

BIRTHS

1789 BenoĆ®t "Claudius" Crozet (December 31, 1789; Villefranche, France – January 29, 1864) was an educator and civil engineer.
After serving in the French military, in 1816, he immigrated to the United States. He taught at the U.S. Military Academy at West Point, New York, and helped found the Virginia Military Institute at Lexington, Virginia. He was Principal Engineer for the Virginia Board of Public Works and oversaw the planning and construction of canals, turnpikes, bridges and railroads in Virginia, including the area which is now West Virginia. He became widely known as the "Pathfinder of the Blue Ridge."
On June 7, 1816, in Paris, Crozet married Agathe Decamp.
Late in fall of 1816, Crozet and his bride headed for the United States. Almost immediately after arriving, Crozet began work as a professor of engineering at the U.S. Military Academy at West Point, New York.
While at West Point, Crozet is credited by some as being the first to use the chalkboard as an instructional tool. (Professor Ricky, a math historian at USMA has written, "old records show that it was introduced at West Point by Mr. George Baron, a civilian teacher, who in the autumn of 1801 gave to Cadet Swift 'a specimen of his mode of teaching at the blackboard' ").He also designed several of the buildings at West Point. Thomas Jefferson referred to Claudius Crozet as "by far the best mathematician in the United States." He also published A Treatise on Descriptive Geometry while at West Point, a copy of which was sent to Jefferson. Jefferson's response on Nov 23, 1821 began, "I thank you, Sir, for your kind attention in sending me a copy of your valuable treatise on Descriptive geometry." He continued the messsage with praise for the work, and the instructor both. The dining hall at the Virginia Military Institute is named in his honor. It has been affectionately nicknamed "Club Crozet" by the Cadets. * Wik & Natl. Archives

1864 Robert Grant Aitken (31 Dec 1864; 29 Oct 1951) American astronomer who specialized in the study of double stars, of which he discovered more than 3,000. He worked at the Lick Observatory from 1895 to 1935, becoming director from 1930. Aitken made systematic surveys of binary stars, measuring their positions visually. His massive New General Catalogue of Double Stars within 120 degrees of the North Pole allowed orbit determinations which increased astronomers' knowledge of stellar masses. He also measured positions of comets and planetary satellites and computed orbits. He wrote an important book on binary stars, and he lectured and wrote widely for the public.*TIS

1896 Carl Ludwig Siegel (December 31, 1896 – April 4, 1981) was a mathematician specializing in number theory and celestial mechanics. He was one of the most important mathematicians of the 20th century.
Among his teachers were Max Planck and Ferdinand Georg Frobenius, whose influence made the young Siegel abandon astronomy and turn towards number theory instead. His best student was JĆ¼rgen Moser, one of the founders of KAM theory (Kolmogorov-Arnold-Moser), which lies at the foundations of chaos theory.
Siegel's work on number theory, diophantine equations, and celestial mechanics in particular won him numerous honours. In 1978, he was awarded the Wolf Prize in Mathematics, one of the most prestigious in the field.
Siegel's work spans analytic number theory; and his theorem on the finiteness of the integer points of curves, for genus greater than 1, is historically important as a major general result on diophantine equations, when the field was essentially undeveloped. He worked on L-functions, discovering the (presumed illusory) Siegel zero phenomenon. His work derived from the Hardy-Littlewood circle method on quadratic forms proved very influential on the later, adele group theories encompassing the use of theta-functions. The Siegel modular forms are recognised as part of the moduli theory of abelian varieties. In all this work the structural implications of analytic methods show through.
AndrĆ© Weil, without hesitation, named Siegel as the greatest mathematician of the first half of the 20th century. In the early 1970s Weil gave a series of seminars on the history of number theory prior to the 20th century and he remarked that Siegel once told him that when the first person discovered the simplest case of Faulhaber's formula then, in Siegel's words, "Es gefiel dem lieben Gott." (It pleased the dear Lord.) Siegel was a profound student of the history of mathematics and put his studies to good use in such works as the Riemann-Siegel formula.*Wik

1929 Jeremy Bernstein (31 Dec 1929, ) American physicist, educator, and writer widely known for the clarity of his writing for the lay reader on the major issues of modern physics. He was a staff writer for the New Yorker for over 30 years until 1993. He has held appointments at the Institute for Advanced Study, Brookhaven National Laboratory, CERN, Oxford, the University of Islamabad, and the Ecole Polytechnique. Berstein has written over 50 technical papers as well as his books popularizing science including Albert Einstein; Cranks, Quarks, and the Cosmos and A Theory for Everything. His passion for science was launched after he entered Harvard University, thereafter combining it with a talent as a writer. *TIS

1930 Jaime Alfonso Escalante Gutierrez (December 31, 1930 — March 30, 2010) was a Bolivian educator well-known for teaching students calculus from 1974 to 1991 at Garfield High School, East Los Angeles, California. Escalante was the subject of the 1988 film Stand and Deliver, in which he is portrayed by Edward James Olmos.*Wik

1945 Leonard Max Adleman (December 31, 1945, ) is an American theoretical computer scientist and professor of computer science and molecular biology at the University of Southern California. He is known for being a co-inventor of the RSA (Rivest-Shamir-Adleman) cryptosystem in 1977, and of DNA computing. RSA is in widespread use in security applications. *Wik

1952 Vaughan Frederick Randal Jones (31 Dec 1952, ) is a New Zealand mathematician who was awarded the Fields Medal in 1990 for his study of functional analysis and knot theory. In 1984, Jones discovered a relationship between von Neumann algebras and geometric topology. As a result, he found a new polynomial invariant for knots and links in 3-space. It was a complete surprise because his invariant had been missed completely by topologists, in spite of intense activity in closely related areas during the preceding 60 years.*TIS

DEATHS

1610 Ludolph van Ceulen, a German mathematician who is famed for his calculation of Ļ to 35 places. In Germany Ļ used to be called the Ludolphine number. Because van Ceulen could not read Greek, Jan Cornets de Groot, the burgomaster of Delft and father of the jurist, scholar, statesman and diplomat, Hugo Grotius​, translated Archimedes' approximation to Ļ for Van Ceulen. This proved a significant point in Van Ceulen's life for he spent the rest of his life obtaining better approximations to Ļ using Archimedes' method with regular polygons with many sides.*SAU He has Pi on his memorial stone.

1679 Giovanni Alfonso Borelli (28 Jan 1608; 31 Dec 1679) Italian mathematician, physiologist and physicist sometimes called “father of biomechanics.” He was the first to apply the laws of mechanics to the muscular action of the human body. In De motu animalium (Concerning Animal Motion, 1680), he correctly described the skeleton and muscles as a system of levers, and explained the mechanism of bird flight. He calculated the forces required for equilibrium in various joints of the body well before the mechanics of Isaac Newton. In 1649, he published a work on malignant fevers. He repudiated astrological causes of diseases and believed in chemical cures. In 1658, he published Euclidus restitutus. He made anatomical dissections, drew a diver's rebreather, investiged volcanoes, was first to suggest a parabolic path for comets, and considered Jupiter had an attractive influence on its moons.*TIS

1719 John Flamsteed (19 Aug 1646; 31 Dec 1719)English astronomer who established the Greenwich Observatory. Science Historian/blogger Thony Christie writes:

" Observational astronomy only produced three significant star catalogues in the two thousand years leading up to the 18th century. The first, the Greek catalogue from Hipparchus and Ptolemaeus published by Ptolemaeus in the 2nd century CE, which contained just over 1000 stars mapped with an accuracy that was astounding for the conditions under which it was produced. The second, containing somewhat more that 700 stars plus another 300 borrowed from the Ptolemaeus catalogue, was produced by the Danish astronomer Tycho Brahe in the last quarter of the 16th century, with an accuracy many factors better than his Greek predecessors. Both of these catalogues were produced with naked eye observations. The first catalogue to be produced using telescopic sights on the measuring instruments was that of John Flamsteed published posthumously in 1725, which contains more than 3000 stars measured to a much higher degree of accuracy than that of Tycho."

He then goes on to correct some misconceptions about Flamsteed's life that are commonly repeated, (he did NOT take part in talking Charles II into creating the observatory) and gives a nice description of a complex man. *Renaissance Mathematicus

1894 Thomas Jan Stieltjes, who did pioneering work on the integral. *VFR Thomas Stieltjes worked on almost all branches of analysis, continued fractions and number theory. *SAU

1913 Seth Carlo Chandler, Jr. (17 Sep 1846, 31 Dec 1913) was an American astronomer best known for his discovery (1884-85) of the Chandler Wobble, a complex movement in the Earth's axis of rotation (now referred to as polar motion) that causes latitude to vary with a period of 14 months. His interests were much wider than this single subject, however, and he made substantial contributions to such diverse areas of astronomy as cataloging and monitoring variable stars, the independent discovery of the nova T Coronae, improving the estimate of the constant of aberration, and computing the orbital parameters of minor planets and comets. His publications totaled more than 200. *TIS

1962 Charles G Darwin was the grandson of the famous biologist and graduated from Cambridge. He lectured on Physics at Manchester and after service in World War I and a period back at Cambridge he became Professor of Physics at Edinburgh. He left eventually to become head of a Cambridge college. He worked in Quantum Mechanics and had controversial views on Eugenics. *SAU

1982 Kurt Otto Friedrichs (September 28, 1901 – December 31, 1982) was a noted German American mathematician. He was the co-founder of the Courant Institute at New York University and recipient of the National Medal of Science.*Wik

<2017>
Credits :
*CHM=Computer History Museum
*FFF=Kane, Famous First Facts
*NSEC= NASA Solar Eclipse Calendar
*RMAT= The Renaissance Mathematicus, Thony Christie
*SAU=St Andrews Univ. Math History
*TIA = Today in Astronomy
*TIS= Today in Science History
*VFR = V Frederick Rickey, USMA
*Wik = Wikipedia
*WM = Women of Mathematics, Grinstein & Campbell

## Friday 30 December 2022

### On This Day in Math - December 30

It requires a very unusual mind to undertake the analysis of the obvious.

### The 364th day of the year; 364 is the total number of gifts in the Twelve Days of Christmas song: 1+(2+1) + (3+2+1) ... which is a series of triangular numbers. The sum of the first n triangular numbers can be expressed as (n+2 Choose 3).

If you put a standard 8x8 chessboard on each face of a cube, there would be 364*(below) squares. Futility closet included this note on such a cube: "British puzzle expert Henry Dudeney once set himself the task of devising a complete knight’s tour of a cube each of whose sides is a chessboard. He came up with this:

If you cut out the figure, fold it into a cube and fasten it using the tabs provided, you’ll have a map of the knight’s path. It can start anywhere and make its way around the whole cube, visiting each of the 364 squares once and returning to its starting point. (*BTW, I've done the arithmetic on this, and that has to be 384 squares, but I didn't notice the discrepancy at first, so it's still here since I don't have a 384th day of the year to post it.)

The number of primes less than 364 = 3*6*4 (is this true for any other number?)

### There are also Smith (or joke) numbers: composite numbers n such that sum of digits of n = sum of digits of prime factors of n (counted with multiplicity).

EVENTS

1610 Galileo in answer to a question from Father Christoph Clavius SJ about why his large aperture was partly covered; answered that he did this for two reasons:
The first is to make it possible to work it more accurately because a large surface is
more easily kept in the proper shape than a smaller one. The other reason is that if
one wants to see a larger space in one glance, the glass can be uncovered, but it is then
necessary to put a less acute glass near the eye and shorten the tube, otherwise the
objects will appear very fuzzy. *Aalbert Vvan Helden, Galileo and the Telescope; Origins of the Telescope - Royal Netherlands Academy of Arts and Sciences, 2010

In 1873, the American Metrological Society was formed in New York City to improve systems of weights, measures and money. Its activities eventually extended with a committee considering units of force and energy, and another concerned with the adoption of Standard Time for the U.S. On 30 Dec 1884, at the meeting of the American Metrological Society at Columbia College in New York City, Charles S. Peirce read a paper on the determination of gravity. He also participated in a discussion of the adequacy of the standards of weight and measure in the United States and pointed out some of the deficiencies in the current system. As a result of his revelations, the Society passed a resolution recommending the appointment of a committee to advise Congress on the need for establishing an efficient bureau of standards. *TIS

1881 The “Four Fours” problem was ļ¬rst published in Knowledge a magazine of popular science edited by the astronomer Richard Proctor. The problem is to express whole numbers using exactly four fours and various arithmetical signs. For example 52 = 44 + 4 + 4. This can be done for the integers from 1 to 112, but 113 is a problem. Variations of the game allow use of factorials, square roots, decimal points (such as .4) etc. A good source for further study is here. And if you are interested, before there was a four-fours problem there was a three-threes problem

1902 Leornard Eugene Dickson married Susan Davis. Later he often said of his honeymoon: “It was a great success, except that I only got two research papers written.” In all he published 18 books and hundreds of articles.*VFR

1915 A two day meeting in Columbus, Ohio began to found a new mathematical organization. The new organization would be called the Mathematical Organization of America, and took over the publishing of the American Mathematical Monthly which had been in operation for three years. The first president was Professor E. R. Hedrick of the University of Missouri. The Earle Raymond Hedrick lectures were established by the Mathematical Association in America in his honor.

In 1924, Edwin Hubble announced the existence of another galactic system in addition to the Milky Way. He had found at least one "island universe," or galaxy of stars, lies outside our own Milky Way. Until then, scientists were not certain whether certain fuzzy clouds of light called "nebulae" that had been seen with telescopes were small clusters of clouds within the Milky Way or separate galaxies. Hubble measured the distance to the Andromeda nebula and showed it to be a hundred thousand times as far away as the nearest stars. This proved it was a separate galaxy, as large as our own Milky Way, but very far away.  More galaxies have been found, some a spiral form like the Milky Way; others spheroidal, others without the spiral arms, or of irregular shape.
1952 Harvard mathematician Andrew Gleason received the Newcomb Cleveland Prize, a \$1000 financial award, for his contributions toward the solution of Hilbert's Fifth Problem about Lie Groups.

1968 The front page of The New York Times reveals Bill Anders' "Earthrise" for the first time, albeit in black and white. (It was one of 13 photographs released by NASA the previous evening.)  *Chasing The Moon: The Book

In 1982, a second full moon of the month was visible. Known as a "blue moon," the name does not refer to its color, but it is a rare event, giving rise to the expression, "once in a blue moon" came from. This blue blue moon was more special as a total lunar eclipse also occurred (U.S.). Although there were 41 blue moons in the twentieth century, this was one of four during an eclipse of the moon, and the only total eclipse of a blue moon in the twentieth century. A blue moon happens every 2.7 years because of a disparity between our calendar and the lunar cycle. The lunar cycle is the time it takes for the moon to revolve around the earth, is 29 days, 12 hours, and 44 minutes. *TIS The next blue moon will occur on September 30 of 2012.

1985 Version 3.2 of the IBM PC​-DOS operating system is announced
PC-DOS, IBM's version of the DOS operating system used on the IBM PC, released Version 3.2 on this date. The system required 128KB RAM and was available on either one 720KB disk or two 51/4” disks. DOS has remained in use since the introduction of the IBM PC in 1981, with PC-DOS 200 being the latest release in 1998. *CHM

BIRTHS

1850 John Milne (30 Dec 1850; 30 Jul 1913) English seismologist who invented the horizontal pendulum seismograph (1894) and was one of the European scientists that helped organize the seismic survey of Japan in the last half of the 1800's. Milne conducted experiments on the propagation of elastic waves from artificial sources, and building construction. He spent 20 years in Japan, until 1895, when a fire destroyed his property, and he returned home to the Isle of Wight. He set up a new laboratory and persuaded the Royal Society to fund initially 20 earthquake observatories around the world, equipped with his seismographs. By 1900, Milne seismographs were established on all of the inhabited continents and he was recognized as the world's leading seismologist. He died of Bright's disease.*TIS

1897 StanisÅaw Saks (December 30, 1897 – November 23, 1942) was a Polish mathematician and university tutor, known primarily for his membership in the Scottish CafĆ© circle, an extensive monograph on the Theory of Integrals, his works on measure theory and the Vitali-Hahn-Saks theorem.*wIK

1931 Sir John (Theodore) Houghton (30 Dec 1931, ) Welsh meteorologist who began in the late 1960's drawing attention to the buildup of carbon dioxide in the earth's atmosphere and its result of global warming, now known as the greenhouse effect. As director-general (1983) of the British Meteorological Office, he began tracking changing climate patterns. In 1990, he co-chaired a team of scientists working for the United Nations that produced the first comprehensive report on the science of climate change. This led to the 1997 U.N. Conference on Climate Change, in Kyoto, Japan. The Kyoto Protocol that resulted there was a treaty among industrialized and developed nations to combat global warming by voluntarily adhering to progressively stiffening emissions-reduction standards.*TIS

1934 John N. Bahcall (30 Dec 1934, ) American astrophysicist who pioneered the development of neutrino astrophysics in the early 1960s. He theorized that neutrinos (subatomic particles that have no charge and exceedingly weak interaction with matter) can be used to understanding how stars shine. They are emitted by the sun and stars during the fusion energy creation process, and most are able to pass through the Earth without being stopped. He calculated the expected output of neutrinos from the sun, which created an experimental challenge to explain the unexpected result. He won the National Medal of Science (1998) for both his contributions to the planning and development of the Hubble Space Telescope and his pioneering research in neutrino astrophysics.*TIS

DEATHS

1691 Robert Boyle (25 Jan 1627, 30 Dec 1691) Anglo-Irish chemist and natural philosopher noted for his pioneering experiments on the properties of gases and his espousal of a corpuscular view of matter that was a forerunner of the modern theory of chemical elements. He was a founding member of the Royal Society of London. From 1656-68, he resided at Oxford where Robert Hooke, who helped him to construct the air pump. With this invention, Boyle demonstrated the physical characteristics of air and the necessity of air for combustion, respiration, and the transmission of sound, published in New Experiments Physio-Mechanical, Touching the Spring of the Air and its Effects (1660). In 1661, he reported to the Royal Society on the relationship of the volume of gases and pressure (Boyle's Law).*TIS

1695 Sir Samuel Morland (born 1625, 30 Dec 1695) English mathematician and inventor of mechanical calculators. His first machine added and subtracted English money using eight dials that were moved by a simple stylus. Another could multiply and divide using 30 discs with numbers marked around the edge - circular versions of Napier's linear bones. Five more discs handled finding square and cube roots. His third machine made trigonometric calculations. Morland built a speaking trumpet (1671) he claimed would allow a conversation to be conducted over a distance of 3/4 mile. By 1675, he had developed various pumps for domestic, marine and industrial applications, such as wells, draining ponds or mines, and fire fighting. He also designed iron stoves for marine use, and improved barometers. *TIS

1883 John Henry Dallmeyer (6 Sep 1830, 30 Dec 1883) German-born British inventor and manufacturer of lenses and telescopes. He introduced improvements in both photographic portrait and landscape lenses, in object glasses for the microscope, and in condensers for the optical lantern. Dallmeyer made photoheliographs (telescopes adapted for photographing the Sun) for Harvard observatory (1864), and the British government (1873). He introduced the "rapid rectilinear" (1866) which is a lens system composed of two matching doublet lenses, symmetrically placed around the focal aperture to remove many of the aberrations present in more simple constructions. He died on board a ship at sea off New Zealand. *TIS

1932 Eliakim Hastings Moore (January 26, 1862 – December 30, 1932) was an American mathematician. He discovered mathematics through a summer job at the Cincinnati Observatory while in high school.  When the University of Chicago opened its doors in 1892, Moore was the first head of its mathematics department, a position he retained until his death in 1931. His first two colleagues were Bolza and Maschke. The resulting department was the second research-oriented mathematics department in American history, after Johns Hopkins University.
Moore first worked in abstract algebra, proving in 1893 the classification of the structure of finite fields (also called Galois fields). Around 1900, he began working on the foundations of geometry. He reformulated Hilbert's axioms for geometry so that points were the only primitive notion, thus turning Hilbert's primitive lines and planes into defined notions. In 1902, he further showed that one of Hilbert's axioms for geometry was redundant. Independently, the twenty year old R.L. Moore (no relation) also proved this, but in a more elegant fashion than E. H. Moore used. When E. H. Moore heard of the feat, he arranged for a scholarship that would allow R.L. Moore to study for a doctorate at Chicago. E.H. Moore's work on axiom systems is considered one of the starting points for metamathematics and model theory. After 1906, he turned to the foundations of analysis. The concept of closure operator first appeared in his 1910 Introduction to a form of general analysis. He also wrote on algebraic geometry, number theory, and integral equations.
At Chicago, Moore supervised 31 doctoral dissertations, including those of George Birkhoff, Leonard Dickson, Robert Lee Moore (no relation), and Oswald Veblen. Birkhoff and Veblen went on to forge and lead the first-rate departments at Harvard and Princeton, respectively. Dickson became the first great American algebraist and number theorist. Robert Moore founded American topology. According to the Mathematics Genealogy Project, as of January 2011, E. H. Moore had over 14,900 known "descendants."
Moore convinced the New York Mathematical Society to change its name to the American Mathematical Society, whose Chicago branch he led. He presided over the AMS, 1901–02, and edited the Transactions of the American Mathematical Society, 1899–1907. He was elected to the National Academy of Sciences, the American Academy of Arts and Sciences, and the American Philosophical Society.
The American Mathematical Society established a prize in his honor in 2002. *Wik

1947 Alfred North Whitehead (15 Feb 1861, 30 Dec 1947) English mathematician and philosopher, who worked in logic, physics,  philosophy of science and metaphysics. He is best known for his work with Bertrand Russell on one of probably the most famous books of the century, Principia Mathematica (1910-13) to demonstrate that logic is the basis for all mathematics. In physics (1910-24) his best known work was a theory of gravity, that competed with Einstein's general relativity for many decades. In his later life from 1924 onward at Harvard, he worked on more general issues in philosophy rather than mathematics, including the development of a comprehensive metaphysical system which has come to be known as process philosophy. *TIS

1956 Heinrich Scholz (December 17 1884 in Berlin , December 30 1956 in Muenster, Westphalia ) was a German logician, philosopher and theologian. *Wik

1982 Philip Hall (11 April 1904 in Hampstead, London, England - 30 Dec 1982 in Cambridge, Cambridge shire, England) Hall was the main impetus behind the British school of group theory and the growth of group theory to be one of the major mathematical topics of the 20th Century was largely due to him.*SAU

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

## Thursday 29 December 2022

### Concurrencies and Coincidences Repost

Steve Phelps, over at concurrencies, just wrote a "What can you do with three random points in the plane?" blog. Coincidentally, I had just finished an interesting old (1902) article about three random points on an equilateral hyperbola (such as y= 1/x for those not familiar with the term). And by another coincidence, the article happened to involve one of the common concurrent centers of a triangle, the orthocenter where the three altitudes from the vertices intersects. It turns out, that if you pick three random points on a equilateral hyperbola (they can be on either branch), then the orthocenter will also fall on the hyperbola. Stated another way, if you pick the three points all on one branch and make them all free to move, the locus of the orthocenter will be the other branch of the hyperbola.  If two points are on one branch, and one on the other is not, then the orthocenter falls on the branch with two points on it,

Poncelet had actually written about this as far back as Jan of 1821 in Gergonne's Annales. Oh, by the way, a little "prove this factoid" for my calc kids... the y-intercept of the tangent line to any point on the rectangular hyperbola is always twice the y-coordinate, and the slope is always the square of the reciprocal of the y-coordinate. SWEET!  [Yikes, I've been busted... Keninwa noticed a mistake in the above (thanks guy) actually what I should have said (and this is only true for the basic y=1/x case), the slope is equal to the negative of the square of the y=value .. (and now, head hanging in shame, he wanders off into the sunset, muttering to himself about proofreading)..

### On This Day in Math - December 29

Folium of Descartes, *Wiki

Die ganze Zahl schuf der liebe Gott, alles Ćbrige ist Menschenwerk.
God made the integers, all else is the work of man.

~Leopold Kronecker

The 363rd day of the year; 363 is the sum of nine consecutive primes and is also the sum of 5 consecutive powers of three. It is the last palindrome of the year.

363 = ${19}^{2}+{1}^{1}+{1}^{2}={17}^{2}+{7}^{2}+{5}^{2}={13}^{2}+{13}^{2}+{5}^{2}$

363 is the numerator of the sum of the reciprocals of the first seven integers,

EVENTS

1566 A part of Tycho Brahe’s nose was cut off in a duel with another Danish nobleman. The dispute was over a point of mathematics. This he replaced with a prosthesis generally stated to be of silver and gold but containing a high copper content. *VFR
On December 10, 1566, Tycho and the Danish blue blood Manderup Parsbjerg were guests at an engagement party at Prof. Bachmeister in Rostock. The party included a ball, but the festive environment did not keep the two men from starting an argument that went on even over the Christmas period. On December 29, they finished the matter with a rapier duel. During the duel, which started at 7 p.m. in total darkness, a large portion of the nose of Brahe was cut off by his Opponent. It was the most famous cut in science, if not the unkindest. *Neatorama

1692 Huygens, in a letter to L’Hospital, gave the ļ¬rst complete sketch of the folium of Descartes. Although the curve was ļ¬rst discussed 23 August 1638 no complete sketch had previously been given due to a reluctance to use negative numbers as coordinates. *VFR

1763 Nevil Maskelyne wrote his brother Edmund, reporting his safe arrival on 7 November after “an agreeable passage of 6 weeks”. He noted that he had been “very sufficiently employed in making the observations recommended to me by the Commissioners of Longitude” and that it was at times “rather too fatiguing”.
The Princess Louise sailed for Barbados on 23 September. During the voyage Maskelyne and Charles Green took many lunar-distance observations (with Maskelyne later claiming that his final observation was within half of degree of the truth) and struggled a couple of times with the marine chair. Maskelyne’s conclusion was that the Jupiter’s satellites method of finding longitude would simply never work at sea because the telescope magnification required was far too high for use in a moving ship.
*Board of Longitude project, Greenwich

1746 Euler writes to praise d'Alembert on his proof of the Fundamental Theorem of Algebra, but disagrees with his idea that log(-x) = log (x).
Euler and d'Alembert's correspondence had begun on August 3, 1746, but several letters between these two, including the one that d'Alembert suggests that log(-x) = log (x) have been lost. *Robert E. Bradley, Ed Sandifer; Leonhard Euler: Life, Work and Legacy

1790 Obituary for Thomas “Tom” Fuller in the Columbian Centinial , Boston Massachusetts. His mathematical ability and its origin became a dueling point between abolitionists and those supporting slavery.

Died- Negro Tom, the famous African Calculator, aged 80 years. He was the property of Mrs. Elizabeth Cox of Alexandria. Tom was a very black man. He was brought to this country at the age of 14, and was sold as a slave.... This man was a prodigy. Though he could never read or write, he had perfectly acquired the art of enumeration.... He could multiply seven into itself, that product by seven, and the products, so produced, by seven, for seven times. He could give the number of months, days, weeks, hours, minutes, and seconds in any period of time that any person chose to mention, allowing in his calculation for all leap years that happened in the time; he would give the number of poles, yards, feet, inches, and barley-corns in any distance, say the diameter of the earth's orbit; and in every calculation he would produce the true answer in less time than ninety-nine men out of a hundred would produce with their pens. And, what was, perhaps, more extraordinary, though interrupted in the progress of his calculation, and engaged in discourse necessary for him to begin again, but he would ... cast up plots of land. He took great notice of the lines of land which he had seen surveyed. He drew just conclusions from facts; surprisingly so, for his opportunities. Had his [Thomas Fuller] opportunity been equal to those of thousands of his fellow-men ... even a NEWTON himself, need have ashamed to acknowledge him a Brother in Science.

*Univ of Buffalo Math Dept

In 1927, Krakatoa began a new volcanic eruption on the seafloor along the same line as the cones of previous activity. By 26 Jan 1928, a growing cone had reached sea level and formed a small island called Anak Krakatoa (Child of Krakatoa). Sporadic activity continued until, by 1973, the island had reached a height of 622 ft above sea level. It was still in eruption in the early 1980s. The volcano Krakatoa is on Pulau (island) Rakata in the Sunda Strait between Java and Sumatra, Indonesia. It had been quiet since its previous catastrophic eruption of 1883. That threw pumice 33 miles high and 36,380 people were killed either by the ash fall or by the resulting tidal wave. The only earlier known eruption was in 1680, and was only moderate.*TIS

1939 Shockley Makes Historic Notebook Entry
William Shockley records in his laboratory notebook that it should be possible to replace vacuum tubes with semiconductors. Eight years later, he, Walter Brattain and John Bardeen at AT&T Bell Laboratories successfully tested the point-contact transistor. Shockley developed much of the theory behind transistor action, and soon postulated the junction transistor, a much more reliable device. It took about ten years after the 1947 discovery before transistors replaced vacuum tubes in computer design as manufacturers learned to make them reliable and a new generation of engineers learned how to use them. *CHM

1947 George Dantzig announced his discovery of the simplex method at the joint annual meeting of the American Statistical Association and the Institute of Mathematical Statistics. The lecture was poorly attended and the result attracted no interest. *Robert Dorfman, “The discovery of linear programming,” Annals of the History of Computing, 6(1984), 283–295, esp. 292.

1979 Edward Lorenz presents a paper at the 139th Annual Meeting of the American Association for the Advancement of Science with the title, "Predictability: Does the flap of a butterfly's wings in Brazil set off a tornado in Texas?" *TIS  According to Lorenz, upon failing to provide a title for a talk he was to present at the meeting Philip Merilees concocted the title. The idea that one butterfly could have a far-reaching ripple effect on subsequent events seems first to have appeared in a 1952 short story by Ray Bradbury about time travel. It seems that Merilees was  was not familiar with Bradbury’s story. *Wik Found this cartoon @NewYorker

BIRTHS

1256 Birthdate of Ibn Al-Banna who studied the magic properties of numbers and letters. *VFR He was an Islamic mathematician who wrote a large number of works including an introduction to Euclid's Elements, an algebra text and various works on astronomy.*SAU

1796 Johann Christian Poggendorff (29 December 1796 – 24 January 1877), was a German physicist and science historian born in Hamburg. By far the greater and more important part of his work related to electricity and magnetism. Poggendorff is known for his electrostatic motor which is analogous to Wilhelm Holtz's electrostatic machine. In 1841 he described the use of the potentiometer for measurement of electrical potentials without current draw.
Even at this early period he had conceived the idea of founding a physical and chemical scientific journal, and the realization of this plan was hastened by the sudden death of Ludwig Wilhelm Gilbert, the editor of Gilbert's Annalen der Physik, in 1824 Poggendorff immediately put himself in communication with the publisher, Barth of Leipzig. He became editor of Annalen der Physik und Chemie, which was to be a continuation of Gilbert's Annalen on a somewhat extended plan. Poggendorff was admirably qualified for the post, and edited the journal for 52 years, until 1876. In 1826, Poggendorff developed the mirror galvanometer, a device for detecting electric currents.
He had an extraordinary memory, well stored with scientific knowledge, both modern and historical, a cool and impartial judgment, and a strong preference for facts as against theory of the speculative kind. He was thus able to throw himself into the spirit of modern experimental science. He possessed in abundant measure the German virtue of orderliness in the arrangement of knowledge and in the conduct of business. Further he had an engaging geniality of manner and much tact in dealing with men. These qualities soon made Poggendorff's Annalen (abbreviation: Pogg. Ann.) the foremost scientific journal in Europe.
In the course of his fifty-two years editorship of the Annalen Poggendorff could not fail to acquire an unusual acquaintance with the labors of modern men of science. This knowledge, joined to what he had gathered by historical reading of equally unusual extent, he carefully digested and gave to the world in his Biographisch-literarisches Handworterbuch zur Geschichte der exacten Wissenschaften, containing notices of the lives and labors of mathematicians, astronomers, physicists, and chemists, of all peoples and all ages. This work contains an astounding collection of facts invaluable to the scientific biographer and historian. The first two volumes were published in 1863; after his death a third volume appeared in 1898, covering the period 1858-1883, and a fourth in 1904, coming down to the beginning of the 20th century.
His literary and scientific reputation speedily brought him honorable recognition. In 1830 he was made royal professor, in 1838 Hon. Ph.D. and extraordinary professor in the University of Berlin, and in 1839 member of the Berlin Academy of Sciences. In 1845, he was elected a foreign member of the Royal Swedish Academy of Sciences.
Many offers of ordinary professorships were made to him, but he declined them all, devoting himself to his duties as editor of the Annalen, and to the pursuit of his scientific researches. He died at Berlin on 24 January 1877.
The Poggendorff Illusion is an optical illusion that involves the brain's perception of the interaction between diagonal lines and horizontal and vertical edges. It is named after Poggendorff, who discovered it in the drawing of Johann Karl Friedrich ZĆ¶llner, in which he showed the ZĆ¶llner illusion in 1860. In the picture to the right, a straight black line is obscured by a dark gray rectangle. The black line appears disjointed, although it is in fact straight; the second picture illustrates this fact.*Wik

1856 Birth of Thomas Jan Stieltjes, who did pioneering work on the integral. *VFR Thomas Stieltjes worked on almost all branches of analysis, continued fractions and number theory. *SAU

1861 Kurt Hensel (29 Dec 1861 in KĆ¶nigsberg, Prussia (now Kaliningrad, Russia) - 1 June 1941 in Marburg, Germany)  invented the p-adic numbers, an algebraic theory which has proved important in later applications. From 1901 Hensel was editor of the prestigious and influential Crelle's Journal.*SAU

1879 Ellen Gleditsch (Dec 29, 1879 -June 5, 1968) was a Norwegian radiochemist and Norway's second female professor. Starting her career as an assistant to Marie Curie, she became a pioneer in radiochemistry, establishing the half-life of radium and helping demonstrate the existence of isotopes
A wonderful story of her life by Dava Soblel is at the Linda Hall Library.
1905 Henri-Gaston Busignies (29 Dec 1905; 20 Jun 1981) French-born American electronics engineer whose invention (1936) of high-frequency direction finders (HF/DF, or "Huff Duff") permitted the U.S. Navy during World War II to detect enemy transmissions and quickly pinpoint the direction from which a radio transmission was coming. Busignies invented the radiocompass (1926) while still a student at Jules Ferry College in Versailles, France. In 1934, he started developing the direction finder based on his earlier radiocompass. Busignies developed the moving target indicator for wartime radar. It scrubbed off the radar screen every echo from stationary objects and left only echoes from moving objects, such as aircraft. *TIS

1911 (Emil) Klaus (Julius) Fuchs (29 Dec 1911; 28 Jan 1988) was a German-born physicist who was convicted as a spy on 1 Mar 1950, for passing nuclear research secrets to Russia. He fled from Nazi Germany to Britain. He was interned on the outbreak of WW II, but Prof. Max Born intervened on his behalf. Fuchs was released in 1942, naturalized in 1942 and joined the British atomic bomb research project. From 1943 he worked on the atom bomb with the Manhattan Project at Los Alamos, U.S. By 1945, he was sending secrets to Russia. In 1946, he became head of theoretical physics at Harwell, UK. He was caught, confessed, tried, imprisoned for nine of a 14 year sentence, released on 23 Jun 1959, and moved to East Germany and resumed nuclear research until 1979. *TIS

1944 Joseph W. Dauben (born 29 December 1944, Santa Monica- ) is a Herbert H. Lehman Distinguished Professor of History at the Graduate Center of the City University of New York. He obtained his Ph.D. from Harvard University.
His fields of expertise are history of science, history of mathematics, the scientific revolution, sociology of science, intellectual history, 17-18th centuries, history of Chinese science, and the history of botany.
His book Abraham Robinson was reviewed positively by MoshĆ© Machover, but he noted that it avoids discussing any of Robinson's negative aspects, and "in this respect [the book] borders on the hagiographic, painting a portrait without warts."
Dauben in a 1980 Guggenheim Fellow and is a Fellow of the American Association for the Advancement of Science, and a Fellow of the New York Academy of Sciences (since 1982).
Dauben is an elected member (1991) of the International Academy of the History of Science and an elected foreign member (2001) of German Academy of Sciences Leopoldina.
He delivered an invited lecture at the 1998 International Congress of Mathematicians in Berlin on Karl Marx's mathematical work. *Wik

DEATHS

1720 Maria Winckelmann (Maria Margarethe Winckelmann Kirch (25 Feb 1670 in Panitzsch, near Leipzig, Germany - 29 Dec 1720 in Berlin, Germany) was a German astronomer who helped her husband with his observations. She was the first woman to discover a comet.*SAU

1731 Brook Taylor (18 Aug 1685, 29 Dec 1731) British mathematician, best known for the Taylor's series, a method for expanding functions into infinite series. In 1708, Taylor produced a solution to the problem of the centre of oscillation. His Methodus incrementorum directa et inversa (1715; “Direct and Indirect Methods of Incrementation”) introduced what is now called the calculus of finite differences. Using this, he was the first to express mathematically the movement of a vibrating string on the basis of mechanical principles. Methodus also contained Taylor's theorem, later recognized (1772) by Lagrange as the basis of differential calculus. A gifted artist, Taylor also wrote on basic principles of perspective (1715) containing the first general treatment of the principle of vanishing points.*TIS

1737 Joseph Saurin (1659 at Courtaison – December 29, 1737 at Paris) was a French mathematician and a converted Protestant minister. He was the first to show how the tangents at the multiple points of curves could be determined by mathematical analysis. He was accused in 1712 by Jean-Baptiste Rousseau of being the actual author of defamatory verses that gossip had attributed to Rousseau.*Wik

1891 Leopold Kronecker (7 Dec 1823, 29 Dec 1891) died of a bronchial illness in Berlin, in his 69th year. Kronecker's primary contributions were in the theory of equations. *VFR
A German mathematician who worked to unify arithmetic, algebra and analysis, with a particular interest in elliptic functions, algebraic equations, theory of numbers, theory of determinants and theory of simple and multiple integrals. However the topics he studied were restricted by the fact that he believed in the reduction of all mathematics to arguments involving only the integers and a finite number of steps. He believed that mathematics should deal only with finite numbers and with a finite number of operations. He was the first to doubt the significance of non-constructive existence proofs, and believed that transcendental numbers did not exist. The Kronecker delta function is named in his honor. *TIS

1941 William James Macdonald (1851 in Huntly, Aberdeenshire, Scotland
Died: 29 Dec 1941 in Edinburgh, Scotland) graduated from the University of St Andrews. He taught at Madras College St Andrews, at Merchiston Castle School and at Donald Stewart's College in Edinburgh. He was a pioneer of the introduction of modern geometry to the mathematical curriculum. He was a founder member of the EMS and became the sixth President in 1887. *SAU

1941 Tullio Levi-Civita (29 Mar 1873, 29 Dec 1941) Italian mathematician who was one of the founders of absolute differential calculus (tensor analysis) which had applications to the theory of relativity. In 1887, he published a famous paper in which he developed the calculus of tensors. In 1900 he published, jointly with Ricci, the theory of tensors MĆ©thodes de calcul differential absolu et leures applications in a form which was used by Einstein 15 years later. Weyl also used Levi-Civita's ideas to produce a unified theory of gravitation and electromagnetism. In addition to the important contributions his work made in the theory of relativity, Levi-Civita produced a series of papers treating elegantly the problem of a static gravitational field. *TIS

1989 Adrien Albert (19 November 1907, Sydney - 29 December 1989, Canberra) was a leading authority in the development of medicinal chemistry in Australia. Albert also authored many important books on chemistry, including one on selective toxicity.
He was awarded BSc with first class honours and the University Medal in 1932 at the University of Sydney. He gained a PhD in 1937 and a DSc in 1947 from the University of London. His appointments included Lecturer at the University of Sydney (1938-1947), advisor to the Medical Directorate of the Australian Army (1942-1947), research at the Wellcome Research Institute in London (1947-1948) and in 1948 the Foundation Chair of Medical Chemistry in the John Curtin School of Medical Research at the Australian National University in Canberra where he established the Department of Medical Chemistry. He was a Fellow of the Australian Academy of Science.
He was the author of Selective Toxicity: The Physico-Chemical Basis of Therapy, first published by Chapman and Hall in 1951.
The Adrien Albert Laboratory of Medicinal Chemistry at the University of Sydney was established in his honour in 1989.[1] His bequest funds the Adrien Albert Lectureship, awarded every two years by the Royal Society of Chemistry *Wik

1989 Hermann (Julius) Oberth (25 Jun 1894, 29 Dec 1989)  was a German scientist who was one of three founders of space flight (with Tsiolkovsky and Goddard). After injury in WWI, he drafted a proposal for a long-range, liquid-propellant rocket, which the War Ministry dismissed as fanciful. Even his Ph.D. dissertation on his rocket design was rejected by the University of Heidelberg. When he published it as Die Rakete zu den PlanetenrĆ¤umen (1923; “The Rocket into Interplanetary Space”) he gained recognition for its mathematical analysis of the rocket speed that would allow it to escape Earth's gravitational pull. He received a Romanian patent in 1931 for a liquid-propellant rocket design. His first such rocket was launched 7 May 1931, near Berlin. *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