## Tuesday 21 December 2021

### On This Day in Math - December 21

 Home Fires in Possum Trot

In his wretched life of less than twenty-seven years Abel accomplished so much of the highest order that one of the leading mathematicians of the Nineteenth Century (Hermite, 1822-1901) could say without exaggeration, 'Abel has left mathematicians enough to keep them busy for five hundred years.' Asked how he had done all this in the six or seven years of his working life, Abel replied, 'By studying the masters, not the pupils.'
~Eric Temple Bell

The 355th day of the year; 355 is the 12th Tribonacci number, Like Fibonacci but start with 1,1,1 and each new term is the sum of the previous three terms.

355 is almost exactly 113π=354.9999699.. No year day is closer to an integer multiple of pi. This leads to a very good mnemonic for a fractional approximation to pi, "113355, divide in the middle, then put big over little." 355/113 = 3.14159292

355 is also the last Smith number of the year. A composite number with the sum of its digits equal to the sum of the digits of it's prime factors 3 + 5 + 5 = 5 + 7 + 1 (355 = 5 x 71)

If you write out the binary expression of 355, and examine it as a decimal number, (101100011) it is prime. 355 is the last day of the year that is such a number.

EVENTS

1614 The first public ecclesiastical attack on Galileo was launched from the pulpit of Santa Maria Novella in Florence by Father Thomas Caccini who denounced Galileo with his biblical proof quoting the scripture when God stopped the sun in the sky to help Joshua defeat the Amorites. His attack included all mathematicians, and indeed, mathematics itself as religious and political heresy. *Brody & Brody, The Science Class You Wish You Had

1671 Newton proposed for membership in the Royal Society of London by Seth Ward. See 11 January 1672. *VFR

1732 A Letter from Mr. Colin MacLaurin, Math. Prof. Edinburg. F. R. S. to Mr. John Machin,. concerning the Description of Curve Lines. Communicated to the Royal Society on December 21, 1732 *Phil. Trans. 1735 39:143-165

1752 A letter of Benjamin Franklin on October 1st, to Mr. Peter Collinson, FRS concerning an electrical kite, was read before the society on Dec 21. Franklin describes the construction of the kite from two light strips of cedar and a large thin silk handerchief,
*Phil. Trans. 1751 47:565-567

1754 Louis-Bertrand Castel, vociferous opponent of Newtonian science, gave a demonstration of his ocular harpsicord, which corresponded colors with the musical tones. *VFR
The ocular harpsichord had sixty small coloured glass panes, each with a curtain that opened when a key was struck. A second, improved model of the harpsichord was demonstrated for a small audience in December of 1754. Pressing a key caused a small shaft to open, in turn allowing light to shine through a piece of stained glass. Castel thought of color-music as akin to the lost language of paradise, where all men spoke alike, and he claimed that thanks to his instrument’s capacity to paint sounds, even a deaf listener could enjoy music. *Wik

1807 Joseph Fourier announced to the French Academy of Science that an arbitrary function could be expanded as an inﬁnite series of sines and cosines (we now call them Fourier series). *VFR Fourier's memoir On the Propagation of Heat in Solid Bodies, was read to the Paris Institute, an important mathematical work, containing what we now call Fourier series, which he had worked upon since around 1804. A committee consisting of Lagrange, Laplace, Monge and Lacroix was set up to report on the work. Although now highly regarded, at the time, this memoir caused controversy. Lagrange and Laplace objected to Fourier's expansions of functions as trigonometrical series (the Fourier series). It was not until 1822 that his prize winning essay Théorie analytique de la chaleur was published by the Académie des Sciences. Delambre, Secretary to the mathematical section, had arranged for the printing before he died.*TIS

In 1829, first stone arch railroad bridge in US was dedicated at Baltimore. The Carrollton Viaduct crosses a wooded stretch of Gwynn's Falls. The viaduct was named for Charles Carroll of Carrollton, signer of the Declaration of Independence, who laid the first stone of the Baltimore & Ohio Railroad on 4 Jul 1828. Construction took over 9 months. Some 1,500 tons of granite were supported on huge wooden frameworks. until the keystones were in place and the massive 80 ft arch over the stream became self-supporting. Overall, the bridge is about 62-ft tall, and 300-ft long. On New Year's Day, 1830, it became America's first railroad destination, using a horse until the locomotive "Tom Thumb" came later in 1830. Trains have used it ever since.*TIS

1857 The paddlewheel steamboat began its exploration up the Colorado River as far as it is Navigable.  Under the direction of Joseph Christmas Ives (can you guess what day he was born?) the ship had been commissioned to be built in Philadelphia only six months before, shipped unassembled to the isthmus of Panama in September of 1857, and carried by rail across to the Pacific side  (For trivia experts, the first "boat" to cross the isthmus of Panama).  From there to the mouth of the Colorado where it was reassembled and began its journey up the mighty river.  My source, and a great sight for more information on the man and his mission, with beautiful pictures can be found at Linda Hall Library

1881 When Ivory soap decided to market its laundry soap as a cosmetic soap, they needed to find an edge.  Turning to science to find such an edge, they wondered how to measure their bar as a quality soap, but no one had a clearly defined definition of what actually was a soap.  So they hired scientist to define it, and the came up with a combination of fatty acids and alkali..., that's it.  The same scientist measured the "purity of the ivory bar and found out it was nearly perfect.  Where popular cosmetic soaps included olive oil and sodium hydroxide, Ivory was over 99% pure.  As the ad on this day in The Independent, a religious weekly touted, "Ivory is 99 and 44/100 % pure."  An outstanding slogan that has lasted for more than a century. * David Feldman, Why do clocks run clockwise.

1893 Scientist Pierre and Marie Curie discovered radium. *VFR

1903 The first K&E Pocket watch slide rule patent was applied for on this date. Prior to this time K&E sold French made Boucher designs. The patent is in the name of Elmer A. Sperry, co-inventor of the gyrocompass. The patent covers the use of the ‘S’ and ‘L’ dials and the geared hands and dials . *Oughtred Society

1913 The ﬁrst crossword puzzle was published, in the Sunday supplement of the New York World. “Unthinkable as it now seems, there were no crossword puzzles until the newspaperman Arthur Wynne’s simple Word Cross appeared ... on the ‘Fun’ page of The New York World Sunday Magazine *FFF
The puzzle is shown below, and if you want to take a trip back in time and try to solve it, you can find the clues (and an answer key if needed) at the American Crossword Puzzle Tournament page.

1946 The Detroit news reports the Purdue yell,
“E to the X, DY , DX —
E to the X, DX —
Cosine, Secant, Tangent, Sine —
Three Point One Four One Five Nine —
Square Root, Cube Root, BTU —
Slipstick, Slide Rule, Yea Purdue.”
*VFR (perhaps some of the Boilermakers had a few too many boilermakers.) (For those in the rest of the world who may not use the term, In USA terminology, the boilermaker consists of a glass of beer and a shot of whiskey.)

1968 Integrated Circuits Used in Moonshot :
The Apollo Guidance Computer (AGC) was responsible for guidance, navigation, and control computations in the Apollo space program. The AGC was the first computer to use integrated circuit logic and occupied less than 1 cubic foot of the spacecraft. It stored data in 15 bit words (with one parity bit) and had a memory cycle time of 11.7 usec. Astronauts communicated with the AGC using the "DSKY" (Display Keyboard) shown on today's homepage. It used digital displays and communicated with austronauts using verb and noun buttons, and a two-digit operation and operand code.
The AGC and DSKY form part of The Computer Museum History Center's permanent collection. *CHM

2006 the journal Science recognized Perelman's proof of the Poincaré conjecture as the scientific "Breakthrough of the Year", the first such recognition in the area of mathematics. *Wik  On Nov 12, 2022 Grigori Perelman had posted the first of a series of eprints to the arXiv, in which he proves the century old Poincaré conjecture.  *Wik

2016 The winter solstice occurs on this date about half of the time.*VFR (This year for example)

2012 The last date of the Mayan “long count” calendar. The first day of the current Mayan “long count” calendar (adjusted for the Gregorian Calendar) was August 13, 3114 BC. The long count calendar lasts 22,507,528 days and the current calendar will end on December 21 of 2012. What happens then depends on who you read. If the world does NOT end, (and it seems it didn't, although perhaps I was too busy to notice) we will be back to year zero of the Mayan calendar.

BIRTHS
1878 Jan Łukasiewicz (Polish pronunciation: [ˈjan wukaˈɕɛvʲitʂ]) (21 December 1878 – 13 February 1956) was a Polish logician and philosopher born in Lwów (Lemberg in German), Galicia, Austria–Hungary (now Lviv, Ukraine). His work centred on analytical philosophy and mathematical logic. He thought innovatively about traditional propositional logic, the principle of non-contradiction and the law of excluded middle.*Wik He created a notation he called Polish Notation (after his homeland) that use the argument of a function before the actual notation for the function to eliminate the need for parenthetical enclosures. This notation is the root of the idea of the recursive stack, a last-in, first-out computer memory store proposed by several researchers including Turing, Bauer and Hamblin, and first implemented in 1957. In 1960, Łukasiewicz notation concepts and stacks were used as the basis of the Burroughs B5000 computer designed by Robert S. Barton and his team at Burroughs Corporation in Pasadena, California. The concepts also led to the design of the English Electric multi-programmed KDF9 computer system of 1963, which had two such hardware register stacks. A similar concept underlies the reverse Polish notation (RPN, a postfix notation) of the Friden EC-130 calculator and its successors, many Hewlett Packard calculators. *Wik

1889 Sewall Green Wright (21 Dec 1889 in Melrose, Massachusetts, USA - 3 March 1988 in Madison, Wisconsin, USA) Wright is famed for his work on evolution, in particular in the use of statistical techniques in the subject. In 1942 he published the Gibbs lecture that he had delivered in the Bulletin of the American Mathematical Society. Opatowski writes in a review, "... a review of the prominent work done by the author in the last twelve years towards the establishment of a mathematical theory of evolution. "
Another paper by Wright which shows his mathematical approach to the subject is The differential equation of the distribution of gene frequencies which he published in 1945. He derives differential equations which are satisfied by the probability density function of the distribution of gene frequencies under certain conditions.
In 1950 Wright gave the Galton lecture at University College, London. In this lecture, which was later published as The genetical structure of populations, he systematically applied his method of path coefficients to problems of population structure in a variety of situations such as: random mating and inbreeding; statistical properties of populations; the inbreeding coefficient F; hierarchic structure; natural populations; the island model of structure; isolation by distance; population structure in evolution; ecologic opportunity; and evolution in general. He also presented a number of mathematical appendices in the paper: the method of path coefficients; general coefficients of inbreeding; properties of populations as related to F; the inbreeding coefficient of breeds; regular systems of mating; and isolation by distance.
Fisher and Wright had differing views on the mechanism and importance of natural selection. Their disagreement began in the late 1920s and became increasingly bitter leading to a split among evolutionists. *SAU

1898 Ira Sprague Bowen (21 Dec 1898; 6 Feb 1973) was an American astrophysicist. His investigation of the ultraviolet spectra of highly ionized atoms led to his explanation of the unidentified strong green spectral lines of gaseous nebulae (clouds of rarefied gas) as forbidden lines of ionized oxygen and nitrogen. This emission, appearing to match no known element, had formerly been suggested to be due to a hypothetical element, "nebulium." Bowen was able to show, that in reality, the emission lines exactly matched those calculated to be the "forbidden lines" of ionized oxygen and nitrogen under extremely low pressure. This made a major advance in the knowledge of celestial composition. He was director of the Mt. Wilson and Palomar Observatories from 1948-64.*TIS

1905 Kate Sperling Fenchel (December 21, 1905 - December 19, 1983) Born in Berlin, Germany. Studied mathematics, philosophy, and physics at the University of Berlin from 1924 to 1928. She was encouraged to write a thesis, but she could not afford to continue her studies and research jobs for women appeared to be difficult to obtain. Thus she never received a Ph.D. in mathematics. From 1931 to 1933 she taught mathematics at the high school level, but was fired when the Nazis came to power in Germany because she was Jewish. She emigrated to Denmark with Werner Fenchel, a former fellow student, and the two married in December, 1933. Fenchel worked from 1933 to 1943 for a Danish mathematics professor. In 1943 she had to escape to Sweden with her husband and 3-year old son while Germany occupied Denmark. They returned to Denmark after the end of the war. Fenchel held a part-time lecturer's job at Aarhus University, Denmark, from 1965-1970.
Fenchel did research in finite nonabelian groups and published several papers, the last at the age of 73. *ASC

1929 Douglas T. Ross is born in Canton, China. He received an AB from Oberlin College in 1951 and an SM from MIT in 1954. He worked with John Ward on the Cape Cod Air Defense System Project, held many positions at MIT, including head of the Computer Applications Group at the Electronic System Laboratory, and was project engineer for the MIT Computer-Aided Design project. He developed APT (Automatically Programmed Tools)--now an international standard--and AED (Automated Engineering Design) projects which were early precursors of the languages and systems of modern CAD and CAM systems. These projects were run in close connection with the WHIRLWIND, TX-0, TX-2, Project MAC, and CTSS.
In 1969 Ross founded SoftTech Corporation, where he is now chairman of the board of directors. *CHM

DEATHS
1792 James Rumsey (1743–Dec 21,1792) was an American mechanical engineer chiefly known for exhibiting a boat propelled by machinery in 1787 on the Potomac River at Shepherdstown in present-day West Virginia before a crowd of local notables, including Horatio Gates. A pump driven by steam power ejected a stream of water from the stern of the boat and thereby propelled the boat forward.
The demonstration took place twenty years before Robert Fulton constructed and demonstrated the Clermont. The idea of jet propulsion was not Rumsey's alone. Daniel Bernoulli (1700–1782) originated the idea of propelling watercraft in that way. In the summer of 1785, while Rumsey and his assistant Joseph Barnes were in the process of assembling his boat, Benjamin Franklin, on board a ship from France, wrote of propelling a boat by water jet. This coincidence has sometimes led people to believe Rumsey got the idea from Franklin. Indeed, if Franklin had wanted to make such a claim it likely would have been accepted, but he did not, and became one of Rumsey's supporters. *Wik

1912 Paul Albert Gordan (27 April 1837 in Breslau, Germany (now Wrocław, Poland)
- 21 Dec 1912 in Erlangen, Germany) Gordan worked with Clebsch on invariant theory and algebraic geometry. He also gave simplified proofs of the transcendence of e and π. *SAU

1956 Lewis M(adison) Terman (15 Jan 1877, 21 Dec 1956) was a U.S. psychologist who pioneered individual intelligence tests. During WW I, he was involved in mass testing of intelligence for the U.S. army. He expanded an English version of the French Binet-Simon intelligence test with which he introduced the IQ (Intelligence Quotient), being a ratio of chronological age to mental age times 100. (Thus an average child has an IQ of 100). He wrote about this metric in The Measurement of Intelligence (1916). He made a long-term study of gifted children (with IQ above 140) examining mental and physical aspect of their lives reported in the multi-volume Genetic Studies of Genius (1926-59). *TIS

1960 Eric Temple Bell (7 Feb 1883, 21 Dec 1960) Scottish-American mathematician and writer who contributed to analytic number theory (in which he found several important theorems), Diophantine analysis and numerical functions. In addition to about 250 papers on mathematical research, he also wrote for the layman in Men of Mathematics (1937) and Mathematics, Queen and Servant of Science (1951) among others. Under the name of John Taine, he also wrote science fiction.*TIS

1976 Vijay Kumar Patodi (March 12, 1945 – December 21, 1976) was an Indian mathematician who made fundamental contributions to differential geometry and topology. He was the first mathematician to apply heat equation methods to the proof of the Index Theorem for elliptic operators.[citation needed] He was a professor at Tata Institute of Fundamental Research, Mumbai (Bombay). *Wik

1980 Vladimir Petrovich Potapov (24 Jan 1914 in Odessa, Ukraine - 21 Dec 1980 in Kharkov, Russia) In 1948 Potapov was invited to the Pedagogical Institute at Odessa. He soon became Head of Mathematics and, from 1952, Dean of the Faculty of Physics and Mathematics. He used his position to invite Livsic and others to the Institute.
During the 1950s Potapov worked on the theory of J-contractive matrix functions and the analysis of matrix functions became his main work. He published papers on the multiplicative theory of analytic matrix functions in the years 1950-55 which contain work from his doctoral thesis. He also worked on interpolation problems.
From 1974 Potapov lectured at Odessa Institute of National Economy, then he went to Kharkov to head the Department of Applied Mathematics at the Institute for low temperature physics. *SAU

1987 Eugene Lukacs (14 August 1906 – 21 December 1987) was a Hungarian statistician born in Szombathely, notable[1] for his work in characterization of distributions, stability theory, and being the author of Characteristic Functions[2], a classic textbook in the field.*Wik

*WM = Women of Mathematics, Grinstein & Campbell
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