Saturday 29 February 2020

On This Day in Math - February 29


Common sense is not really so common.
~Antoine Arnauld (1612 - 1694) in
The Art of Thinking: Port-Royal Logic

The 60th day of the year; 60 is the smallest composite number which is the order of a simple group.

7! is the smallest # with 60 divisors.

There are four Archimedean solids with 60 vertices , : the truncated icosahedron, (shown) the rhombicosidodecahedron, the snub dodecahedron, and the truncated dodecahedron.

Oh, and Pi day is coming up in a couple of weeks, so ... suppose you were scrolling through the digits of pi and wondered how long it would take until you found a string of ten digits that had all ten of 0 through nine in it... Benjamin Vitale ‏@BenVitale thought to find out and :

You can arrange the whole numbers from 1 to 60 into pairs so that the sum of the numbers in each pair is a perfect square; in fact, you can do it in   4,366,714 ways. Here is one of those presented in a pretty fashion using only five squares for the sums. *Gordon Hamilton, Kiran S. Kedlaya, and Henri Picciotto; Square–Sum Pair Partitions(Won the George Polya Prize from MAA for 2016)

---Leap day is also called “bissextile” or “second sixth.” Under the Julian Calendar the leap day was added just before February 25, more specifically “ante diem sexto Kalendas Martius” (sixth day before the Calends of March) and was called “bissexto Kalendas Martius” (the second-six of the Calends of March). [Scientific American] *VFR

1712 Sweden briefly had a February 30. In planning to switch from the Julian to the Gregorian calendar, the Swedish Empire resolved to omit leap days from 1700 to 1740. It followed through on this plan in 1700, but through error 1704 and 1708 remained leap years. With the time now out of joint, the empire abandoned its plan and returned to the Julian calendar by observing two leap days, February 29 and February 30, in 1712. (Sweden finally converted to the Gregorian calendar in 1753.)
If the original plan had been carried out, a person born on Feb. 29, 1696, would not celebrate a birthday until 1744. As it was, a person born on Feb. 30, 1712, would never celebrate a birthday at all. *Greg Ross, Futility Closet

1504 On Feb. 29, 1504, Columbus and his men had been shipwrecked in Jamaica for eight months, relying on the local natives to feed them. After six months, the natives cut off the charity. Columbus, who had an astronomical almanac with him, summoned the native leaders and warned that if the natives did not reconsider, God would make the Moon disappear. When, as Columbus had predicted, the Moon became fully eclipsed that night, the natives panicked. * (Somewhat skeptical of this story. Did astronomical almanacs this early already include information like this about Jamaica?)

1880 On Leap Day in 2012, John D Cook at The Endeavor blog posted a tribute from Pirates of Penzance by Gilbert & Sullivan :

For some ridiculous reason, to which, however, I’ve no desire to be disloyal,
Some person in authority, I don’t know who, very likely the Astronomer Royal,
Has decided that, although for such a beastly month as February, twenty-eight days as a general rule are plenty,
One year in every four, its days shall be reckoned as nine and twenty.

In 1916, Maria Montessori of Rome, Italy, received a U.S. patent for “Cut-Out Geometrical Figure for Didactical Purposes” (No. 1,173,298). Montessori is famous for her educational methods. The patent covered her invention of a plate with recesses into which geometrical shapes can be fitted so the “fundamental principles of geometry may be easily and rapidly taught to young pupils.” The recesses can be filled with, for example, several smaller trianges that fill the larger triangular cavity.*TIS

1924 The first Josiah Willard Gibbs lecture was delivered by Professor M. I. Pupin of Columbia University to an AMS meeting in New York City. In introducing him, AMS president Veblen said “It is hoped that the Willard Gibbs Lecturers will remind the mathematicians of something that we fear they sometimes forget, – the existence of an outside world. It is equally hoped that they will remind the outside world that mathematics is a growing concern, – not a pedantic exercise for the torment of schoolboys, but a living organism growing larger and stronger each year.” See BAMS 30(1924), p. 289. *VFR

In 1936, Nature carried Niels Bohr's “bowl of balls” explanation for the effect of bombarding particles on a nucleus (Vol. 137, p. 344). He followed up in an article in Science (20 Aug 1937, p. 161) explaining that “to understand the typical features of nuclear transmutations initiated by impacts of material particles... A simple mechanical model which illustrates these features of nuclear collisions is ... a shallow basic with a numbler of billard balls in it. If the bowl were empty, then a ball which was sent in would go down one clope and pass out on the opposite side with its original energy. When, however, there are other balls in the bowl, then the incident one will not be able to pass through freely but will divide its energy first with one of the balls, these two will share their energy ... divided among all the balls.”*TIS

Suspended In Language: Niels Bohrs Life, Discoveries, And The Century He Shaped
by Jim Ottaviani, Leland Purvis and Jeff Parker

1968 British astronomer, Jocelyn Burnell, announced the discovery of a pulsar, a pulsating radio source believed to be a rapidly rotating neutron star. *VFR


1860 Herman Hollerith (29 Feb 1860, 17 Nov 1929) American inventor of a tabulating machine that was an important precursor of the electronic computer. For the 1890 U.S. census, he invented several punched-card machines to automate the sorting of data. The machine which read the cards used a pin going through a hole in the card to make an electrical connection with mercury placed beneath. The resulting electrical current activated a mechanical counter. It saved the United States 5 million dollars for the 1890 census by completing the analysis of the data in a fraction of the time it would have taken without it and with a smaller amount of  manpower than would have been necessary otherwise. In 1896, he formed the Tabulating Machine Company, a precursor of IBM. *TIS

1932 Gene Howard Golub (February 29, 1932 – November 16, 2007), Fletcher Jones Professor of Computer Science (and, by courtesy, of Electrical Engineering) at Stanford University, was one of the preeminent numerical analysts of his generation.
Credits. *Wik

1744 John Theophile Desaguliers (12 Mar 1683, 29 Feb 1744 at age 60)French-English chaplain and physicist who studied at Oxford, became experimental assistant to Sir Isaac Newton. As curator at the Royal Society, his experimental lectures in mechanical philosophy and electricity (advocating, substantiating and popularizing the work of Isaac Newton) attracted a wide audience. In electricity, he coined the terms conductor and insulator. He repeated and extended the work of Stephen Gray in electricity. He proposed a scheme for heating vessels such as salt-boilers by steam instead of fire. He made inventions of his own, such as a planetarium, and improvements to machines, such as Thomas Savery's steam engine (by adding a safety valve, and using an internal water jet to condense the steam in the displacement chambers) and a ventilator at the House of Commons. He was a prolific author and translator. *TIS

1932 Giuseppe Vitali (26 August 1875 – 29 February 1932) was an Italian mathematician who worked in several branches of mathematical analysis. He was the first to give an example of a non-measurable subset of real numbers, see Vitali set. His covering theorem is a fundamental result in measure theory. He also proved several theorems concerning convergence of sequences of measurable and holomorphic functions. Vitali convergence theorem generalizes Lebesgue's dominated convergence theorem. Another theorem bearing his name gives a sufficient condition for the uniform convergence of a sequence of holomorphic functions on an open domain D⊂ℂ to a holomorphic function on D. This result has been generalized to normal families of meromorphic functions, holomorphic functions of several complex variables, and so on. *Wik

1960 Teiji Takagi (21 April 1875 in Kazuya Village (near Gifu), Japan - 29 Feb 1960 in Tokyo, Japan) Takagi worked on class field theory, building on Heinrich Weber's work.*SAU

*VFR = V Frederick Rickey, USMA
*TIS= Today in Science History
*Wik = Wikipedia
*SAU=St Andrews Univ. Math History
*CHM=Computer History Museum
*FFF=Kane, Famous First Facts

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