Tuesday 3 April 2018

On This Day in Math - April 3

Alberti's Statue in the courtyard of the Uffizi Gallery, Florence; *Wik

Knowing what is big and what is small is more important than being able to solve partial differential equations.
~Stan Ulam

The 93rd day of the year; The first 93 digits of 93! form a prime number. *Prime Curios ( Can students find a smaller number n for which the first n digits of n! form a prime? Send results to me.)
93! = 1156772507081641574759205162306240436214753229576413535186142281213246807121467
315215203289516844845303838996289 ...

93 is the sum of three distinct squares, 93 = 22 + 52+ 82 )
and six consecutive integers 93= 13 + 14 + 15 + 16 + 17 + 18

There are 93 five-digit prime palindromes. The smallest (I think) is 10301

A potato can be cut into 93 pieces with just nine straight cuts.

and 93 in base 10 is 333 in base 5


1736 Euler replied to Ehler on Konigsberg Bridge Challenge, "Not a Mathematical Problem..."
... Thus you see, most noble Sir, how this type of solution bears little relationship to mathematics, and I do not understand why you expect a mathematician to produce it, rather than anyone else, for the solution is based on reason alone, and its discovery does not depend on any mathematical principle. Because of this, I do not know why even questions which bear so little relationship to mathematics are solved more quickly by mathematicians than by others. In the meantime, most noble Sir, you have assigned this question to the geometry of position, but I am ignorant as to what this new discipline involves, and as to which types of problem Leibniz and Wolff expected to see expressed in this way ...
(See March 9th for Ehler's challenge to Euler) *Brian Hopkins, Robin Wilson; The Truth About Konigsberg

- See more at: http://www.maa.org/programs/maa-awards/writing-awards/the-truth-about-konigsberg#sthash.c6jO9L76.dpuf

1753 Goldbach wrote Euler with a conjecture that every odd number greater than 3 is the sum of an odd number and twice a square (he allowed 02). Euler would reply on Dec 16 that it was true for the first 1000 odd numbers, and then again on April 3, 1753, to confirm it for the first 2500. A hundred years later, German mathematician Moritz Stern found two contradictions, 5777 and 5993. The story appears in Alfred S. Posamentier's Magnificent Mistakes in Mathematics, (but gloriously, has a mistake for the date, using 1852, but such a wonderful book can forgive a print error.)

1763 Easter Saturday 1763, Lalande recorded that the Astronomer Royal Nathaniel Bliss said ‘that Mr Lemonnier attached the wire to his quadrant with wax from his ears, that he went to Oxford with his sword broken, and that his observations agree less well with those of Mr Bevis than those of Caille.’ Pierre Charles Lemonnier or Le Monnier was a talented French astronomer 17 years Lalande’s senior who had a penchant for British instruments and astronomical methods and was a member of the Royal Society and the French Academy of Sciences. *Royal Museum Greenwich blog "MEOW!"

1769 A letter from Mr. Richard Price, F. R. S. to Benjamin Franklin, Esq; LL.D. discusses De Moivre's work on Population and survival rates. The paper runs to 38 pages. "Observations on the Expectations of Lives, the Increase of Mankind, the Influence of Great Towns on Population, and Particularly the State of London with Respect to Healthfulness and Number of Inhabitants." *Phil. Trans. January 1, 1769 59:89-125;

In 1934, a British patent application for the first catseye road marker was recorded for inventor Percy Shaw (1889-1975), described as "Improvements relating to Blocks for Road Surface." These are the familiar reflectors which mark the lines that are lit up at night by the lights of passing vehicles. The raised surface in which the reflectors are mounted have a construction that "will yield when traveled over by a vehicle wheel and sink to the level of the road surface" such as a resilient white rubber cushion mounted in a metal holder sunk below the road surface. The patent No. 436,290 was accepted 3 Oct 1935. A revised design was patented the following year as No. 457,536. Shaw started Reflecting Roadstuds Ltd. to manufacture them. *TIS (While this is of little mathematical interest, before I learned what the term meant, I regularly wondered about a sign I passed on the way from Stoke Ferry to King's Lynn in Norfolk Shire which said, "Cat's Eyes Removed Ahead."

1964 It is reported in the New York Times that the casinos in Las Vegas have changed their rules in blackjack so as to defeat the winning strategy devised by Edward O. Thorp. See 27 March 1964. *VFR
Thorp is described as an American mathematics professor, author, hedge fund manager, and blackjack player. He was a pioneer in modern applications of probability theory, including the harnessing of very small correlations for reliable financial gain.*Wik

1983 The Republic of China (Taiwan) marks the 400th anniversary of the arrival of Father Matteo Ricci (1552–1610) in China with a pair of stamps. [Scott #2359–2360] *VFR

2016 First day of the major league baseball season. The exact width of home plate is irrational: 12 times the square root of two.
History: The plate was originally a circle of diameter one, then a square of the same size(!), which, by mistake was a one-by-one square. Then the corners were filled in to make the current pentagonal plate. *VFR Home plate is an irregular pentagon. The front is 17 inches wide, faces the pitcher, and defines the width of the strike zone. Then parallel sides 8.5 inches long connect to the foul lines. Finally 12 inch sides run down the foul lines, connecting where the foul lines meet.
It can be thought of as a 17 inch square with the parts that would be in foul territory removed. The figure described in the official rules of MLB, as well as above, is technically impossible. One of two things must be true to make it possible:

the parallel sides of 8.5" are in reality approximately 8.5295" (the square root of 71.75)
the 12" sides that run along the foul lines are approximately 12.0208" (square root of 144.5)
The latter is more likely the case, as it would produce the angle measurements of 90º at the base and rear point and 135º at the sides.

Rick Pearce ‏@MrPearceMath has written to object: "The width is 17", not irrational. Other 4 sides are. But you're right about impossibility of defn." I'm not sure the difference of 17 and 12 square root (2) is a miniscule .0295" (Will wander down to nearest ball park with steel tape in hand, this challenge will not stand!)

1529 – Michael Neander (April 3, 1529 – October 23, 1581) German mathematician and astronomer was born in Joachimsthal, Bohemia, and was educated at the University of Wittenberg, receiving his B.A. in 1549 and M.A. in 1550.
From 1551 until 1561 he taught mathematics and astronomy in Jena, Germany. He became a professor in 1558 when the school where he taught became a university. From 1560 until his death he was a professor of medicine at the University of Jena. He died in Jena, Germany. The crater Neander on the Moon is named after him. *Wik

1835 John Howard Van Amringe (3 April 1835 in Philadelphia, Pennsylvania, USA - 10 Sept 1915 in Morristown, New Jersey, USA) was a U.S. educator and mathematician. He was born in Philadelphia, and graduated from Columbia in 1860. Thereafter, he taught mathematics at Columbia, holding a professorship from 1865 to 1910 when he retired. Van Amringe was also the first Dean of Columbia College, the university's undergraduate school of arts and sciences, which he defended from dismemberment and incorporation into the larger university. During his long presence at the school, he made many addresses and enjoyed unrivaled popularity. He is memorialized with a bust enshrined in a column-supported cupola on "Van Am Quad" in the southeastern portion of the campus, surrounded by three College dormitories (John Jay Hall, Hartley Hall, and Wallach Hall) and by the main College academic building, Hamilton Hall. He is buried in Greenwood Cemetery in Brooklyn.
Van Amringe served as the first president of the American Mathematical Society between 1888 and 1890.
In honor of Van Amringe, Columbia University's Department of Mathematics has presented a "Van Amringe Mathematical Prize" each year (since 1911) to the best freshman or sophomore mathematics student, based on a very challenging examination. *Wik

1842 Hermann Karl Vogel (3 Apr 1842; died 13 Aug 1907 at age 65) German astronomer who discovered spectroscopic binaries (double-star systems that are too close for the individual stars to be discerned by any telescope but, through the analysis of their light, have been found to be two individual stars rapidly revolving around one another). He pioneered the study of light from distant stars, and introduced the use of photography in this field.*TIS

1859 Karl Heun (3 April 1859 in Wiesbaden, Germany - 10 Jan 1929 in Karlsruhe, Germany) was a German mathematician best known for the Heun differential equation which generalizes the hypergeometric differential equation. *SAU

1892 Hans Rademacher (3 April 1892 in Wandsbeck (part of Hamburg), Schleswig-Holstein, Germany - 7 Feb 1969 in Haverford, Pennsylvania, USA) It was philosophy that he intended to take as his main university subject when he entered the university of Göttingen in 1911, but he was persuaded to study mathematics by Courant after having enjoyed the excellent mathematics teaching of Hecke and Weyl. He is remembered for the system of orthogonal functions (now known as Rademacher functions) which he introduced in a paper published in 1922. Berndt writes "Since its discovery, Rademacher's orthonormal system has been utilised in many instances in several areas of analysis." Rademacher's early arithmetical work dealt with applications of Brun's sieve method and with the Goldbach problem in algebraic number fields. About 1928 he began research on the topics for which he is best known among mathematicians today, namely his work in connection with questions concerning modular forms and analytic number theory. Perhaps his most famous result, obtained in 1936 when he was in the United States, is his proof of the asymptotic formula for the growth of the partition function (the number of representations of a number as a sum of natural numbers). This answered questions of Leibniz and Euler and followed results obtained by Hardy and Ramanujan. Rademacher also wrote important papers on Dedekind sums and investigated many problems relating to algebraic number fields. *SAU

1900 Albert Edward Ingham (3 April 1900–6 September 1967) was an English mathematician. His book On the distribution of prime numbers published in 1932 was his only book and it is a classic. Many of the ideas here, as in other work of Ingham's, came from the joint work undertaken by Harald Bohr and Littlewood.

1907 Mark Grigorievich Krein (3 April 1907 – 17 October 1989) was a Soviet Jewish mathematician, one of the major figures of the Soviet school of functional analysis. He is known for works in operator theory (in close connection with concrete problems coming from mathematical physics), the problem of moments, classical analysis and representation theory.
He was born in Kiev, leaving home at age 17 to go to Odessa. He had a difficult academic career, not completing his first degree and constantly being troubled by anti-Semitic discrimination. His supervisor was Nikolai Chebotaryov.
He was awarded the Wolf Prize in Mathematics in 1982 (jointly with Hassler Whitney), but was not allowed to attend the ceremony.
He died in Odessa.
On 14 January 2008, the memorial plaque of Mark Krein was unveiled on the main administration building of I.I. Mechnikov Odessa National University. *Wik


1472 Leone Battista Alberti (18 Feb 1404 in Genoa, French Empire (now Italy)- 3 April 1472 in Rome, Papal States (now Italy) The date of his death is given by Wikipedia as April 20, 1472) Italian mathematician who wrote the first general treatise on the laws of perspective and also wrote a book on cryptography containing the first example of a frequency table. Alberti died in Rome, but his ashes were brought from Rome and put in the family vault in the Santa Croce Cathedral (where Galileo is buried).

1717 Jacques Ozanam (16 June 1640, Sainte-Olive, Ain - 3 April 1718, Paris)In 1670, he published trigonometric and logarithmic tables more accurate than the then existing ones of Ulacq, Pitiscus, and Briggs. An act of kindness in lending money to two strangers secured for him the notice of M. d'Aguesseau, father of the chancellor, and an invitation to settle in Paris. There he enjoyed prosperity and contentment for many years. He married, had a large family, and derived an ample income from teaching mathematics to private pupils, chiefly foreigners. *Wik
He is remembered for his book on mathematical recreations. “He was wont to say that it was the business of the Sorbonne doctors to discuss, of the pope to decide, and of a mathematician to go straight to heaven in a perpendicular line.” [DSB 10, 264]. *VFR
On the flyleaf of J. E. Hofmann's copy of the 1696 edition of Ozanam's Recreations is a pencil portrait labelled Ozanam -- the only one I know of. This copy is at the Institut für Geschichte der Naturwissenschaft in Munich. *David Singmaster

1817 Friedrich Ludwig Wachter (1792–1817), a student of Gauss, called the geometry obtained by denying Euclid’s parallel postulate “anti-Euclidean geometry”. Had he returned from his cus­tomary evening walk on this date he might now be known as one of the founders of non-Euclidean geometry. [G. E. Martin, Foundations of Geometry and the Non-Euclidean Plane, p. 306] *VFR
(… In a letter to Gauss in 1816 he states that as a circle’s radius increases toward infinity as being identical to a plane, “even in the case of the fifth postulate being false, there would be geometry on this surface identical with that of the ordinary plane.)

 Chladni pattern on plate

1827 Ernst Florenz Friedrich Chladni, physicist and amateur musician, died. He is best remembered for the spectacular symmetrical patterns formed when a sand covered plate is vibrated with a violin bow. He was a Professor of Physics in Breslau when he developed Chladni figures c1800. He came to Paris in 1808 to present his work at the Institut and Laplace had him give a two hour demonstration to Napoleon, who gave him 6000 francs.
German physicist who is known as the “father of acoustics” for his mathematical investigations of sound waves. Chladni figures, seen when thin plates covered in sand at set in vibration, are complex patterns of vibration with nodal lines that remain stationary and retain sand. He demonstrated these to an audience of scientists in Paris in 1809. He measured the speed of sound in various gases by determining the pitch of the note of an organ pipe filled with different gases. To determine the speed of sound in solids, Chladni used analysis of the nodal pattern in standing-wave vibrations in long rods. He performed on the euphonium, an instrument he invented, made of glass and steel bars vibrated by rubbing with a moistened finger. He also investigated meteorites. *TIS

1900 Joseph-Louis-François Bertrand (11 Mar 1822; 5 Apr 1900 at age 78) was a French mathematician and educator and educator remembered for his elegant applications of differential equations to analytical mechanics, particularly in thermodynamics, and for his work on statistical probability and the theory of curves and surfaces. In 1845 Bertrand conjectured that there is at least one prime between n and (2n-2) for every n greater than 3, as proved five years later by Chebyshev. In 1855 he translated Gauss's work on the theory of errors and the method of least squares into French. He wrote a number of notes on the reduction of data from observations. *TIS At age 11 he started to attend classes at the Ecole Polytechnique, where his Uncle Duhamel was a well-known professor of mathematics. At 17 he received his doctor of science degree. *VFR

1998 – Mary Cartwright, English mathematician (b. 1900) G.H. Hardy was her Doctorial advisor, She did early investigations with Littlewood of fine structure of solutions to some types of differential equations, today seen to be a typical instance of the butterfly effect. She was the first woman:

to receive the Sylvester Medal
to serve on the Council of the Royal Society
to be President of the London Mathematical Society (in 1961–62)

She also received the De Morgan Medal of the Society in 1968. In 1969 she received the distinction of being honoured by the Queen, becoming Dame Mary Cartwright, Dame Commander of the Order of the British Empire.

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

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