Saturday 9 September 2023

On This Day in Math - September 9

There are in this world optimists who feel that any symbol that starts off with an integral sign must necessarily denote something that will have every property that they should like an integral to possess. This of course is quite annoying to us rigorous mathematicians; what is even more annoying is that by doing so they often come up with the right answer.
~McShane, E. J.

The 252nd day of the year; 252 is the smallest number which is the product of two distinct numbers that are reverses of each other: 252 = 12*21 *Number Gossip
(and the next would be?)

252 is a palindrome in base ten, and also in base five 20025 (How many three digit numbers are (non-trivial) palindromes in base ten and one other base less than ten)

If you flip a coin 10 times in a row, there are exactly 252 ways in which it can turn out that you get exactly 5 heads and 5 tails. That is, \( 252 = \binom{10}{5} = \frac{10*9*8*7*6}{5*4*3*2*1} \)

1508 What was probably the first Dutch language arithmetic was published in Brussels by Thomas van der Noot. The Way to Learn to Reckon According to the Right Art of Algorismi, in whole and broken numbers. In 1537 much of the book would be copied into English to become the earliest known arithmetic in that language, An Introduction for to learne to reckon with the pen or with the counters. John Herford published the book at his presses in St. Albens. After introducing the terms numerator and denominator, he reverts to the Dutch terms "teller" (counter)  and and used number in place of "noemer" (noemer rekenkunde is the more complete term, I think. any help?) ; both terms of which are/were, at the least, unusual in English. *P. Bockstaele, Notes on the First Arithmetics Printed in Dutch and English, Isis 51(1960) pg 315

Van der Noot is also credited with writing and publishing the first cookbook in Dutch.

At Thrift Books website  I found an add for a copy of Herford's arithmetic with more detail about the history of the first English arithmetic:
"This book is a facsimile of the second edition of the earliest printed work in English entirely devoted to Arithmetic. The author is unknown, although the book comprises a compilation of material from two other works, one Dutch and one French, translated into English and with the addition of some new material. It was imprinted in Aldersgate Street, London by Nicolas Bourman in 1539. The first edition was produced two years earlier by John Herford, whose press was located in the abbey of St Albans and who printed under the patronage of the abbot, Richard Boreman. It was long thought that no copies of the first edition were extant, with the exception of a small fragment in the British Library. However, in 2005 a complete text turned up at a Sotheby's auction in New Bond Street, London. This rare survivor sold under the hammer to the British Library for the staggering sum of 97,500. Among the problems posed in An Introduction is the "rule and question of a catte". This concerns a cat which climbs a 300 foot high tree, ascending 17 feet each day but descending again 12 feet each night. The problem to be solved is - how long does the cat take to reach the top? The answer given is 60 days, which of course is quite wrong. Another problem concerns "The rule and question of zaracins, for to cast them within the see". Given that on a sinking ship there are thirty merchants, 15 of whom are Christian and the other 15 Saracens, half of whom must be thrown overboard to save the ship, how should they be ordered so that counting off by nines will always result in a Saracen being sacrificed and never a Christian? Not a problem that fits easily with current ideas about political correctness. Then there is "a dronkart who drynketh a barell of bere in 14 days", but "when his wife drinketh with him" they empty it in 10 days How quickly, the reader is asked, could his wife drink it alone? These are just a few of the beguiling puzzles set within the pages of this fascinating book. "

1699 Advertisement for Mathematical training, with lodging from London Paper,

*Flying Post (London, England), September 9, 1699 - September 12, 1699; Issue 677.

1713 The St. Petersburg Paradox is born?: Nicolas Bernoulli to Montmort. Basel, 9 September, 1713.
Printed in Essay d'Analysis, p. 402
THE FOURTH PROBLEM SAID: A promises to give an écu to B, if with an ordinary die he achieves 6 points on the first throw, two écus if he achieves 6 on the second throw, 3 écus if he achieves this point on the third throw, 4 écus if he achieves it on the fourth and thus consecutively; one asks what is the expectation of B? Fifth Problem. One asks the same thing if A promises to B to give him some écus in this progression 1, 2, 4, 8, 16 etc. or 1, 3, 9, 27 etc. or 1, 4, 9, 16, 25 etc. or 1, 8, 27, 64 instead of 1, 2, 3, 4, 5 etc. as beforehand. Although for the most part these problems are not difficult, you will find however something most curious.
The St. Petersburg Paradox is based on a simple coin flip game with an infinite expected winnings. The paradox arises by the fact that no rational human would risk a large finite amount to play the game, even though the expected value implies that a rational person should risk any finite amount to play it. Here I describe the St. Petersburg Paradox and give some proposed methods of resolving it.

1751 Euler presents his famous “Gem”; Vertices + Faces -2 = Edges in two papers Euler presented several results relating the number of plane angles of a solid to the number of faces, edges, and vertices (he referred to “solid angles”). Euler also classified polyhedra by the number of solid angles they had. According to C. G. J. Jacobi, a treatise with this title was read to the Berlin Academy on November 26, 1750. The proofs were contained in a second paper. According to C. G. J. Jacobi, it might have been read to the Berlin Academy on September 9, 1751. According to the records there, it was presented to the St. Petersburg Academy on April 6, 1752.*VFR
I highly recommend Dave Richeson's wonderful Euler's Gem for any teacher or student.

In 1839, John Herschel made the first (remaining) photograph on glass plate. The image he captured was of the 40-foot, 48" aperture telescope used by his father William Herschel, in Slough, England. It had sat decades without use, and was dismantled a short time later. Twenty years earlier, in 1819, Herschel published the results of his experiments with silver and salts. A chance comment about Daguerre's experiments in a letter to his wife on 22 Jan 1839 from a friend prompted John into new activity, and within a few days, he had prepared some photographs. In papers he published in 1840-42, he coined the new words "emulsion", "positive" and "negative" and reinforced Stenger's earlier introduction of the word "photography."*TIS

1892 Jupiter's moon Amalthea was discovered by E.E. Barnard. It was the last moon discovered by observation. *David Dickinson ‏@Astroguyz
He found it using the 36 inch (91 cm) refractor telescope at Lick Observatory. It was the first new satellite of Jupiter since Galileo Galilei's discovery of the Galilean satellites in 1610 *Wik

1945 First computer “bug” logged at 1545 hrs. Grace Hopper was running the computer at the time and there was a failure. When she investigated she found that a moth had gotten into the machinery and caused the problem. She removed it and taped it into the log book of the computer. Thus a bit of computer jargon was born. *VFR (the term "bug" in the meaning of technical error dates back at least to 1878 and Thomas Edison , and "debugging" seems to have been used as a term in aeronautics before entering the world of computers. Indeed, in an interview Grace Hopper remarked that she was not coining the term. The moth fit the already existing terminology, so it was saved.)

1967 The Soviet Union issued a postage stamp showing checker players with part of a board in the background. Although more than 50 stamps have been issued on chess, this was the first on checkers. [Journal of Recreational Mathematics, 2(1969), 50] *VFR That same year, Andris Andreiko challenged world champion Iser Koeperman for the checkers World Champion Title but Koeperman successfully retained his title. As a result of this competition between the two Soviet contenders, the Russian government issued postage stamps as commemorative of the World Title match.*

1974 "1974 Albert Ghiorso & Glenn T. Seaborg announced the discovery of seaborgium" * chemheritage@ChemHeritage Seaborgium is the first element to be named after a person who was alive when the name was announced. The second element to be so named is oganesson, in 2016, after Yuri Oganessian.
 He influenced the naming of so many elements that with the announcement of seaborgium, it was noted in Discover magazine's review of the year in science that he could receive a letter addressed in chemical elements: seaborgium, lawrencium (for the Lawrence Berkeley Laboratory where he worked), berkelium, californium, americium. *Wik
Seaborg in 1964, *Wik

In 2000, the hole in the ozone layer over Antarctica stretched over a populated city for the first time, after ballooning to a new record size. For two days, Sept. 9-10, the hole extended over the southern Chile city of Punta Arenas, exposing residents to very high levels of ultra violet radiation. Too much UV radiation can cause skin cancer and destroy tiny plants at the beginning of the food chain. Previously, the hole had only opened over Antarctica and the surrounding ocean. Data from the U.S. space agency NASA showed the hole covered 11.4 million square miles - an area more than three times the size of the United States. *TIS
Image:   The top image shows the average total column ozone values over Antarctica for September 2000. In October, however (bottom image), the hole shrank dramatically, much more quickly than usual. By the end of October, the hole was only one-third of it’s previous size. 


1737 "Luigi Galvani, (9 September 1737 – 4 December 1798)) was an Italian physician. In the 1770s, Galvani, a professor at Bologna, began experimenting with electricity, searching in particular for electrical effects in living tissue. For a tissue source, he settled on frogs, or portions of frogs, and Galvani found that when an electrical generator was operating nearby, or there was an electrical storm, frog torsos with metallic hooks inserted into their spines would twitch. The big surprise came when he inserted a brass hook into a frog trunk and then laid the frog on an iron grate. As soon as the brass touched the iron, the legs contracted violently, and continued to do so whenever the brass hook touched the iron grate. Galvani had, unknowingly, invented a battery, which is nothing more than two different metals separated by a liquid electrolyte (like frog flesh). But Galvani didn't see it that way--he thought he had discovered a new kind of electricity, animal electricity, that was produced only by living things. It was Alessandro Volta who figured out what was going on with the frogs, and who in 1800 made a battery with copper and zinc and salt water--and no frog."  *Linda Hall org


1789 William Cranch Bond (9 Sep 1789; 29 Jan 1859)American astronomer who, with his son, George Phillips Bond (1825-65), discovered Hyperion, the eighth satellite of Saturn, and an inner ring called Ring C, or the Crepe Ring. While W.C. Bond was a young clockmaker in Boston, he spent his free time in the amateur observatory he built in part of his home. In 1815 he was sent by Harvard College to Europe to visit existing observatories and gather data preliminary to the building of an observatory at Harvard. In 1839 the observatory was founded. He supervised its construction, then became its first director. Together with his son he developed the chronograph for automatically recording the position of stars. They also took some of the first recognizable photographs of celestial objects.*TIS  
Hyperion is distinguished by its irregular shape, its chaotic rotation, and its unexplained sponge-like appearance. It was the first non-round moon to be discovered.

1852 John Henry Poynting (9 Sep 1852; 30 Mar 1914)British physicist who introduced a theorem (1884-85) that assigns a value to the rate of flow of electromagnetic energy known as the Poynting vector, introduced in his paper On the Transfer of Energy in the Electromagnetic Field (1884). In this he showed that the flow of energy at a point can be expressed by a simple formula in terms of the electric and magnetic forces at that point. He determined the mean density of the Earth (1891) and made a determination of the gravitational constant (1893) using accurate torsion balances. He was also the first to suggest, in 1903, the existence of the effect of radiation from the Sun that causes smaller particles in orbit about the Sun to spiral close and eventually plunge in.*TIS

1860 Frank Morley (September 9, 1860 – October 17, 1937) wrote mainly on geometry but also on algebra.*SAU Morley is remembered most today for a singular theorem which bears his name in recreational
literature. Simply stated, Morley's Theorem says that if the angles at the vertices of any triangle (A, B, and C in the figure) are trisected, then the points where the trisectors from adjacent vertices intersect (D, E, and F) will form an equilateral triangle.
In 1899 he observed the relationship described above, but could find no proof. It spread from discussions with his friends to become an item of mathematical gossip. Finally in 1909 a trigonometric solution was discovered by M. Satyanarayana. Later an elementary proof was developed. Today the preferred proof is to begin with the result and work backward. Start with an equilateral triangle and show that the vertices are the intersection of the trisectors of a triangle with any given set of angles. For those interested in seeing the proof, check Coxeter's Introduction to Geometry, Vol 2, pages 24-25.  Find more about this unusual man here.

1908 Mary Golda Ross (August 9, 1908 – April 29, 2008) was the first known Native American female engineer, and the first female engineer in the history of Lockheed. She was one of the 40 founding engineers of the renowned and highly secretive Skunk Works project at Lockheed Corporation. She worked at Lockheed from 1942 until her retirement in 1973, where she was best remembered for her work on aerospace design – including the Agena Rocket program – as well as numerous "design concepts for interplanetary space travel, crewed and uncrewed Earth-orbiting flights, the earliest studies of orbiting satellites for both defense and civilian purposes." In 2018, she was chosen to be depicted on the 2019 Native American $1 Coin by the U.S. Mint celebrating American Indians in the space program. *Wik

1910 Bjorn Kjellstrom (9 Sep 1910; 2 Sep 1995) Swedish inventor of the Silva compass which featured a rotating compass dial, and a transparent protractor base plate. As founder of Silva, Inc. in North America, Kjellstrom helped introduce the orienteering sport to the U.S. in the 1940s, in part as a way to promote his product. He wrote "Be Expert with Map and Compass", considered to be the "bible of orienteering." *TIS

1914 Marjorie Lee Browne (September 9, 1914 – October 19, 1979) was a notable mathematics educator, the second African-American woman to receive a doctoral degree in the U.S., and one of the first black women to receive a doctorate in mathematics in the U.S. Browne's work on classical groups demonstrated simple proofs of important topological properties of and relations between classical groups. Her work in general focused on linear and matrix algebra.
Browne saw the importance of computer science early on, writing a $60,000 grant to IBM to bring a computer to NCCU in 1960 -- one of the first computers in academic computing, and probably the first at a historically black school.
Throughout her career, Browne worked to help gifted mathematics students, educating them and offering them financial support to pursue higher education. Notable students included Joseph Battle, William Fletcher, Asamoah Nkwanta, and Nathan Simms. She established summer institutes to provide continuing education in mathematics for high school teachers.*Wik

Dennis MacAlistair Ritchie (September 9, 1941; found dead October 12, 2011), was an American computer scientist who "helped shape the digital era." He created the C programming language and, with long-time colleague Ken Thompson, the UNIX operating system. Ritchie and Thompson received the Turing Award from the ACM in 1983, the Hamming Medal from the IEEE in 1990 and the National Medal of Technology from President Clinton in 1999. Ritchie was the head of Lucent Technologies System Software Research Department when he retired in 2007. He was the 'R' in K&R C and commonly known by his username dmr. *Wik


1883 Victor Alexandre Puiseux  ​
(16 April 1820, 9 September 1883) was a French mathematician and astronomer. Puiseux series are named after him, as is in part the Bertrand–Diquet–Puiseux theorem. Excelling in mathematical analysis, he introduced new methods in his account of algebraic functions, and by his contributions to celestial mechanics advanced knowledge in that direction. In 1871, he was unanimously elected to the French Academy.*Wik He worked on elliptic functions and studied computational methods in astronomy.*SAU

1885 Claude Bouquet (7 Sept 1819 in Morteau, Doubs, France - 9 Sept 1885 in Paris, France) was a French mathematician who worked on differential geometry and on series expansions of functions and elliptic functions.*SAU

1973 Giovanni Ricci (17 Aug 1904 , 9 Sept 1973) Italian mathematician who is esteemed as an outstanding teacher. His major mathematical input was on distribution of primes.

2000 Herbert Friedman (21 Jun 1916, 9 Sep 2000)American astronomer who made made seminal contributions to the study of solar radiation. He joined the Naval Research Laboratory in 1940 and developed defense-related radiation detection devices during WW II. In 1949, he obtained the first scientific proof that X rays emanate from the sun. When he directed the firing into space of a V-2 rocket carrying a detecting instrument. Through rocket astronomy, he also produced the first ultraviolet map of celestial bodies, and gathered information for the theory that stars are being continuously formed, on space radiation affecting Earth and on the nature of gases in space. He also made fundamental advances in the application of x rays to material analysis. *TIS

2003 Edward Teller(15 Jan 1908, 9 Sep 2003) Hungarian-born American nuclear physicist who participated in the production of the first atomic bomb (1945) and who led the development of the world's first thermonuclear weapon, the hydrogen bomb. After studying in Germany he left in 1933, going first to London and then to Washington, DC. He worked on the first atomic reactor, and later working on the first fission bombs during WW II at Los Alamos. Subsequently, he made a significant contribution to the development of the fusion bomb. His work led to the detonation of the first hydrogen bomb (1952). He is sometimes known as "the father of the H-bomb." Teller's unfavorable evidence in the Robert Oppenheimer security-clearance hearing lost him some respect amongst scientists*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

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