## Friday, 8 April 2016

### On This Day in Math - April 8

For Bourbaki, Poincaré was the devil incarnate. For students of chaos and fractals, Poincaré is of course God on Earth.
~Marshall Stone
The 99th day of the year; there are 9 ways to express 99 as p + 2q, where p and q are prime. *Prime Curios (Students might wish to collect the whole set.)

If 99 divides some 4-digit number ABCD, then 99 also divides BCDA, CDAB, and DABC

There are 9 ways to express 99 as p + 2q, where p and q are prime.

99 is the largest number that is equal to the sum of its digits plus the product of its digits: 99 = 9 + 9 + 9 * 9

and 99 is the alphanumeric value of THIRTEEN *Number Gossip

992 = 9801 and 98 + 01 = 99 so it is a Kaprekar number, named after D. R. Kaprekar, an Indian recreational mathematician.

and David Marain ‏@dmarain recently reminded me 1/992 = 0.000102030405060708091011121314151617181920212223242526272... The question for students, It must be a repeating decimal, when does it start to repeat?

(and there was something about bottles of beer on the wall, but they don't seem to be there anymore. Maybe someone took them down...)

EVENTS
1610 On 8 April Kepler received a copy of Galileo’s Sidereus nuncius, and a few days later the Tuscan ambassador in Prague transmitted Galileo’s request for an opinion about the startling new telescopic discoveries. What a contrast with 1597, when Kepler, an unknown high-school teacher, had sought in vain Galileo’s reaction to his own book! Kepler was now the distinguished imperial mathematician, whose opinion mattered; he responded generously and quickly with a long letter of approval.
He promptly published his letter as dissertatio cum nuncio sidereo; in accepting the new observations with enthusiasm, he also reminded his readers of the earlier history of the telescope, his own work on the regular solids and on possible inhabitants of the moon, and his arguments against an infinite universe. A few months later, in the second of the only three known letters that Galileo wrote directly to Kepler, the Italian astronomer stated, “I thank you because you were the first one, and practically the only one, to have complete faith in my assertions.” *Encyclopedia.com
Thony Christie sent me some corrections on Kepler's introduction to this document:
"I quote from Mario Biagioli's Galileo Courtier:
Kepler's dedication of his Conversation with the Sidereal Messenger to Giuliano de' Medici (the Medici ambassador in Prague […]) offers interesting clues about the ways in which scientific networks were often embedded in noble patronage networks. Kepler acknowledged that he obtained a copy of the Sidereus from Giuliano de' Medici and that, when called to the Medici palace in Prague on April 13 [note date!], he was read Galileo's invitation to respond to the Sidereus, an invitation which was reinforced by the ambassador's "own exhortions". It is important to not that Kepler did not receive the letter from Galileo but that it was read to him by the Medici ambassador.

As you can see the copy of the Sidereus was sent by Galileo to Giuliano de' Medici who gave it to Kepler with what amounted to an order to write a criticism of it.
As always during their rather brief and fragmentary correspondence Galileo's behaviour towards Kepler was less than civil."
The University of Oklahoma has a digitized copy of Siderus Nunci with Galileo's signature on the title page.

1794 Joseph and Mary Priestley sailed from England on April 8, 1794 and after a long and rough passage, reached New York on June 4th. They joined their sons who had preceded them and who were engaged in purchasing land in Pennsylvania where they hoped to found a settlement of English immigrants. Although Priestley was fully informed about this venture and had decided to join them in living in the settlement when it was established, he was not one of the planners and, in fact, was not overly enthusiastic about it.
During the 10 days he was in New York, he was visited by Governor Clinton and other leading citizens and several public expressions of welcome were made. However some of the local clergy used the occasion of Trinity Sunday, June 15th, to preach against Priestley's religious views. They appeared to fear his influence.
On June 18th, Priestley went on to Philadelphia where he was also honored and invited to stay. However, he was determined to press on to Northumberland to join his sons. At this time he seemed to have some idea that he would be able to live in the country, in Northumberland, and make frequent trips into the city of Philadelphia. *Bill Weston, A Brief Biography of Joseph Priestley

1796 Guass enters in his diary a note that he has proved quadratic reciprocity. He will prove it again seven times in his life. Euler stated the theorem in 1783 without proof. Legendre was the first to publish a proof, but it was fallacious. Gauss became the first to publish a correct proof. The quadratic reciprocity theorem was Gauss's favorite theorem from number theory. He referred to it as the "aureum theorema" (golden theorem). The theorem says that if p and q are distinct odd primes, then the congruences x2=q (mod p) x2=p (mod q)are either both solvable, or both unsolvable except when they are both equal to 3 (mod 4). If they are both equal to 3 (mod 4) then one is solvable and the other is not *Mathworld, Wolfram
 *Genial Guass Gottingen

1799 The date of the still uninterpreted cryptic entry "REV. GALEN" in Gauss’s scientiﬁc diary. *VFR
There is a previous insertion that also remains uninterpreted.He entered "Vicimus GEGAN" for October 21, 1796.

1829 After having met Niels Henrik Abel in Berlin, August Leopold Crelle had published his work in his journal, and tried to help him acquire a University position. After Abel returned to Norway he lived on gifts and loans that he never repaid. On the 8th of April, Crelle wrote to tell him that the University of Berlin had offered him a Professorship, not knowing that Abel had died of tuberculosis two days earlier. *John Derbyshire, Unknown Quantity

1940 Samual F. B. Morse appears on a two cent stamp in the U.S.

1943 The Rockerfeller Foundation review announced that the “differential analyzer” at MIT was built at a cost of \$130,500.

1991 Java development begins in earnest:
On this day, Sun's Java team moves from Sun Microsystems to work in secret on its "Oak" development project (later re-named "Java.")*CHM

In 1947, the largest sunspot group recorded was observed on the sun's southern hemisphere. Its size was estimated at 7 billion square miles, or an area of 6100 millionths of the Sun's visible hemisphere. Sunspots are areas of somewhat cooler surface than the surrounding solar gases, and appear as dark spots on the solar surface. Astronomers measure the sizes of sunspots as millionth fractions of the Sun's visible area. Typically, a big sunspot measures 300 to 500 millionths, whereas the entire surface area of the Earth is only 169 millionths of the solar disk. *TIS

BIRTHS
1608 Honoré Fabri (8 April 1608 in Le Grand Abergement, Ain, France - 8 March 1688 in Rome, Italy)was a French Jesuit who worked on astronomy, physics and mathematics. His lectureson natural philosophy were published in 1646 as Tractatus physicus de motu locali. In this work he uses the parallelogram law for forces, correctly applying it to deduce the law of reflection and the motion of a body acted on simultaneously by two forces.*SAU (This seems to be one of the earlier statements of the law)

1732 David Rittenhouse (8 Apr 1732; died 26 Jun 1796 at age 64) American astronomer, instrument maker and inventor who was an early observer of the atmosphere of Venus. For observations for the transit of Venus on 3 Jun 1769, he constructed a high precision pendulum clock, an astronomical quadrant, an equal altitude instrument, and an astronomical transit. He was the first one in America to put spider web as cross-hairs in the focus of his telescope. He is generally credited with inventing the vernier compass and possibly the automatic needle lifter. He was professor of astronomy at the University of Pennsylvania. Benjamin Franklin consulted him on various occasions. For Thomas Jefferson he standardized the foot by pendulum measurements in a project to establish a decimal system of weights and measures.*TIS I recently discovered a blog about Rittenhouse at The Renaissance Mathematicus by the wonderful Thony Christie that tells a wonderful story about Rittenhouse I had never heard.  So as not to spoil it, I'll tease you with the last line: "the man who worked so hard to witness a once in a lifetime event and then missed it."

1779 Johann Salamo Christoph Schweigger (8 Apr 1779; 6 Sep 1857 at age 78)
German physicist who invented the galvanometer (1820), a device to measure the strength of an electric current. He developed the principle from Oersted's experiment (1819) which showed that current in a wire will deflect a compass needle. Schweigger realized that suggested a basic measuring instrument, since a stronger current would produce a larger deflection, and he increased the effect by winding the wire many times in a coil around the magnetic needle. He named this instrument a “galvanometer” in honour of Luigi Galvani, the professor who gave Volta the idea for the first battery. Thomas Seebeck (1770-1831) named the innovative coil, Schweigger's multiplier. It became the basis of moving coil instruments and loudspeakers. *TIS

1903 Marshall Harvey Stone (April 8, 1903, New York City – January 9, 1989, Madras, India) was an American mathematician who contributed to real analysis, functional analysis, and the study of Boolean algebras. He is best known for the Stone-Weierstrass theorem on uniform approximation of continuous functions by polynomials.
Stone was the son of Harlan Fiske Stone, who was the Chief Justice of the United States in 1941–1946. Marshall Stone’s family expected him to become a lawyer like his father, but he became enamored of mathematics while he was a Harvard University undergraduate. He completed a Harvard Ph.D. in 1926, with a thesis on differential equations that was supervised by George David Birkhoff. Between 1925 and 1937, he taught at Harvard, Yale University, and Columbia University. Stone was promoted to a full Professor at Harvard in 1937. Stone did an outstanding job of making the Chicago department eminent again, mainly by hiring Paul Halmos, André Weil, Saunders Mac Lane, Antoni Zygmund, and Shiing-Shen Chern.*Wik

1903 Aurel Friedrich Wintner (8 April 1903, Budapest, Hungary – 15 January 1958, Baltimore, Maryland, USA) was a mathematician noted for his research in mathematical analysis, number theory, differential equations and probability theory. He was one of the founders of probabilistic number theory. He received his Ph.D from the University of Leipzig in 1928 under the guidance of Leon Lichtenstein. *Wik
In 1929 he published the ﬁrst proofs of the basic facts in Hilbert space— the fundamental mathematical construct in the then-developing physical theory of quantum mechanics. [DSB 14, 454] *VFR

DEATHS
1461 Georg von Peurbach, (30 May 1423, 8 Apr 1461 at age 37) Austrian mathematician and astronomer who promoted the use of Arabic numerals (introduced 250 years earlier in place of Roman numerals), especially in a table of sines he calculated with unprecedented accuracy. He died before this project was finished, and his pupil, Regiomontanus continued it until his own death. Peurbach was a follower of Ptolomy's astronomy. He insisted on the solid reality of the crystal spheres of the planets, going somewhat further than in Ptolomy's writings. He calculated tables of eclipses in Tabulae Ecclipsium, observed Halley's comet in Jun 1456 and the lunar eclipse of 3 Sep 1457 from a site near Vienna. Peurbach wrote on astronomy, his observations and devised astronomical instruments.*TIS
Peuerbach's Theoricae Novae Planetarum, (New Theories of the Planets- below) was composed about 1454 was published in 1473 by Regiomontanus' printing press in Nuremburg. While the book was involved in attempting a technical resolution of the theories of Eudoxus and Ptolemy, Peuerbach claimed that the movement of the planets was determined by the Sun, and this has been seen as a step towards the Copernican theory. This book was read by Copernicus, Galileo and Kepler and became the standard astronomical text well into the seventeenth century.

1913 Julius (Gyula )König (16 December 1849 – 8 April 1913) was a Hungarian mathematician. His mathematical publications in foreign languages appeared under the name Julius König. His son Dénes Kőnig is the famous graph theorist. Kőnig worked in many mathematical fields. His work on polynomial ideals, discriminants and elimination theory can be considered as a link between Leopold Kronecker and David Hilbert as well as Emmy Noether. Later on his ideas were simplified considerably, to the extent that today they are only of historical interest.
Kőnig already considered material influences on scientific thinking and the mechanisms which stand behind thinking.*Wik One of his early ideas was a paper of 1872 which looked at intuitive ways to prove the consistency of non-Euclidean geometries. He published many research papers in analysis, but his greatest significance in this area comes from the excellent textbooks which he wrote on the topic.*VFR

1919 Roland Baron von Eötvös (27 Jul 1848, 8 Apr 1919 at age 70)was a Hungarian physicist who studied at Heidelberg where he was taught by Kirchhoff, Helmholtz and Bunsen. Eötvös introduced the concept of molecular surface tension and published on capillarity (1876-86). For the rest of his life he concentrated on study of the Earth's gravitational field. He developed the Eötvös torsion balance, long unsurpassed in precision, which gave experimental proof that inertial mass and gravitational mass, to a high degree of accuracy, are equivalent - which later was a major principle of Albert Einstein.*TIS

1925 Frank Stephen Baldwin (10 Apr 1838, 8 Apr 1925 at age 87) American inventor best-known for his development of the Monroe calculator. Baldwin began in 1870 to experiment with the design of mechanical calculators. The device was patented and marketed in 1875 (No. 159,244). The improved 1875 machine initiated the development of the second fundamental principle in rotary four-rules calculators which became known as "The Baldwin Principle." Baldwin developed many more calculators during his life. His last model was the forerunner of the Monroe machine. The Monroe Calculator Company was formed in 1912 and was a pioneer in electric adding machines. The Monroe Calculator was used extensively in the 1930's. *TIS

1968 Harold Delos Babcock (24 Jan 1882, 8 Apr 1968 at age 86) American astronomer who with his son, Horace, invented the solar magnetograph (1951), for detailed observation of the Sun's magnetic field. With their magnetograph the Babcocks measured the distribution of magnetic fields over the solar surface to unprecedented precision and discovered magnetically variable stars. In 1959 Harold Babcock announced that the Sun reverses its magnetic polarity periodically. Babcock's precise laboratory studies of atomic spectra allowed others to identify the first "forbidden" lines in the laboratory and to discover the rare isotopes of oxygen. With C.E. St. John he greatly improved the precision of the wavelengths of some 22,000 lines in the solar spectrum, referring them to newly-determined standards. *TIS

2005, Douglas Geoffrey Northcott, FRS (31 December 1916, London – 8 April 2005) was a British mathematician who worked on ideal theory.
... while a prisoner of war, ... Northcott was able to think about mathematics; indeed, thinking about mathematics probably helped him survive his war experiences. Sometimes he tried to reconstruct proofs of results that he had learnt as a student; at other; he attempted to build up a theory of integration for functions with values in a Banach space. He recorded his results about this theory in a notebook that he kept in his gas-mask case. On one occasion his gas-mask was stolen and he never saw it again, and so he had to start again. His second notebook survived the war and, in due course, provided material for his Ph.D. thesis and his fellowship dissertation. *SAU

2008 Graham Higman (19 Jan 1917 in Louth, Lincolnshire, England - 8 April 2008 in Oxford, England) is known for his outstanding work in all aspects of the theory of groups. He published on units in group rings, the subject of his doctoral thesis, in 1940 then there was a break in his publication record during the time he worked in the Meteorological Office. His 1948 papers are on somewhat different topics, being on topological spaces and linkages. They show the influences of Henry Whitehead and, to a lesser extent, Max Newman. *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