**To throw in a fair game at Hazards only three-spots, when something great is at stake, or some business is the hazard, is a natural occurrence and deserves to be so deemed; and even when they come up the same way for a second time if the throw be repeated. If the third and fourth plays are the same, surely there is occasion for suspicion on the part of a prudent man.**

~Girolamo Cardano

The 264th day of the year; 264 = 2

^{3}x3x11 is a harshad number (a number divisible by the sum of its digits). The word "Harshad" comes from the Sanskrit harṣa (joy) + da (give), meaning joy-giver. The numbers were defined and named by the famous Indian Mathematician D. R. Kaprekar.

**EVENTS**

**1781**Writing to his friend and mentor d’Alembert, Lagrange expressed concern that mathematics was reaching its creative end. “It seems,” he wrote, “that the mine is almost too deep already, and unless new seams are discovered, it will be necessary to abandon it sooner or later. Physics and chemistry now offer riches that are more brilliant and easier to exploit.” *Amir R. Alexander , Tragic Mathematics, Isis, Vol. 97, No. 4, December 2006

**1784**The nation's first daily newspaper, the Pennsylvania Packet and Daily Advertiser, began publication on September 21, 1784. Many independent newspapers ran before that on a weekly or monthly basis. America's first independent newspaper, the New England Courant, was published by Benjamin Franklin's older brother in 1721. By the start of the Revolutionary War in 1775, there were 37 independent newspapers to keep the colonists informed. *Libray of Congress

**1984**Science reported (pp. 1379-1380) that Narendra Karmarkar of AT & T Bell Labs found a practical polynomial-time algorithm that is far faster than the simplex algorithm for linear programming problems. [Mathematics Magazine 58 (1985), p. 53]. *VFR

**BIRTHS**

**1623 Stefano degli Angeli**(21 Sept 1623 , 11 Oct 1697) His many mathematical works were on infinitesimals and he used them to study spirals, parabolas and hyperbolas. While in Venice he published De infinitorum parabolis (1654), De infinitorum spiralium spatiorum mensura (1660) which contains a generalisation of Archimedes' spiral, and De infinitorum cochlearum mensuris ac centris gravitatis (1661) which carries out Torricelli's intention of finding the centre of gravity of a solid body called a cochlea. The approach followed by Angeli in all these works is that of his teacher Cavalieri and of Torricelli, so when Guldin and Tacquet attacked these methods and defended the approach of the ancient Greeks, Angeli disputed with them over indivisibles. One has to see both sides in this argument for although Angeli's methods were much more powerful, they were less rigorous than the method of exhaustion adopted by Archimedes. Angeli examined fluid statics based on Archimedes' principle and Torricelli's experiments. He published Della gravita dell aria e fluidi in 1671 while holding the chair at Padua. He also considered the motion bodies falling towards a rotating Earth. Of course Angeli held the chair at Padua which had been held earlier by Galileo and his work shows strong influences from his predecessor. For example Angeli often refers to Galileo in his writings on physics, showing clearly how he has been influenced, particularly in terms of ways of approaching problems via the experimental method. Also clearly influenced by Galileo is Angeli's writings on the two systems of Ptolemy and Copernicus which he writes in Galileo's dialogue style.*SAU

**1853 Heike Kamerlingh Onnes**(21 Sep 1853; 21 Feb 1926) Dutch winner of the Nobel Prize for Physics in 1913 for his work on low-temperature physics and his production of liquid helium. He discovered superconductivity, the almost total lack of electrical resistance in certain materials when cooled to a temperature near absolute zero.*TIS

**1884 Denes König**(21 Sept 1884, 19 Oct 1944) His book, Theorie der endlichen und unendlichen Graphen, was published in 1936, and was a major factor in the growth of interest in graph theory worldwide. It was eventually translated into English under the title Theory of finite and infinite graphs (translated by R McCoart), Birkhauser, 1990; this also contains a biographical sketch by Tibor Gallai.

König's work on the factorisation of bipartite graphs relates closely to the marriage problem of Philip Hall. König's use of graphs to give a simpler proof of a determinant result of Frobenius seems to have led to some hostility between the two men.

After the Nazi occupation of Hungary, König worked to help persecuted mathematicians. This led to his death a few days after the Hungarian National Socialist Party took over the country. *SAU

**1895 Joseph Leonard Walsh**(21 Sept 1895, 6 Dec 1973) Walsh had a remarkable publication record. An obituary by Morris Marden (a student of Walsh) lists 279 articles, 7 books and 31 PhD students. He studied the relative location of the zeros of pairs of rational functions, zeros and topology of extremal polynomials, the critical points and level lines of Green's functions and other harmonic functions, conformal mappings, Padé approximation, and the interpolation and approximation of continuous, analytic or harmonic functions. Sewell writes "Polynomial approximation was neither discovered nor invented by J L Walsh (which may come as a surprise to some mathematicians). He is the one individual, however, who took a few scattered results on the subject and extended them, added mightily to them, and knit the whole together into a comprehensive, coherent theory." *SAU

**1907 Sir Edward Crisp Bullard**(21 Sep 1907; 3 Apr 1980) English marine geophysicist noted for his work in geomagnetism who made the first satisfactory measurements of geothermal heat-flow through the oceanic crust. In early work, he measured minute gravitational variations by timing the swings of an invariant pendulum, which he used to study the East African Rift Valley. Bullard helped to develop the theory of continental drift. He made a computer analysis of the precise fit of the rifted continental borders along the two sides of the Atlantic Ocean, and presented his results to the Royal Society of London. He developed a "dynamo" theory of geomagnetism, which explained the Earth's magnetic field results from the convection of molten material within the Earth's core. He was knighted in 1953.*TIS

**1926 Donald A. Glaser**(21 Sep 1926, )American physicist, who was awarded the Nobel Prize for Physics in 1960 for his invention of the bubble chamber in which the behaviour of subatomic particles can be observed by the tracks they leave. A flash photograph records the particle's path. Glaser's chamber contains a superheated liquid maintained in a superheated, unstable state without boiling. A piston causing a rapid decrease in pressure creates a tendency to boil at the slightest disturbance in the liquid. Then any atomic particle passing through the chamber leaves a track of small gas bubbles caused by an instantaneous boiling along its path where the ions it creates act as bubble-development centers.*TIS

**DEATHS**

**1576 Girolamo Cardano died**. One story says that it was by his own hand so as to fulﬁll his ear¬lier astrological prediction of of his death on this date. *H. Eves, Introduction to the History of Mathematics, Pg 221... He was the first to give a clinical description of typhus fever. His book, Ars magna ("Great Art," 1545) was one of the great achievements in the history of algebra, in which he published the solutions to the cubic and quartic equations.(Ars Magna was the first Latin treatise devoted solely to algebra. In it he gave the methods of solution of the cubic and quartic equations which he had learned from Tartaglia.*SAU) His mechanical inventions included the combination lock, the compass gimbal consisting of three concentric rings, and the universal joint to transmit rotary motion at various angles (as used in present-day vehicles). He contributed to hydrodynamics and held that perpetual motion is impossible, except in celestial bodies. He published two encyclopedias of natural science and introduced the Cardan grille, a cryptographic tool (1550).*TIS

1842 Sir James Ivory (17 February 1765 – 21 September 1842) was a Scottish mathematician born in Dundee. He was essentially a self-trained mathematician, and was not only deeply versed in ancient and modern geometry, but also had a full knowledge of the analytical methods and discoveries of the continental mathematicians.

His earliest memoir, dealing with an analytical expression for the rectification of the ellipse, is published in the Transactions of the Royal Society of Edinburgh (1796); and this and his later papers on Cubic Equations (1799) and Kepler's Problem (1802) evince great facility in the handling of algebraic formulae. In 1804 after the dissolution of the flax-spinning company of which he was manager, he obtained one of the mathematical chairs in the Royal Military College at Marlow (afterwards removed to Sandhurst); and until the year 1816, when failing health obliged him to resign, he discharged his professional duties with remarkable success.*Wik

**1936 Frank Hornby**(15 May 1863, 21 Sep 1936) English inventor and toy manufacturer who patented the Meccano construction set in 1901. This toy used perforated metal strips, wheels, roods, brackets, clips and assembly nuts and bolts to build unlimited numbers of models. His original sets, marketed as "Mechanics Made Easy" produced in a rented room, were initially sold at only one Liverpool toy shop. By 1908, he had formed his company, Meccano Ltd., and within five more years had established manufacturing in France, Germany, Spain and the U.S. He introduced Hornby model trains in 1920, originally clockwork and eventually electrically powered with tracks and scale replicas of associated buildings. The "Dinky" range of miniature cars and other motor vehicles was added in 1933. *TIS

**1937 Chrystal Macmillan**was the first female science graduate at Edinburgh University and the first female honours graduate in Mathematics. She went on to study at Berlin. She was the first woman to plead a case before the House of Lords. She became active in the Women's Suffrage Movement and went on to become a lawyer.*SAU

**1950 Edward Arthur Milne**(14 Feb 1896, 21 Sep 1950) English astrophysicist and cosmologist best known for his development of kinematic relativity. Poor eyesight prevented him from active service in WWI, he did important war service in research in ballistics and sound ranging, and problems related to the atmosphere of the earth.. From 1920-29, he studied problems of radiative equilibrium and the theory of stellar atmospheres. He extended work done earlier by Schuster and by Schwarzschild, which he combined in a mathematical interesting integral equation now known as Milne's integral equation. Later, he turned to the theory of stellar structure and cosmology. After 1932, he concentrated on a new form of relativity called kinematic relativity, an alternative to Einstein's general theory.*TIS (

*In Eurekas and Euphorias Walter Gratzer tells an interesting story about Milne's rejected offer to provide his services to the war effort in WWII. Milne had given important service (above) in WWI and wrote to offer his services for this war as well, but received a rather dismissive letter to which he took offense. He used his extensive connections to have his anger made known to the higher-ups at the War Office. Eventually he received a request from a Brigadier General to come to his office. Milne arrived and amidst his tirade advised the General that the War Office should know that this war would be a scientific one, and the way he was treated was not the way to make the best use of eminent scientists. The General waited out Milne's outburst, and then asked a single question, "Did you win the Adams Prize in your year?" When Milne said he had not, but asked what that had to do with anything, the General replied, "I did!"*

I'm not sure what, if any, Milne's contributions to the war effort in WWII were.)

I'm not sure what, if any, Milne's contributions to the war effort in WWII were.

**1981 Henry George Forder**(27 Sept 1889, 21 Sept 1981) Forder spent much of his career in the Chair of Mathematics at Auckland. In fact he only once left New Zealand after settling there, this being in 1947 when he spent part of his leave in England. He spent 21 years building up the Mathematics Department at Auckland from a Department of a professor with one assistant when he arrived to one of six staff by the time he retired in 1955.

It is the books that Forder wrote which have given him a high reputation in the mathematical world. These are: The Foundations of Euclidean Geometry (1927), A School Geometry (1930), Higher Course Geometry (1931), The Calculus of Extension (1941), Geometry (1950), and Coordinates in Geometry (1953). In the Preface to the first of these, Forder writes, "Although the Euclidean geometry is the oldest of the sciences and has been studied critically for over two thousand years, it seems there is no textbook which gives a connected and rigorous account of that doctrine in the light of modern investigations. It is hoped that this book will fill the gap."

Geometry (1950) was reviewed by Donald Coxeter who was clearly fascinated by Forder's use of language, "The two-cusped epicycloid is described as the bright curve seen "when the sun shines on a cup of tea." ... The chapter on logical structure stresses the abstract nature of the order relation (ABC) by comparing it with the human relation "A prefers C to B." The possibility of coordinatising any descriptive geometry of three or more dimensions is epitomized in the statement that "we can create magnitudes from a mere muchness," and Archimedes' axiom in the statement that "you will always reach home, if you walk long enough." *SAU

Credits

*VFR = V Frederick Rickey, USMA

*TIS= Today in Science History

*Wik = Wikipedia

*SAU=St Andrews Univ. Math History

*CHM=Computer History Museum