## Monday, 15 February 2016

### On This Day in Math - February 15

Mathematics is the key and door to the sciences.
~Galileo

The 46th day of the year; there are 46 fundamental ways to arrange nine queens on a 9x9 chessboard so that no queen is attacking any other. (Can you find solutions for smaller boards?)

46 is the ninth "Lazy Caterer" number.  The maximum number of  pieces that can be formed with 9 straight cuts across a pancake.

On Oct 29, 2008 the 46th discovered Mersenne Prime, then the world's largest prime was featured on the in Time magazine as one of the "great inventions" of the year. It was discovered by Smith, Woltman, Kurowski, et al. of the GIMPS (Great Internet Mersenne Prime Search) program. Three more have been discovered since.

EVENTS
1671 James Gregory wrote Collins that he found inﬁnite series for the tangent and secant functions:
tan x = x + 1/3 x^3 + 2/15 x^5 + 7/315 ^7 ...
sec x = 1 +1/2 x^2 + 5/24 x^4 + 61/720 x^6 ...
*VFR

1729 A Letter from Gabriel Cramer, Prof. Math. Genev. to James Jurin, M. D. and F. R. S. to be read at the Royal Society, gives an “account of an Aurora Borealis Attended with Unusual Appearances” . The borealis occurred on Feb 15, and the letter was sent on Feb 20. Transactions of the Royal Society

5 Feb 1675 (OS) 15 Feb 1676(NS) Newton wrote Hooke: "What DesCartes did was a good step....If I have seen further it is bystanding on ye sholders of Giants." *VFR
The letter is at the Historical Society of Pennsylvania.

In 1897, Ferdinand Braun published a paper in the journal Annalen der Physik und Chemie describing his "Braun tube", which was the first cathode-ray oscilloscope. He developed this as a method to record and study the time dependance of alternating currents. Cathode-ray tubes had previously been characterized by uncontrolled rays; Braun produced a narrow stream of electrons, guided by means of alternating voltage, that could be traced on a fluorescent screen. A coil wrapped around the Braun tube produced a vertical deflection of the electron beam. Horizontal deflection of the image to create a "time" axis was achieved by means of a small rapidly rotating mirror placed in front of the CRT. *TIS

1958 France issued stamps honoring Joseph Louis Lagrange, Urbain Jean Joseph Leverrier, Jean Bernard Leon Foucault and Claude Louis Berthollet. [Scott #869–872] *VFR

1970 Martin Davis telephoned Julia Robinson from New York that John Cocke had just returned from Moscow with the report that the 22-year old Leningrad mathematician Yuri Matijaseviˇc had solved Hilbert’s tenth problem. The problem asked for an algorithm to solve all Diophantane equations. Matijaseviˇc showed no such algorithm exists. [The College Mathematics Journal, vol. 17 (1986), p. 19; More Mathematical People (1990), edited by Donald J. Albers,
G. L. Alexanderson and Constance Reid, p. 276]
*VFR

1971 The United Kingdom changed to a decimal system of currency. Previously the British pound was worth 20 shillings, each of which was 12 pence (plural of penny). Eves, Mathematical Circles Revisited #85 Mathematical Circles Revisited: A Second Collection of Mathematical Stories and Anecdotes (Eves Series in Mathematics)

1980 The U.S. issued a 15/c stamp in its Black Heritage Commemorative Series honoring the mathematician and astronomer Benjamin Bannecker (1731–1806). He is pictured beside a transit, for he was L’Enfant’s chief assistant in laying out the city of Washington, D.C. More importantly, he determined the boundaries of the district. At the annual NCTM meeting in Chicago in 1988 the Bannecker Association, which promotes the education of Black students, distributed buttons with a picture of this stamp. They were a great hit. [Scott #1804]
*VFR

2013 NEAR MISS (The Earth heard me yell, "Duck". ) The near earth asteroid 2012 DA14 has an estimated diameter of about 44 meters and an estimated mass of about 120,000 metric tons. It was discovered on February 23, 2012, by the OAM Observatory, La Sagra in Spain (J75). Calculations show that on February 15, 2013, the distance between the asteroid and the Earth was 0.07 LD (27,000 km; 17,000 mi) *Science Daily

2013 And a hit, A meteor streaks across the sky on Feb. 15 near Chelyabinsk, Russia. A ten ton meteor streaked at supersonic speed over Russia's Ural Mountains before exploding over Chelyabinsk. The blast injured more than 500 people and caused a factory roof to collapse. *Nasha Gazeta via AP

BIRTHS
1564 Galileo  (15 Feb 1564; 8 Jan 1642 at age 77) Italian natural philosopher, astronomer, and mathematician who applied the new techniques of the scientific method to make significant discoveries in physics and astronomy. His great accomplishments include perfecting (though not inventing) the telescope and consequent contributions to astronomy. He studied the science of motion, inertia, the law of falling bodies, and parabolic trajectories. His formulation of the scientific method parallel the writings of Francis Bacon. His progress came at a price, when his ideas were in conflict with religious dogma.*TIS He is (re)buried at the Basilica of Sante Croce in Florence. The Grand Duke of Tuscany, Ferdinando II, wished to bury him in the main body of the Basilica of Santa Croce, next to the tombs of his father and other ancestors, and to erect a marble mausoleum in his honour. These plans were scrapped, however, after Pope Urban VIII and his nephew, Cardinal Francesco Barberini, protested, because Galileo was condemned by the Catholic Church for "vehement suspicion of heresy". He was instead buried in a small room next to the novices' chapel at the end of a corridor from the southern transept of the basilica to the sacristy. He was reburied in the main body of the basilica in 1737 after a monument had been erected there in his honour; during this move, three fingers and a tooth were removed from his remains. One of these fingers, the middle finger from Galileo's right hand, is currently on exhibition at the Museo Galileo in Florence, Italy. *Wik

1588 Benjamin Bramer (15 Feb 1588 in Felsberg, Germany- 17 March 1652 in Ziegenhain, Germany) was a German architect who published work on the calculation of sines. He was tutored by Bürgi in a wide range of subjects but it was mathematics that he loved and he passed this love on to Bramer. Bramer followed Alberti (1435), Dürer (1525) and Bürgi (1604) when in 1630 he constructed a device that enabled one to draw accurate geometric perspective. The instrument had been described in a 1617 publication Trigonometrica planorum mechanica oder Unterricht und Beschreibung eines neuen und sehr bequemen geometrischen Instrumentes zu allerhand Abmessung. Bramer designed several other mathematical instruments, for example a description of the pantograph appears in the same 1617 publication. The instrument is designed to copy a geometric shape and reproduce it at a reduced or enlarged scale. It consists of an assemblage of rigid bars adjustably joined by pin joints; as the point of one bar is moved over the outline to be duplicated, the motion is translated to a point on another bar, which makes the desired copy according to the predetermined scale. Bramer has not been recognised as the inventor of the pantograph, this distinction going to the Jesuit Christoph Scheiner who describes a similar instrument in his 1631 publication Pantographice seu acre delineandi res quaslibet by parallelogrammum linear seu cavum mechanicum, mobile. Although Scheiner's publication did much to spread knowledge of the pantograph, the instrument he describes is technically inferior to the earlier instrument as described by Bramer. *SAU

1826 George Johnstone Stoney (15 Feb 1826; 5 Jul 1911 at age 85) Irish physicist who introduced the term electron for the fundamental unit of electricity. At the Belfast meeting of the British Association in Aug 1874, in a paper: On the Physical Units of Nature, Stoney called attention to a minimum quantity of electricity. He wrote, "I shall express 'Faraday's Law' in the following terms ... For each chemical bond which is ruptured within an electrolyte a certain quantity of electricity traverses the electrolyte which is the same in all cases." Stoney offered the name electron for this minimum electric charge. When J.J. Thomson identified cathode rays as streams of negative particles, each carrying probably Stoney's minimum quantity of charge, the name was applied to the particle rather than the quantity of charge. *TIS

1839 Hieronymus Georg Zeuthen (15 February 1839 – 6 January 1920) was a Danish mathematician. He is known for work on the enumerative geometry of conic sections, algebraic surfaces, and history of mathematics. After 1875 Zeuthen began to make contributions in other areas such as mechanics and algebraic geometry, as well as being recognised as an expert on the history of medieval and Greek mathematics. He wrote 40 papers and books on the history of mathematics, which covered many topics and several periods.*Wik

1839 Christian Gustav Adolph Mayer (February 15, 1839 – April 11, 1907) was a German mathematician.
Mayer studied at Heidelberg, and submitted his habilitation thesis to the University of Heidelberg. He gained the permission to teach at universities in 1866. He taught mathematics at the University of Heidelberg for the rest of his life. He did research on differential equations, the calculus of variations and mechanics. His research on the integration of partial differential equations and a search to determine maxima and minima using variational methods brought him close to the investigations which Sophus Lie was carrying out around the same time.
Several letters were exchanged between Mayer and mathematician Felix Klein from 1871 to 1907. Those letters provide insights into the scientific and personal relations among Felix Klein, Mayer and Lie over the period.
Mayer's students included : Friedrich Engel, Felix Hausdorff and Gerhard Kowalewski. *Wik

1850 Sophie Willock Bryant (15 February 1850 Sandymount, near Dublin, Ireland - 14 August 1922 in Chamonix, France) While studying for her D.Sc., Bryant was elected to the London Mathematical Society in 1882. She became the third women member of the Society (Charlotte Angas Scott and Christine Ladd-Franklin were the first and second respectively in the previous year). Bryant, however, does have the distinction of being the first woman to have a paper published in the Proceedings of the London Mathematical Society. This was in 1884 when she published The ideal geometrical form of natural cell structure. The paper investigates the hexagonal form of honeycombs.
She was one of the first three women to be appointed to a Royal Commission, the Bryce Commission on Secondary Education in 1894 - 95, and she was one of the first three women to be appointed to the Senate of London University. While on the Senate she advocated setting up a Day Training College for teachers which eventually became the Institute of Education. Later in 1904, when Trinity College Dublin opened its degrees to women, Bryant was one of the first to be awarded an honorary doctorate. She was also instrumental in setting up the Cambridge Training College for Women which eventually became Hughes Hall, the first postgraduate college in Cambridge.
She died while she was on a climbing holiday in Chamonix, France. Climbing was one of Bryant's loves and she had climbed many of the mountains in the Alps, for example the Matterhorn and Mount Blanc. However her death occurred in a valley with fields and paths. Her body was discovered on 28 August 1922, two weeks after she had failed to return to her lodgings. *SAU

1851 Spiru C. Haret (15 February 1851 – 17 December 1912) was a Romanian mathematician, astronomer and politician. He made a fundamental contribution to the n-body problem in celestial mechanics by proving that using a third degree approximation for the disturbing forces implies instability of the major axes of the orbits, and by introducing the concept of secular perturbations in relation to this.
As a politician, during his three terms as Minister of Education, Haret ran deep reforms, building the modern Romanian education system. He was made a full member of the Romanian Academy in 1892.
He also founded the Astronomical observatory in Bucharest, appointing Nicolae Coculescu as its first director. The crater Haret on the Moon is named after him. *Wik

1858 William Henry Pickering (15 Feb 1858; 16 Jan 1938 at age 79) American astronomer who discovered Phoebe, the ninth moon of Saturn (1899). This was the first planetary satellite with retrograde motion to be detected, i.e., with orbital motion directed in an opposite sense to that of the planets. He set up a number of observing stations for Harvard. He made extensive observations of Mars and claimed, like Lowell, that he saw signs of life on the planet by observing what he took to be oases in 1892. He went further than Lowell however when in 1903 he claimed to observe signs of life on the Moon. By comparing descriptions of the Moon from Giovanni Riccioli's 1651 chart onward, he thought he had detected changes that could have been due to the growth and decay of vegetation. *TIS

1861 Alfred North Whitehead (15 Feb 1861, 30 Dec 1947) English mathematician and philosopher, who worked in logic, physics, philosophy of science and metaphysics. He is best known for his work with Bertrand Russell on one of probably the most famous books of the century, Principia Mathematica (1910-13) to demonstrate that logic is the basis for all mathematics. In physics (1910-24) his best known work was a theory of gravity, that competed with Einstein's general relativity for many decades. In his later life from 1924 onward at Harvard, he worked on more general issues in philosophy rather than mathematics, including the development of a comprehensive metaphysical system which has come to be known as process philosophy. *TIS

1882 Paul Koebe(15 Feb 1882 in Luckenwalde, Germany - 6 Aug 1945 in Leipzig, Germany) Koebe's work was all on complex functions, his most important results being on the uniformisation of Riemann surfaces. Shortly after 1900 Koebe established the general principle of uniformisation which had been originally conceived by Klein and Poincaré. Koebe's proof of the uniformisation theorem has been described as: ... arguably one of the great theorems of the century. *SAU

1884 Albert Carlton Gilbert (15 Feb 1884, 24 Jan 1961) was an American inventor who patented the Erector set after he founded the A.C. Gilbert Co. New Haven, Connecticut (1908) to manufacture boxed magic sets. In 1913, he introduced Erector Sets. Similar construction toys then existed, such as Hornby's Meccano set made in England. Meccano sets included pulleys, gears, and several 1/2" wide strips of varying length with holes evenly spaced on them. Gilbert needed something unique for his Erector sets, so he created the square girder, made using several 1" wide strips with triangles cut in them. These had their edges bent over so 4 strips could be screwed together to form a very sturdy square girder. Over the next 40 years, some 30 million Erector Sets were sold.*TIS

1915 Chuan-Chih Hsiung (15 Feb 1915 in Shefong, Jiangsi, China - 6 May 2009 in Needham, Massachusetts, USA), also known as Chuan-Chih Hsiung, C C Hsiung, or Xiong Quanzhi, is a notable Chinese-born American differential geometer. He was Professor Emeritus of Mathematics at Lehigh University, Bethleham PA USA.
He is the founder and editor-in-chief of the Journal of Differential Geometry, an influential journal in the domain. During his early age, he focused on projective geometry. His interests were largely extended after his research in Harvard, including two-dimensional Riemannian manifolds with boundary, conformal transformation problems, complex manifold, curvature and characteristic classes, etc. *Wik

1934 Niklaus Wirth is Born, the inventor of the programming language Pascal, is born in Winterhur, Switzerland. He received an M.S. from University Laval in 1960, and a Ph.D. from University of California, Berkeley in 1963. During 1963-1967 he had taught at Stanford, and from 1967 to 1975 he was professor of computer science at the University of Zurich. Since 1975 Wirth has become professor of computer science at the Federal Institute of Technology, Zurich
Originally Pascal was intended to serve only as a tool for teaching programming. Wirth's another development, Oberon, is rather a combination of a programming language and operating system for single user personal workstations. His most recent project, CADtools for hardware design, aimes to bridge the gap between software and hardware.
Niklaus Wirth has received ACM's A.M. Turing Award, and IEEE Computer Society's Computer Pioneer Award. *CHM

DEATHS

1847 Germinal Pierre Dandelin (12 April 1794 – 15 February 1847) was a mathematician, soldier, and professor of engineering. He was born near Paris to a French father and Belgian mother, studying first at Ghent then returning to Paris to study at the École Polytechnique. He was wounded fighting under Napoleon. He worked for the Ministry of the Interior under Lazare Carnot. Later he became a citizen of the Netherlands, a professor of mining engineering in Belgium, and then a member of the Belgian army.
He is the eponym of the Dandelin spheres, of Dandelin's theorem in geometry, and of the Dandelin–Gräffe numerical method of solution of algebraic equations. He also published on the stereographic projection, algebra, and probability theory. *Wik He is known for his ingenious use of spheres in a cone to show that the deﬁnitions of the conics as sections of a cone are equivalent to the loci deﬁnitions. *VFR

1849 Pierre François Verhulst (28 October 1804, Brussels, Belgium – 15 February 1849, Brussels, Belgium) was a mathematician and a doctor in number theory from the University of Ghent in 1825. Verhulst published in 1838 the equation:
dN/dt = r N (1-N/k)
when N(t) represents number of individuals at time t, r the intrinsic growth rate and k is the carrying capacity, or the maximum number of individuals that the environment can support. In a paper published in 1845 he called the solution to this the logistic function, and the equation is now called the logistic equation. This model was rediscovered in 1920 by Raymond Pearl and Lowell Reed, who promoted its wide and indiscriminate use.*Wik

1868 William Rutter Dawes (19 Mar 1799, 15 Feb 1868 at age 68) English amateur astronomer who set up a private observatory and made extensive measurements of binary stars and on 25 Nov 1850 discovered Saturn's inner Crepe Ring (independently of American William Bond). In 1864, he was the first to make an accurate map of Mars. He was called "Eagle-eyed Dawes" for the keenness of his sight with a telescope (though otherwise, he was very near-sighted). He devised a useful empirical formula by which the resolving power of a telescope - known as the Dawes limit - could be quickly determined. For a given telescope with an aperture of d cm, a double star of separation 11/d arcseconds or more can be resolved, that is, be visually recognized as two stars rather than one. *TIS

1900 John James Walker (2 Oct 1825, 15 Feb 1900) The range of Walker's mathematical research was quite impressive. He wrote some articles on theoretical mechanics but his more elaborate papers were on advanced algebra and geometry. Walker was a strong advocate of Hamilton's quaternions and strongly believed that they had not been given as wide a use as they merited. He applied quaternions to a variety of problems, mostly of an elementary nature.
The three most important papers that Walker wrote were on the analysis of plane curves and curved lines. The papers were closely connected and all appeared in the Proceedings of the London Mathematical Society. He wrote further articles on cubic curves and in this area he wrote the memoir On the diameters of cubic curves which was published in the Transactions of the Royal Society in 1889. *SAU

1940 Otto Toeplitz (1 Aug 1881 in Breslau, Germany (now Wrocław, Poland) - 15 Feb 1940 in Jerusalem (under the British Mandate at the time)) In 1905 he received his Ph.D. in algebraic geometry at the university there and then moved to G¨ottingen, where he was deeply inﬂuenced by the work of Hilbert. He was also interested in the history of mathematics and held that only a mathematician of stature is qualiﬁed to be a historian of mathematics. In 1949 he published an introduction to the calculus on a historical basis. This delightful book is available in English as The Calculus. A Genetic Approach. *VFR

1959 Sir Owen Willans Richardson (26 Apr 1879, 15 Feb 1959 at age 79) English physicist who was awarded the Nobel Prize for Physics in 1928 for “his work on the thermionic phenomenon [electron emission by hot metals] and especially for the discovery of the law named after him.”This effect is why a heated filament in a vacuum tube releases a current of electrons to travel an anode, which was essential for the development of such applications as radio amplifiers or a TV cathode ray tube. Richardson's law mathematically relates how the electron emission increases as the absolute temperature of the metal surface is raised. He also conducted research on photoelectric effects, the gyromagnetic effect, the emission of electrons by chemical reactions, soft X-rays, and the spectrum of hydrogen. *TIS

1988 Richard P(hillips) Feynman (11 May 1918, 15 Feb 1988 at age 69) was an American theoretical physicist who was probably the most brilliant, influential, and iconoclastic figure in his field in the post-WW II era. By age 15, he had mastered calculus. He took every physics course at MIT. His lifelong interest was in subatomic physics. In 1942, he went to Los Alamos where Hans Bethe made the 24 year old Feynman a group leader in the theoretical division, to work on estimating how much uranium would be needed to achieve critical mass for the Manhattan (atomic bomb) Project. After the war, he developed Feynman Diagrams, a simple notation to describe the complex behavior of subatomic particles. In 1965, he shared the Nobel Prize in Physics for work in quantum electrodynamics. *TIS He was (still is) famous for his unusual life style and for his popular books and lectures on mathematics and physics. *SAU

1999 Henry Way Kendall (9 Dec 1926; 15 Feb 1999)American nuclear physicist who shared the 1990 Nobel Prize for Physics with Jerome Isaac Friedman and Richard E. Taylor for obtaining experimental evidence for the existence of the subatomic particles known as quarks. To study the internal structure of the proton, they worked with the 3-km linear accelerator recently opened at Stanford (SLAC). Electrons were accelerated to an energy of 20,000 million electronvolts and directed against a target of liquid hydrogen. In 1969 Kendall helped found the Union of Concerned Scientists. In 1997, in connection with the Kyoto Climate Summit, he helped produce a statement signed by 2,000 scientists calling for action on global warming.*TIS

2008 Walter Warwick Sawyer (or W. W. Sawyer) (April 5,1911–February 15, 2008) was a mathematician, mathematics educator and author, who taught on several continents.
Born in London, England , he attended Highgate School and was an undergraduate at St. John's College, Cambridge, obtaining a BA in 1933. He was an assistant lecturer in mathematics from 1933 to 1937 at University College, Dundee and from 1937 to 1944 at Manchester University. From 1945 to 1947, he was the head of mathematics at Leicester College of Technology.
In 1948 W. W. Sawyer became the first head of the mathematics department of what is now the University of Ghana. From 1951 to 1956, he was at Canterbury College (now the University of Canterbury in New Zealand). He left Canterbury College to become an associate professor at the University of Illinois, where he worked from winter 1957 through June 1958. While there, he criticized the New Math movement, which included the people who had hired him. From 1958 to 1965, he was a professor of mathematics at Wesleyan University. In the fall of 1965 he became a professor at the University of Toronto, appointed to both the College of Education and the Department of Mathematics. He retired in 1976.
W. W. Sawyer was the author of some 11 books. He is probably best known for his semi-popular works Mathematicians Delight and Prelude to Mathematics. Both of these have been translated into many languages. Mathematician's Delight was still in print 65 years after it was written. Some mathematicians have credited these books with helping to inspire their choice of a career.
W.W. Sawyer died on February 15, 2008, at the age of 96. He was survived by a daughter, Anne. *Wik
His first book "Mathematician’s Delight" (1943), was written with the aim "to dispel the fear of mathematics." It is one of the most successful math book ever written, going through numerous editions, translations into 10 languages, and selling more than 500,000 copies.

My favorite Sawyer quote:
Complete success would mean that every individual felt,
"I enjoyed the mathematics that I had time to learn.
If I ever need or want to learn some more,
I shall not be afraid to do so."

And one of my favorite Sawyer books:

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