## Sunday, 15 October 2017

### On This Day in Math - October 15

Many have argued that a vacuum does not exist, others claim it exists only with difficulty in spite of the repugnance of nature; I know of no one who claims it easily exists without any resistance from nature.
— Evangelista Torricelli in a Letter to Michelangelo Ricci

The 288th day of the year; 288 is the super-factorial of four. 1! x 2! x 3! x 4! =288. It is important that math students learn not to say this number in public as it is two gross. (I apologize for the really bad pun)

288 is also the sum of the first four integers raised to their own power $1^1 + 2^2 + 3^3 + 4^4 = 288$

288 is the smallest non-palindrome, non-square, that when multiplied by its reverse is a square: 288 x 882 = 254,016 = 5042.

EVENTS

1582 St Theresa of Avila died overnight on the night between the 4th and the 15th of October. On that day the Gregorian calendar went into effect in Spain and the day after the 4th, was the 15th in order to catch up for the misalignment of the Julian Calendar. *VFR

1698 King William III commissioned Edmund Halley as Royal Naval Captain of the HMS
Paramore and provided him with a complete set of instructions. The Admiralty’s instructions to Halley dated 15 October 1698 were :
Whereas his Maty. has been pleased to lend his Pink the Paramour for your proceeding with her on an Expedition, to improve the knowledge of the Longitude and variations of the Compasse, which Shipp is now compleatly Man’d, Stored and Victualled at his Mats. Charge for the said Expedition ... *Lori L. Murray, The Construction of Edmond Halley’s 1701 Map of Magnetic Declination

1759 Euler's paper "An arithmetic theorem proved by a new method" was presented at the Saint-Petersburg Academy. In This paper he introduces the idea that has come to be called Euler's Phi function, but did not include a symbol or name. Euler defined the function as "the multitude of numbers less than D, and which have no common divisor with it." (This is slightly different than the current definition which used Greatest Common Divisor is one). He revisited the idea in a paper read to the Academy on October 9, 1775 In the earlier papers he had not used a symbol, but in the 1775 paper he chose πD for symbol. In 1801 Gauss's Disquisitiones Arithmeticae introduced the Phi notation, although Gauss didn't use parentheses around the argument and wrote φA. The term Totient was applied by J J Sylvester in 1879. So it's not Euler's Phi, and it's not Euler's Totient, and in fact, the function is now not exactly Euler's function. *Wik

1783 The ﬁrst manned ascension in a balloon. After the ﬂight of September 19, 1783, Louis XVI forbade men to go aloft, making the adventurers furious. Later he extended the privilege to convicts, ﬁguring they were expendable. de Rozier’s loud fulmigations against such glory for “vile criminals” soon changed the king’s mind. The hydrogen balloon, Aerostat Reveillon, carrying Pilâtre, first man to leave the earth, rose to the end of its 250- ft tether. It stayed aloft for 15 minutes, then landed safely nearby.
On 21 Nov 1783, untethered, Pilâtre and Marquis d'Arlande made the first manned free flight, across Paris. On 15 Jun 1785, Pilâtre attempt the first east-to-west crossing of the English Channel with a hybrid balloon combining lift from both hydrogen and hot air. Within minutes of launch, the craft exploded, and plunged to the rocks on the coast of Wimereux. Neither Pilâtre nor his co-pilot, Romain, survived the crash. *TIS (American Scientist and U S emissary to the court of Louis XVI, Ben Franklin, was present for some of the Balloon ascensions in 1783. When asked what was the use of Ballooning, he replied, “Of what use is a newborn baby?”)

In 1827, Charles Darwin was accepted into Christ's College at Cambridge, but did not start until winter term because he needed to catch up on some of his studies. A grandson of Erasmus Darwin of Lichfield, and of Josiah Wedgwood, he had entered the University of Edinburgh in 1825 to study medicine, intending to follow his father Robert's career as a doctor. However, Darwin found himself unenthusiastic about his studies, including that of geology. Disappointing his family that he gave up on a medical career, he left Edinburgh without graduating in April 1827. His scholastic achievements at Cambridge were unremarkable, but after graduation, Darwin was recommended by his botany professor to be a naturalist to sail on HM Sloop Beagle. *TIS

1956 The first FORTRAN reference manual is released on October 15, 1956, six months before the first compiler's release. Only 60 pages long, with large print and wide margins, that first programming language was miniscule by today's standard. The original FORTRAN development team comprised John Backus, Sheldon Best, Richard Goldberg, Lois Mitchell Haibt, Harlan Herrick, Grace Mitchell, Robert Nelson, Roy Nutt, David Sayre, Peter Sheridan, and Irving Ziller.*CHM

In 2003, China became the third nation to send a man into space. Lieutenant Colonel Yang Liwei, 38, was launched on a Long March CZ-2F rocket in the Shenzhou-5 spacecraft at 9 am local time (1 am GMT). He completed 14 Earth orbits during a 21-hour flight which ended with a parachute-assisted landing in the on the grasslands of Inner Mongolia in northern China. The Shenzhou spacecraft was based on the three-seat Russian Soyuz capsule, but with extensive modifications. The country began planning manned spaceflight in 1992. Russia began providing advice on technology and astronaut training in 1995. The first of four unmanned test flights of a Shenzhou craft (took place in Nov 1999. The name Shenzhou translates as "divine vessel." *TIS

BIRTHS

1608 Evangelista Torricelli (15 Oct 1608; 25 Oct 1647) Born in Faenza, Italy, Torricelli was an Italian physicist and mathematician who invented the barometer and whose work in geometry aided in the eventual development of integral calculus. Inspired by Galileo's writings, he wrote a treatise on mechanics, De Motu ("Concerning Movement"), which impressed Galileo. He also developed techniques for producing telescope lenses. The barometer experiment using "quicksilver" filling a tube then inverted into a dish of mercury, carried out in Spring 1644, made Torricelli's name famous. The Italian scientists merit was, above all, to admit that the effective cause of the resistance presented by nature to the creation of a vacuum (in the inverted tube above the mercury) was probably due to the weight of air. *TIS He succeeded his teacher, Galileo as professor of mathematics at Florence. One of his most amazing discoveries was a solid which had inﬁnite length but ﬁnite volume. He also invented the mercury barometer.*VFR

1735 Jesse Ramsden FRSE (15 October 1735 – 5 November 1800) was an English astronomical and scientific instrument maker.
Ramsden created one of the first high-quality dividing engines. This machine permitted the automatic and highly accurate division of a circle into degrees and fractions of degrees of arc.The machine  led to mass production of precision octants and sextants and gave British manufacturers dominance in the field of marine instruments for decades.  His invention was so valuable to the nation’s maritime interests that he received a share of the Longitude Prize.
His most celebrated work was a 5-feet vertical circle, which was finished in 1789 and was used by Giuseppe Piazzi at Palermo in constructing his catalog of stars. He was the first to carry out in practice a method of reading off angles (first suggested in 1768 by the Duke of Chaulnes) by measuring the distance of the index from the nearest division line by means of a micrometer screw which moves one or two fine threads placed in the focus of a microscope.
Ramsden's transit instruments were the first which were illuminated through the hollow axis; the idea was suggested to him by Prof. Henry Ussher in Dublin. He published a Description of an Engine for dividing Mathematical Instruments in 1777.
Ramsden is also responsible for the achromatic eyepiece named after him, and also worked on new designs of electrostatic generators. He was elected to the Royal Society in 1786. The exit pupil of an eyepiece was once called the Ramsden disc in his honour. In 1791 he completed the Shuckburgh telescope, an equatorial mounted refractor telescope.
In about 1785, Ramsden provided a new large theodolite for General William Roy of the Royal Engineers, which was used for a new survey of the distance between Greenwich, London and Paris. This work provided the basis for the subsequent Ordnance Survey of the counties of Britain. For his part with Roy in this work he received the Copley Medal in 1795. He died five years later at Brighton, England.*Wik

1745 George Atwood (Baptized October 15, 1745, Westminster,London – 11 July 1807, London) was an English mathematician who invented a machine for illustrating the effects of Newton's first law of motion. He was the first winner of the Smith's Prize in 1769. He was also a renowned chess player whose skill for recording many games of his own and of other players, including François-André Danican Philidor, the leading master of his time, left a valuable historical record for future generations.
He attended Westminster School and in 1765 was admitted to Trinity College, Cambridge. He graduated in 1769 with the rank of third wrangler and was awarded the inaugural first Smith's Prize. Subsequently he became a fellow and a tutor of the college and in 1776 was elected a fellow of the Royal Society of London.
In 1784 he left Cambridge and soon afterwards received from William Pitt the Younger the office of patent searcher of the customs, which required but little attendance, enabling him to devote a considerable portion of his time to mathematics and physics.
He died unmarried in Westminster at the age of 61, and was buried there at St. Margaret's Church. Over a century later, a lunar crater was renamed Atwood in his honour. *Wik

1776 Peter Barlow (15 Oct 1776, 1 March 1862) Peter Barlow was self-educated but this education was sufficiently good that he was able to compete successfully to became an assistant mathematics master at the Royal Military Academy at Woolwich. He was appointed to the post in 1801 and he began publishing mathematical articles in the Ladies Diary and he became sufficiently well established as a leading authority on mathematics that after a while he was asked to contribute various articles on mathematics for encyclopedias.
In addition to these articles, Barlow also published several important books, for example in 1811 he published An elementary investigation of the theory of numbers and three years later he published A new mathematical and philosophical dictionary.
He is remembered most for two important contributions. In 1814 he produced a second book, in addition to the one described above, entitled New mathematical tables. These soon became known as Barlow's Tables and this work gives factors, squares, cubes, square roots, reciprocals and hyperbolic logarithms of all numbers from 1 to 10 000. The book "...was considered so accurate and so useful that it has been regularly reprinted ever since. "
In the mathematical library at the University of St Andrews we have several well worn copies of these tables which must have been used intensely for many years. Today, however, they are only of historical interest since they were made completely obsolete by calculators and computers.
Barlow's second major contribution makes his name still well known by amateur astronomers today. He invented the Barlow lens, a telescope lens consisting of a colorless liquid between two pieces of glass, the "Barlow lens", a modification of this telescope lens, is a negative achromatic combination of flint glass and crown glass.
In 1819 Barlow began work on the problem of deviation in ship compasses caused by the presence of iron in the hull. For his method of correcting the deviation by juxtaposing the compass with a suitably shaped piece of iron, he was awarded the Copley Medal ... *SAU
Barlow is quoted on SAU as saying, "230(231-1) is the greatest perfect number that will ever be discovered, for, as they are merely curious without being useful, it is not likely that any person will attempt to find a number beyond it."

1829 Asaph Hall (15 Oct 1829; 22 Nov 1907) American astronomer, discovered and named the two moons of Mars, Phobos and Deimos, and calculated their orbits.Born in Goshen, Conn. and apprenticed as a carpenter at age 16, he had a passion for geometry and algebra. Hall obtained a position at the Harvard Observatory in Cambridge, Mass. in 1857 and became an expert computer of orbits. In August 1862, he joined the staff of the Naval Observatory in Washington, D.C. where he made his discoveries, in mid- Aug 1877, using the Observatory's 26-inch "Great Equatorial" refracting telescope, then the largest of its kind in the world. He stayed there 30 years until 1891. His son, Asaph Hall, Jr., followed him and worked at the Observatory at various times between 1882-1929.*TIS

1837 Leo Königsberger (15 October 1837 – 15 December 1921) was a German mathematician, and historian of science. He is best known for his three-volume biography of Hermann von Helmholtz, which remains the standard reference on the subject. The biography of Helmholtz was published in 1902 and 1903. He also wrote a biography of C. G. J. Jacobi.
Königsberger's own research was primarily on elliptic functions and differential equations. He worked closely with Lazarus Fuchs, a childhood friend.*Wik

1867 Jacques Inaudi (October 15, 1867 – November 10, 1950) Born to a poor family in the Italian Piedmont, Jacques Inaudi began life as a shepherd but soon discovered a prodigious talent for calculation, and soon he was giving exhibitions in large cities.
Camille Flammarion wrote, “He was asked, for example, how many minutes have elapsed since the birth of Jesus Christ, or what the population would be if the dead from the past ten centuries were resurrected, or the square root of a number of twelve digits, and he gave the response accurately and in two or three minutes — while amusing himself with another activity.”
“The subtraction of numbers consisting of twenty-four figures is an easy matter for him,” reported Scientific American. “Problems for which logarithm tables are generally used he solves mentally with wonderful precision.”
Unlike other prodigies, Inaudi did not visualize his work. “I hear the figures,” he told Alfred Binet, “and it is my ear which retains them; I hear them resounding after I have repeated them, and this interior sensation remains for a long time.”
Inaudi’s father had approached Flammarion hoping that his son could be educated toward a career in astronomy. “It had been an error, whichever way one looked at it,” Flammarion wrote 10 years later. “In science, one cannot make use of his methods, of his adapted formulae, which are tailored to mental calculation.” It was just as well: “Regarding his financial position, he now has, as a result of the curiosity his ability has aroused, a salary, which is over three times that of the Director of the Paris Observatory.” *Greg Ross, Futility Closet

1905 Baron C(harles) P(ercy) Snow (15 Oct 1905; 1 Jul 1980) British former physicist, turned novelist and government administrator. In 1959, C.P. Snow gave a controversial lecture called The Two Cultures and the Scientific Revolution claiming there were two cultures - the literary intellectuals and the scientists, who didn't understand each other and didn't trust each other. The split was not new; Snow noted that in the 1930s, literary theorists had begun to use the word "intellectual" to refer only to themselves. He illustrated this gap by asking a group of literary intellectuals to tell him about the Second Law of Thermodynamics, which he called the scientific equivalent of `Have you read a work of Shakespeare?'" Since then, debate about this polarization has continued.*TIS

1875 André-Louis Cholesky (October 15, 1875 – August 31, 1918,) a French military officer and mathematician. He worked in geodesy and map-making, was involved in surveying in Crete and North Africa before World War I. But he is primarily remembered for the development of a matrix decomposition known as the Cholesky decomposition which he used in his surveying work. He served the French military as engineer officer and was killed in battle a few months before the end of World War I; his discovery was published posthumously by his fellow officer in the "Bulletin Géodésique".*Wik

Bernhard Hermann Neumann (15 Oct 1909, 21 Oct 2002) Neumann is one of the leading figures in group theory who has influenced the direction of the subject in many different ways. While still in Berlin he published his first group theory paper on the automorphism group of a free group. However his doctoral thesis at Cambridge introduced a new major area into group theory research. In his thesis he initiated the study of varieties of groups, that is classes of groups defined which are by a collection of laws which must hold when any group elements are substituted into them. *SAU
(check the dates of birth and death between this entry and the next... I checked, it seems to be correct, PB)

1909 Jesse L. Greenstein (15 Oct 1909; 21 Oct 2002) American astronomer who was a co-discoverer of quasars. His interest in astronomy began at age 8 when his grandfather gave him a brass telescope. By age 16, he was a student at Harvard University, and later earned his Ph.D.(1937), then joined the Yerkes Observatory under Otto Struve. Thereafter, he spent most of his career at the California Institute of Technology.. He measured the composition of stars, through which he found less heavy elements in the stars of globular clusters, thus proving they are younger than our Sun. In 1963, he and Maarten Schmidt were the first to correctly describe the nature of quasars, by interpreting their red shift as compact, very distant and thus very old objects. With Louis Henyey he designed and constructed a new spectrograph and wide-view camera to improve astronomical observations. *TIS

1921 Lillian Katie Bradley (born October 15, 1921) is a mathematician and mathematics educator who in 1960 became the first African-American woman to earn a doctorate in any subject at the University of Texas at Austin. She accomplished this ten years after African-Americans were first admitted to the school, and despite the dominance of the mathematics department at Austin by R. L. Moore, known for his segregationist views and for his snubs of African-American students. (In 1973, UT had named its mathematics building in honor of Robert Lee Moore, an accomplished mathematician who was also a strong segregationist. He famously walked out of lectures by black speakers, and refused to teach any black students. *PB)
Bradley was born in Tyler, Texas. She earned a bachelor's degree in mathematics in 1938 from Texas College, and a master's degree in mathematics education in 1946 from the University of Michigan. She became a teacher at a segregated black high school in Hawkins, Texas, at Paul Quinn College, and at Texas College, before becoming an assistant professor of mathematics at Prairie View A&M College. There, in 1957–1958, she was awarded a National Science Faculty Fellowship, one of only 100 awarded in the inaugural year of the program.
She completed her doctorate at the University of Texas in July 1960. Her dissertation, in mathematics education, was An Evaluation of the Effectiveness of a Collegiate General Mathematics Course. In 1962 she moved from Prairie View to Texas Southern University, as an associate professor. *Wik

DEATHS

1959 Lipót Fejér (9 Feb 1880, 15 Oct 1959) Fejér's main work was in harmonic analysis working on Fourier series and their singularities. Fejér collaborated to produce important papers with Carathéodory on entire functions and with Riesz on conformal mappings. *SAU

1965 Abraham Halevi (Adolf) Fraenkel (February 17, 1891, Munich, Germany – October 15, 1965, Jerusalem, Israel) known as Abraham Fraenkel, was an Israeli mathematician born in Germany. He was an early Zionist and the first Dean of Mathematics at the Hebrew University of Jerusalem. He is known for his contributions to axiomatic set theory, especially his addition to Ernst Zermelo's axioms which resulted in Zermelo–Fraenkel axioms.*Wik

1980 Mikhail Alekseevich Lavrentev(19 Nov 1900 in Kazan, Russia, 15 Oct 1980 in Moscow) is remembered for an outstanding book on conformal mappings and he made many important contributions to that topic.*SAU

1990 Wilhelm Magnus (February 5, 1907, Berlin, Germany – October 15, 1990, New York City) made important contributions in combinatorial group theory, Lie algebras, mathematical physics, elliptic functions, and the study of tessellations.*Wik

2016 Marcel Berger, (14 April 1927 – 15 October 2016) one of the world’s leading differential geometers and a corresponding member of the French Academy of Sciences for half a century, passed away at the age of eighty-nine. Marcel Berger’s contributions to geometry were both broad and deep. The classification of Riemannian holonomy groups provided by his thesis has had a lasting impact on areas ranging from theoretical physics to algebraic geometry. His 1960 proof that a complete oriented even-dimensional manifold with strictly quarter-pinched positive curvature must be a topological sphere is the direct ancestor of a vast sector of subsequent research in global Riemannian geometry. Through his many students and collaborators, he created a school which carried the torch of differential geometry into a new era. *Notices of the AMS

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