## Thursday, 18 February 2016

### On This Day in Math - February 18

##### Leon Battista Alberti, De pictura and Elementa *Museo Galileo
The power of mathematics rests on its evasion of all unnecessary thought and on its wonderful saving of mental operations.
~Ernst Mach

The 49th day of the year; lots of numbers are squareful (they are divisible by a square number) but 49 is the smallest number so that it, and both its neighbors are squareful. (Many interesting questions arise for students.. what's next, can there be four in a row?, etc)

And Prof. William D Banks of the University of Missouri has recently proved that every integer in base ten is the sum of 49 or less palindromes. (August 2015) (Building on Prof. Banks groundbreaking work, by February 22, 2016 JAVIER CILLERUELO AND FLORIAN LUCA had proved that for any base > 4
EVERY POSITIVE INTEGER IS A SUM OF THREE PALINDROMES )

The 49th Mersenne prime is discovered. On Jan 19th, 2016 The GIMPS program announced a new "largest known" prime, 274,207,281 -1. called M74,207,281 for short, the number has 22,338,618 digits.

EVENTS
3102 B.C. The Kaliyuga begins according to the Indian mathematician Aryabhata (born A.D. 476). He believed all astronomical phenomena were periodic, with period 4,320,000= 20 × 603 years, and that all the planets had mean longitude zero on this date. [College Mathematics Journal, 16 (1985), p. 169.] *VFR

1670 “Joannes Georgius Pelshower [Regimontanus Borussus] giving me a visit, and desiring an example of the like, I did that night propose to myself in the dark without help to my memory a number in 53 places: 2468135791011121411131516182017192122242628302325272931 of which I extracted the square root in 27 places: 157103016871482805817152171 proxim´e; which numbers I did not commit to paper till he gave me another visit, March following, when I did from memory dictate them to him.” So wrote John Wallis. [American Journal of Psychology, 4(1891), 38] *VFR

1673: Robert Hooke writes in his Journal: "Bought Copernicus tower hill 2sh " *‏@HookesLondon Thony Christie points out that current first editions run about $2,500,000$ GB Pounds.

1727 Leonhard Euler defends his De Sono essay in a public disputation at the law auditorium at Basal. His paper had been submitted as his "habilitationsschrift", part of his application for the Physics Professorship at Basal. Fortunately, he did not get the position, and soon departed for a position at Petersburg Academy of Science in Russia. Among other competitors overlooked for the position was Jakob Hermann. *Ronald S. Calinger; Leonhard Euler: Mathematical Genius in the Enlightenment

1772 the Royal Danish Academy of Sciences and Letters presented Alexander Wilson with a gold medal for his work on sunspots. Wilson was a Scottish surgeon, type-founder, astronomer, mathematician and meteorologist and the first scientist to record the use of kites in meteorological investigations. Wilson noted that sunspots viewed near the edge of the Sun's visible disk appear depressed below the solar surface, a phenomenon referred to as the Wilson effect. When the Royal Danish Academy of Sciences and Letters announced a prize to be awarded for the best essay on the nature of solar spots, Wilson submitted an entry which won. *Wik

1879 “I will do the same for the young women that I do for the young men. I shall take pleasure in giving gratuitous instruction to any person whom I ﬁnd competent to receive it. I give no elementary instruction, but only in the higher mathematics.” Benjamin Peirce to Arthur V. Gilman, president of Harvard. [Scripta Mathematica, 11(1945), 259
*VFR

1879 J. J. Sylvester, in a lecture at the Peabody Institute in Baltimore, read “Rosalind”, a mock-sentimental poem of four hundred lines all ending in “ind”. For the ﬁrst few lines of this dreadful poem, see Osiris, 1(1936), p. 106. *VFR Encyclopedia.com says that Sylvester was the author of this poem, and another which had two hundred lines rhyming with “Winn.” These were products of his later residence in Baltimore. Sylvester had perhaps a better appreciation of music.

In 1913, chemist Frederick Soddy introduced the term "isotope". Soddy was an English chemist and physicist who received the Nobel Prize for Chemistry in 1921 for investigating radioactive substances. He suggested that different elements produced in different radioactive transformations were capable of occupying the same place on the Periodic Table, and on 18 Feb 1913 he named such species "isotopes" from Greek words meaning "same place." He is credited, along with others, with the discovery of the element protactinium in 1917. *TIS He also wrote the mathematical poem, The Kiss Precise, which includes a solution to Descartes Circle Problem. the poem begins:
For pairs of lips to kiss maybe
Involves no trigonometry.
'Tis not so when four circles kiss
Each one the other three.
To bring this off the four must be
As three in one or one in three.
If one in three, beyond a doubt
Each gets three kisses from without.
If three in one, then is that one
Thrice kissed internally.
The complete poem and more about the history of the problem can be found here.

1930 Clyde Tombaugh (1906–1997) discovered Pluto on photographic plates under the direction of V M Slipher at the Lowell Observatory at Flagstaff, Az. For 45 minutes, before he showed his superiors, he was the only person in the world who knew it existed. When he later went to college he was not allowed to take Astronomy I, the instructor thinking it unsuitable for the discoverer of a planet. (On August 24th of 2006 the International Astronomical Union decided to rescind Pluto’s status as a planet and reclassify it as another entity called a “dwarf planet”. ) *FFF, pg 537

2006 The game of Connect Four was first solved by James D. Allen (Oct 1, 1988), and independently by Victor Allis (Oct 16, 1988). First player can force a win. Strongly solved by John Tromp's 8-ply database (Feb 4, 1995). It was weakly solved for all boardsizes where width+height is at most 15 (Feb 18, 2006). *Wik

BIRTHS
1201 Muhammad ibn Muhammad ibn al-Hasan al-Tusi (18 Feb 1201; 26 Jun 1274 at age 73) Persian philosopher, scientist, mathematician and astronomer who made outstanding contributions in his era. When The Mongol invasion, started by Genghis Khan, reached him in 1256, he escaped likely death by joining the victorious Mongols as a scientific adviser. He used an observatory built at Maragheh (finished 1262), assisted by Chinese astronomers. It had various instruments such as a 4 meter wall quadrant made from copper and an azimuth quadrant which was Tusi's own invention. Using accurately plotted planetary movements, he modified Ptolemy's model of the planetary system based on mechanical principles. The observatory and its library became a center for a wide range of work in science, mathematics and philosophy. He was known by the title Tusi from his place of birth (Tus)*TIS

1404 Leon Battista Alberti (18 Feb 1404; 25 Apr 1472 at age 68) Italian artist and geometrist who “wrote the book,” the first general treatise Della Pictura (1434) on the the laws of perspective, establishing the science of projective geometry. Alberti also worked on maps (again involving his skill at geometrical mappings) and he collaborated with Toscanelli who supplied Columbus with the maps for his first voyage. He also wrote the first book on cryptography which contains the first example of a frequency table. *TIS
. This noted architect took up the study of mathematics for relaxation. He contributed to the study of perspective. *VFR

1677 Jacques Cassini (18 Feb 1677; 16 Apr 1756 at age 79) French astronomer whose direct measurement of the proper motions of the stars (1738) disproved the ancient belief in the unchanging sphere of the stars. He also studied the moons of Jupiter and Saturn and the structure of Saturn's rings. His two major treatises on these subject appeared in 1740: Elements of Astronomy and Astronomical Tables of the Sun, Moon, Planets, Fixed Stars, and Satellites of Jupiter and Saturn. He also wrote about electricity, barometers, the recoil of firearms, and mirrors. He was the son of astronomer, mathematician and engineer Giovanni Cassini (1625-1712) with whom he made numerous geodesic observations. Eventually, he took over his father's duties as head of the Paris Observatory.*TIS Cassini was born at the Paris Observatory and died at Thury, near Clermont. Admitted at the age of seventeen to membership of the French Academy of Sciences, he was elected in 1696 a fellow of the Royal Society of London, and became maître des comptes in 1706. *Wik

1745 Count Alessandro Giuseppe Antonio Anastasio Volta (18 Feb 1745; 5 Mar 1827 at age 82) Italian physicist who invented the electric battery (1800), which for the first time enabled the reliable, sustained supply of current. His voltaic pile used plates of two dissimilar metals and an electrolyte, a number of alternated zinc and silver disks, each separated with porous brine-soaked cardboard. Previously, only discharge of static electricity had been available, so his device opened a new door to new uses of electricity. Shortly thereafter, William Nicholson decomposed water by electrolysis. That same process later enabled Humphry Davy to isolate potassium and other metals. Volta also invented the electrophorus, the condenser and the electroscope. He made important contributions to meteorology. His study of gases included the discovery of methane. The volt, a unit of electrical measurement, is named after him.*TIS

1832 Octave Chanute(18 Feb 1832, 23 Nov 1910) U.S. aeronaut whose work and interests profoundly influenced Orville and Wilbur Wright and the invention of the airplane. Octave Chanute was a successful engineer who took up the invention of the airplane as a hobby following his early retirement. Knowing how railroad bridges were strengthened, Chanute experimented with box kites using the same basic strengthening method, which he then incorporated into wing design of gliders. Through thousands of letters, he drew geographically isolated pioneers into an informal international community. He organized sessions of aeronautical papers for the professional engineering societies that he led; attracted fresh talent and new ideas into the field through his lectures; and produced important publications. *TIS The town of Chanute, Kansas is named after him, as well as the former Chanute Air Force Base near Rantoul, Illinois, which was decommissioned in 1993. The former Base, now turned to peacetime endeavors, includes the Octave Chanute Aerospace Museum, detailing the history of aviation and of Chanute Air Force base. He was buried in Springdale Cemetery, Peoria, Illinois. *Wik

1838 Ernst Mach (18 Feb 1838; 19 Feb 1916 at age 77) Austrian physicist and philosopher who established important principles of optics, mechanics, and wave dynamics. His early physical works were devoted to electric discharge and induction. Between 1860 and 1862 he studied in depth the Doppler Effect by optical and acoustic experiments. He introduced the "Mach number" for the ratio of speed of object to speed of sound is named for him. When supersonic planes travel today, their speed is measured in terms that keep Mach's name alive. His lifetime interest, however, was in psychology and human perception. He supported the view that all knowledge is a conceptual organization of the data of sensory experience (or observation). *TIS

1844 Jacob Lüroth (18 Feb 1844 in Mannheim, Germany - 14 Sept 1910 in Munich, Germany) Lüroth was taught by Hesse and Clebsch and continued to develop their work on geometry and invariants. He published results in the areas of analytic geometry, linear geometry and continued the directions of his teachers in his publications on invariant theory. In 1869 Lüroth discovered the "Lüroth quartic". This came out of an investigation he was carrying out into when a ternary quartic form could be represented as the sum of five fourth powers of linear forms.
Some of his work on rational curves, published in Mathematische Annalen in 1876, was extended to surfaces by Castelnuovo in 1895. In 1883 Lüroth published his method on constructing a Riemann surface for a given algebraic curve.
Lüroth also worked on the big problem of the topological invariance of dimension. He made some useful progress but this difficult problem was not completely solved until the work of Brouwer in 1911.
Among his other work, Lüroth undertook editing. He was an editor of the complete works of Hesse and of Grassmann. He also has some fine results on logic, a topic he worked on in collaboration with his friend Ernst Schröder.
Von Staudt's ideas of geometry interested Lüroth and he further developed von Staudt's complex geometry. He published Grundriss der Mechanik in 1881. This mechanics book makes heavy use of the vector calculus. *sau

1871 George Udny Yule (18 Feb 1871 in Morham (near Haddington), Scotland - 26 June 1951 in Cambridge, Cambridgeshire, England) graduated in Engineering from University College London and then studied in Bonn. He worked with Karl Pearson on the statistics of regression and correlation. He took a post with an examinations board before being appointed to a Cambridge fellowship. He is best known for his book: Introduction to the Theory of Statistics.*SAU

DEATHS
901 Al-Sabi Thabit ibn Qurra al-Harrani (born c. 836, 18 Feb 901) was a Mesopotamian scholar and mathematician who greatly contributed to preparing the way for such important mathematical discoveries as the extension of the concept of number to (positive) real numbers, integral calculus, theorems in spherical trigonometry, analytic geometry, and non-euclidean geometry. In astronomy he was one of the first reformers of the Ptolemaic system, writing Concerning the Motion of the Eighth Sphere. He believed (wrongly) that the motion of the equinoxes oscillates. Including observations of the Sun, eight complete treatises by Thabit on astronomy have survived. In mechanics he was a founder of statics. He wrote The Book on the Beam Balance in which he finds the conditions for the equilibrium of a heavy beam. *TIS

1851 Karl Gustav Jacob Jacobi (10 Dec 1804; 18 Feb 1851) German mathematician who, with the independent work of Niels Henrik Abel of Norway, founded the theory of elliptic functions. He also worked on Abelian functions and discovered the hyperelliptic functions. Jacobi applied his work in elliptic functions to number theory. He also investigated mathematical analysis and geometry. Jacobi carried out important research in partial differential equations of the first order and applied them to the differential equations of dynamics. His work on determinants is important in dynamics and quantum mechanics and he studied the functional determinant now called the Jacobian. *TIS He died from smallpox, in his 47th year.*VFR

1856 Baron Wilhelm von Biela (19 Mar 1782, 18 Feb 1856 at age 73) Austrian astronomer who was known for his measurement (1826) of a previously known comet as having an orbital period of 6.6 years. Subsequently, known as Biela's Comet, it was observed to break in two (1846), and in 1852 the fragments returned as widely separated twin comets that were not seen again. However, in 1872 and 1885, bright meteor showers (known as Andromedids, or Bielids) were observed when the Earth crossed the path of the comet's known orbit. This observation provided the first concrete evidence for the idea that some meteors are composed of fragments of disintegrated comets.*TIS

1877 Charles Henry Davis (16 Jan 1807; 18 Feb 1877) U.S. naval officer and scientist who published several hydrographic studies, was a superintendent of the Naval Observatory (1865–67, 1874–77) and worked to further scientific progress. Between his naval duties at sea, he studied mathematics at Harvard. He made the first comprehensive survey of the coasts of Massachusetts, Rhode Island, and Maine, including the intricate Nantucket shoals area. He helped establish and then supervised the preparation of the American Nautical Almanac (1849) for several years. Davis was a co-founder of the National Academy of Sciences (1863), and wrote several scientific books.*TIS

1899 (Marius) Sophus Lie (17 Dec 1842; 18 Feb 1899) was a Norwegian mathematician who made significant contributions to the theories of algebraic invariants, continuous groups of transformations and differential equations. Lie groups and Lie algebras are named after him. Lie was in Paris at the outbreak of the French-German war of 1870. Lie left France, deciding to go to Italy. On the way however he was arrested as a German spy and his mathematics notes were assumed to be coded messages. Only after the intervention of French mathematician, Gaston Darboux, was Lie released and he decided to return to Christiania, Norway, where he had originally studied mathematics to continue his work. *TIS

1900 Eugenio Beltrami (November 16, 1835, Cremona – February 18, 1900, Rome) was an Italian mathematician notable for his work concerning differential geometry and mathematical physics. His work was noted especially for clarity of exposition. He was the first to prove consistency of non-Euclidean geometry by modeling it on a surface of constant curvature, the pseudosphere, and in the interior of an n-dimensional unit sphere, the so-called Beltrami–Klein model. He also developed singular value decomposition for matrices, which has been subsequently rediscovered several times. Beltrami's use of differential calculus for problems of mathematical physics indirectly influenced development of tensor calculus by Gregorio Ricci-Curbastro and Tullio Levi-Civita.*Wik
Beltrami studied elasticity, wave theory, optics, thermodynamics, and potential theory, and was among the first to explore the concepts of hyperspace and time as a fourth dimension. His investigations in the conduction of heat led to linear partial differential equations. Some of Beltrami's last work was on a mechanical interpretation of Maxwell's equations. *TIS

1944 Charles Benedict Davenport (1 Jun 1866, 18 Feb 1944 at age 77) American zoologist who contributed substantially to the study of eugenics (the improvement of populations through breeding) and heredity and who pioneered the use of statistical techniques in biological research. Partly as a result of breeding experiments with chickens and canaries, he was one of the first, soon after 1902, to recognize the validity of the newly discovered Mendelian theory of heredity. In Heredity in Relation to Eugenics (1911), he compiled evidence concerning the inheritance of human traits, on the basis of which he argued that the application of genetic principles would improve the human race. These data were at the heart of his lifelong promotion of eugenics, though he muddled science with social philosophy. *TIS

1957 Henry Norris Russell (25 Oct 1877; 18 Feb 1957) American astronomer and astrophysicist who showed the relationship between a star's brightness and its spectral type, in what is usually called the Hertzsprung-Russell diagram, and who also devised a means of computing the distances of binary stars. As student, professor, observatory director, and active professor emeritus, Russell spent six decades at Princeton University. From 1921, he visited Mt. Wilson Observatory annually. He analyzed light from eclipsing binary stars to determine stellar masses. Russell measured parallaxes and popularized the distinction between giant stars and "dwarfs" while developing an early theory of stellar evolution. Russell was a dominant force in American astronomy as a teacher, writer, and advisor. *TIS

1967 Julius Robert Oppenheimer (22 Apr 1904, 18 Feb 1967 at age 62) was an American theoretical physicist and science administrator, noted as director of the Los Alamos laboratory during development of the atomic bomb (1943-45) and as director of the Institute for Advanced Study, Princeton (1947-66). Accusations as to his loyalty and reliability as a security risk led to a government hearing that resulted the loss of his security clearance and of his position as adviser to the highest echelons of the U.S. government. The case became a cause célèbre in the world of science because of its implications concerning political and moral issues relating to the role of scientists in government. *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