## Friday, 4 January 2019

### On This Day in Math - January 4

HP 35 calculator

The task is ... not so much to see what no one has yet seen; but to think what nobody has yet thought, about that which everybody sees.
~Erwin Schrödinger

The 4th day of the year; it is the smallest composite number. Every positive integer is the sum of at most 4 squares. There are 44 numbers in a year which can not be expressed with less than four squares.  The smallest is 7, the largest is 359

Brocard conjectured that there are at least four primes between the squares of any two consecutive primes, with the exception of 2 and 3.

For any number k, real or complex, $4 = k^2 - (k+1)^2 - (k+2)^2 + (k+3)^2$

Fourth dimension has more regular "solids" than other dimensions. Euclid, in the Elements, proves that there are exactly five regular solids in three dimensions. Schläfli proves that there are exactly six regular solids in four dimensions, There are no higher dimensions with more.

EVENTS

1652-3 Seth Ward writes to Oughtred sending measurements of the “recent comet” (Dec of 1652) “Being last week at London I called on Mr. Gratorex, who shewed me a letter which he had received from you concerning the late comet, wherein you desired that he would communicate your observations to such as he should meet with, and desire them to do the like. I took the boldness, therefore, to transcribe that part of your letter which concerned it, and I have here inclosed sent you such observations as were in my absence (for I was then in a journey) made here by Mr. Rooke, and one who belongs to me. “ *De Morgan, Correspondence of Scientific Men of the Seventeenth Century.

1754 Kings College, renamed Columbia College in 1784, founded in New York City by royal charter of George II of Great Britain. Now Columbia University, it is the oldest institution of higher learning in the state of New York, the fifth oldest in the United States, and one of the country's nine Colonial Colleges founded before the American Revolution.*Wik

1845 The Italian geometer Giusto Bellavitis (1803–1880) was appointed, via a competitive examination, full professor of descriptive geometry at the University of Padua. He held no degrees until the university awarded an honorary doctorate in philosophy and mathematics the following year. *VFR

In 1851, The first observation by the Airy transit circle was taken on 4 January 1851, three days later than Airy had intended due to the English weather. Its importance for everyone dates from a conference held in Washington DC in 1884 to create an international time-zone system. It was agreed that the meridian line marked by the cross-hairs in the Airy Transit Circle eyepiece would indicate 0° longitude and the start of the Universal Day.*Royal Observatory Web page
The circle remained in continual use until 1938, and the last ever observation was taken in 1954.the Airy Transit Circle was first used at the Royal Observatory, Greenwich. The instrument was designed by George Biddell Airy, the Astronomer Royal. It was set up on the Prime Meridian - the north-south line of longitude 0° - which marks the start of the Universal day for the world. The time at which a star passed over the meridian was measured with a regulator (an extremely accurate clock). The transit was used to measure the angle of a star at that instant. From this data, the co-ordinates of that star could be determined and plotted on a star chart. Navigation at sea depended on the accuracy of these charts, and the Airy Transit Circle was a great improvement on the previous technology.*TIS

In 1912, the closest approach to earth by the moon was 221,441 miles apart center to center..(In 2013 the Moon will make its closest approach to the Earth (at perigee) for the year on Sunday, 23 June, at 11:11 (UTC), and at this time the Moon will be 356,989 km from the Earth. )*Bob Mrotek

1952 While still a movie actor and before he entered politics, Ronald Reagan wrote to a high school student who had asked advice on how to become a sports announcer (one of Reagan’s earlier jobs). In the letter Reagan confessed that he had a weakness in mathematics. [Eves, Return to Mathematical Circles, ◦33.] *VFR

1958 The first artificial earth satellite, the Russian Sputnik(companion) I, fell out of orbit and burned up on re-entering earth's atmosphere.

1972 Hewlett-Packard introduces the HP-35, the first scientific handheld calculator and the final step in ending reliance on slide rules among scientists and students alike. The HP-35 was named for its 35 keys, weighed nine ounces, and sold for \$395. One of the tests HP co-founder Dave Packard applied to the device was to throw it across his office and see if it still worked. It did. *CHM

1987 The New York Times reported that an Energy Expo in Seattle unveiled “high-tech, energy-efficient buildings. ... Some of the judges’ favorites include ... an office building with ‘parabolic’ lighting ﬁxtures designed to focus light better than ﬂat systems.” Isn’t it amazing how long it takes technology to catch up with theory? *VFR

In 2004, Spirit, a robot rover landed on Mars to analyze the planet's rocks, looking for evidence of water. It has taken the only photo of Earth from another planet. Surviving dust storms, it far outlasted its expected useful life. A twin robot rover, Opportunity, landed three weeks after Spirit on the other side of the planet.*TIS

BIRTHS
 Rubens illustration of projection
1567 François d'Aguilon (also d'Aguillon or in Latin Franciscus Aguilonius) (4 January 1567 – 20 March 1617) was a Belgian Jesuit mathematician, physicist and architect.
D'Aguilon was born in Brussels. He became a Jesuit in 1586. In 1611, he started a special school of mathematics, in Antwerp, which was intended to perpetuate mathematical research and study in among the Jesuits. This school produced geometers like André Tacquet and Jean Charles della Faille.
His book, Opticorum Libri Sex philosophis juxta ac mathematicis utiles (Six Books of Optics, useful for philosophers and mathematicians alike), published in Antwerp in 1613, was illustrated by famous painter Peter Paul Rubens. It was notable for containing the principles of the stereographic and the orthographic projections, and it inspired the works of Desargues and Christiaan Huygens. *Wik

1643 Sir Isaac Newton was born in the manor house of Woolsthorpe, near Grantham in Lincolnshire. Although by the calendar in use at the time of his birth he was born on Christmas Day 1642, we give the date of 4 January 1643 which is the "corrected" Gregorian calendar date bringing it into line with our present calendar. (The Gregorian calendar was not adopted in England until 1752.) *SAU

1797 Wilhelm Beer (4 Jan 1797, 27 Mar 1850 at age 53) German banker and amateur astronomer who owned a fine Fraunhofer refractor which he used in his own a private observatory. He worked jointly with Johann Heinrich von Mädler, to produce the first large-scale moon map to be based on precise micrometric measurements. Their four-year effort was published as Mappa Selenographica (1836). This fine lithographed map provided the most complete details of the Moon's surface in the first half of the 19th century. It was the first lunar map divided in quadrants, and recorded the Moon's face in great detail detail. It was drawn to a scale of scale of just over 38 inches to the moon's diameter. Mädler originated a convention for naming minor craters with Roman letters appended to the name of the nearest large crater (ex. Egede A,B, and C).

1809 Louis Braille (4 Jan 1809; 6 Jan 1852) French educator who developed a tactile form of printing and writing, known as braille, since widely adopted by the blind. He himself knew blindness from the age four, following an accident while playing with an awl. In 1821, while Braille was at a school for the blind, a soldier named Charles Barbier visited and showed a code system he had invented. The system, called "night writing" had been designed for soldiers in war trenches to silently pass instructions using combinations of twelve raised dots. Young Braille realized how useful this system of raised dots could be. He developed a simpler scheme using six dots. In 1827 the first book in braille was published. Now the blind could also write it for themselves using a simple stylus to make the dots.*TIS

1846 Edward Hibberd Johnson (4 Jan 1846; 9 Sep 1917) was an American electrical engineer and inventor. He spent many years in various business projects with Thomas Edison, including being the vice-president of the Edison Electric Light Company. Johnson created the first electric lights on a Christmas tree on 22 Dec 1882.*TIS

1848 Heinrich Suter (4 January 1848, Hedingen near Zurich, Switzerland – 17 March 1922) was a historian of science specializing in Islamic mathematics and astronomy.*Wik

1890 Raymond Woodard Brink (4 Jan 1890 in Newark, New Jersey, USA - 27 Dec 1973 in La Jolla, California, USA) mathematician who studied at Kansas State University, Harvard and Paris. He taught at the University of Minnesota though he spent a year in Edinburgh in 1919. He worked on the convergence of series. He was a President of the Mathematical Association of America.*SAU

1913 Sixto Ríos García (January 4, 1913; Pelahustán, Toledo - July 8, 2008; Madrid,) was a Spanish mathematician, known as the father of Spanish statistics.
He has held the positions of Director of the School of Statistics at the University of Madrid, Director of the Institute for Operations Research and Statistics CSIC, Director, Department of Statistics, Faculty of Mathematical Sciences at the Complutense University and President of the Spanish Society Operational Research, Statistics and Information. It was academic correspondent of the National Academy of Sciences of Buenos Aires, and organizer and founder, commissioned by Unesco, School of Statistics, University of Caracas. He was a member of the drafting committee of Statistical Abstracts and fellow of the International Statistical Institute and the Institute of Mathematical Statistics. Wik-ES

1940 Brian D. Josephson (4 Jan 1940, ) British physicist who discovered the Josephson effect (1962) - a flow of electric current as electron pairs, called Cooper Pairs, between two superconducting materials that are separated by an extremely thin insulator. This arrangement is called a Josephson Junction. He was a graduate student, 22 years old, at the time. Subsequently, he was awarded a share of the 1973 Nobel Prize for Physics (with Leo Esaki and Ivar Giaever).*TIS

DEATHS

1752 Gabriel Cramer . He is best known for “Cramer’s Rule,” a method for solving systems of simultaneous linear equations using determinants. *VFR Gabriel Cramer (31 July 1704 – 4 January 1752) was a Swiss mathematician, born in Geneva. He showed promise in mathematics from an early age. At 18 he received his doctorate and at 20 he was co-chair of mathematics. In 1728 he proposed a solution to the St. Petersburg Paradox that came very close to the concept of expected utility theory given ten years later by Daniel Bernoulli​. He published his best known work in his forties. This was his treatise on algebraic curves, "Introduction à l'analyse des lignes courbes algébriques", published in 1750. It contains the earliest demonstration that a curve of the nth degree is determined by n(n + 3)/2 points on it, in general position. He edited the works of the two elder Bernoullis; and wrote on the physical cause of the spheroidal shape of the planets and the motion of their apsides (1730), and on Newton's treatment of cubic curves (1746). He was professor at Geneva, and died at Bagnols-sur-Cèze.*Wik

1826 Nikolai Fuss (30 Jan 1755 in Basel, Switzerland - 4 Jan 1826 in St Petersburg, Russia) was a Swiss mathematician whose most important contribution was as amanuensis to Euler after he lost his sight. Most of Fuss's papers are solutions to problems posed by Euler on spherical geometry, trigonometry, series, differential geometry and differential equations. His best papers are in spherical trigonometry, a topic he worked on with A J Lexell and F T Schubert. Fuss also worked on geometrical problems of Apollonius and Pappus. He made contributions to differential geometry and won a prize from the French Academy in 1778 for a paper on the motion of comets near some planet Recherche sur le dérangement d'une comète qui passe près d'une planète (see [4]). Fuss won other prizes from Sweden and Denmark. He contributed much in the field of education, writing many fine textbooks. *SAU

1882 John William Draper (May 5, 1811 – January 4, 1882) was an American (English-born) scientist, philosopher, physician, chemist, historian and photographer. He is credited with producing the first clear photograph of a female face (1839–40) and the first detailed photograph of the Moon (1840). He was also the first president of the American Chemical Society (1876–77) and a founder of the New York University School of Medicine. One of Draper's books, History of the Conflict between Religion and Science, received worldwide recognition and was translated into several languages, but was banned by the Catholic Church. His son, Henry Draper, and his granddaughter, Antonia Maury, were astronomers, and his eldest son, John Christopher Draper, was a chemist. *Wik

1950 Virgil Snyder (9 Nov 1869 in Dixon, Iowa, USA 4 Jan 1950 in Ithaca, New York, USA ) Up until the 1920s, Snyder's prolific output and his talents as a teacher made him, together with Frank Morley of Johns Hopkins, one of the most influential algebraic geometers in the nation. Together with Henry White, in fact, Snyder emerged as a principal heir to Klein's geometric legacy. *SAU

1961 Erwin Schrödinger (12 Aug 1887, 4 Jan 1961) Austrian theoretical physicist who shared the 1933 Nobel Prize for Physics with the British physicist P.A.M. Dirac. Schrödinger took de Broglie's concept of atomic particles as having wave-like properties, and modified the earlier Bohr model of the atom to accommodate the wave nature of the electrons. This made a major contribution to the development of quantum mechanics. Schrödinger realized the possible orbits of an electron would be confined to those in which its matter waves close in an exact number of wavelengths. This condition, similar to a standing wave, would account for only certain orbits being possible, and none possible in between them. This provided an explanation for discrete lines in the spectrum of excited atoms.*TIS

1990 Harold E(ugene) Edgerton (6 Apr 1903, 4 Jan 1990) American electrical engineer and ultra-high-speed photographer. As a graduate at the Massachusetts Institute of Technology (1926), he used a strobe light in his studies. By 1931, he applied the strobe to ultra-high-speed photography. He formed a company (1947) to specialize in electronic technology, which led to inventing the Rapatronic camera, capable of photographing US nuclear bomb test explosions from a distance of 7 miles. Throughout his career he applied high-speed photography as a tool in various scientific applications. He also developed sonar to study the ocean floor. Using side-scan sonar, in 1973, he helped locate the sunken Civil War battleship USS Monitor, lost since 1862, off Cape Hatteras, NC. *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