Sunday 1 February 2015

On This Day in Math - February 1

Some physicists describe gravity in terms of ten dimensions all curled up. But those aren't real words—just placeholders, used to refer to parts of abstract equations.
~Scott Adams

The 32nd day of the year; 32 is conjectured to be the highest power of two with all prime digits. *Number Gossip (Could 27 hold the similar property for powers of three?)
Also, 131 is the 32nd prime and the sum of the digits of both numbers is 5. 32 & 131 is the smallest n, P(n) with this property.
\( 32 = 1^1 + 2^2 + 3^3 \)
On an 8x8 chessboard, the longest closed non-crossing knight's path is 32 moves.

1634 Descartes writes from Deventer in Holland to Father Marin Mersenne and explains that he had retracted his book, The World, which supported the Copernican theory, “thus losing four years of my work in order to give full obeisance to the Church…. I do not dare publish my own sentiment.” Ironically it would be a decision by the Dutch Protestant theologians to declare his writings as “atheistic” that led to his leaving Holland to accept a position in Sweden which led to his death. *VFR (See 1650 below)

1650 Descartes contracted a chill, while tutoring Queen Christina of Sweden, which developed into inflamation of the lungs. 10 days later he was dead at age 53. *J. F. Scott, The Scientific World of Rene Descartes, p. 6.

1673 (1672 os) Leibniz, during his first visit to London, exhibited his calculating machine to the Royal Society. *VFR Called the Stepped Reckoner, it as the first machine that could do all four arithmetic operations. It was about this time that Leibniz says he met Pell at the house of Robert Boyle and during a discussion of sequences and series Leibniz was informed that this work had been done by Nicholas Mercator. (with hints at plagiarism from Mouton.)

1891 The first bimagic square (the numbers form a magic square, and when the numbers are replaced by their squares, they still form a magic square) in the world by G. Pfeffermann in France. Created in 1890, this 8x8 square was published in a french magazine "Les Tablettes du Chercheur" January 15, 1891, with only half of the numbers shown as a problem for the readers. The solution, and so the full first bimagic square, was published in the next issue of "Les Tablettes du Chercheur", February 1st 1891. Here is the original puzzle and the solution. *The Magic Encyclopedia ™ DataBase The famous Edouard Lucas (1842-1891), who was a writer of articles in Les Tablettes, wrote that this first bimagic square was a "very remarkable square". He would go on to prove that no 3x3 bimagic square could exist, even with non-consecutive digits, and that no 4x4 could be created with consecutive digits. Unfortunately he also died that same year (see link above) in as the result of a most unusual accident. 8x8 is still the smallest order bimagic square that can be formed with consecutive digits.

The lower image shows the squares of the digits in the first square.  images from *

1894 Nature magazine covers Newcomb's speech to the New York Mathematical Society. On 28 December, 1893, Simon Newcomb had given a speech to the Society with comments on the fourth dimension; "It is a perfectly legitimate exercise .... if we should not stop at three dimensions in geometry, but construct one for space having four... and there is room for an indefinite number of universes". He also called his speculations on the fourth dimension, "the fairlyland of geometry."
The speech appears a short time later on February 1, 1894 in Nature. His comments would also be commented on in H. G. Wells, Time Machine. "But some philosophical people have been asking ... - Why not another direction at right angles to the other three? ... Professor Simon Newcomb was expanding on this only a month or so ago." *Alfred M. Bork, The Fourth Dimenson in Nineteenth-Century Physics, Isis, Sept 1964 pg 326-338

1911, Thomas Jennings was found guilty with the first use of fingerprint evidence in the U.S. He was convicted at the Criminal Court of Cook County for killing Clarence B. Hiller. Upon appeal, 21 Dec 1911, the Illinois Supreme Court ruled the evidence was admissible. Two months later, Jennings was executed on 16 Feb 1912. *TIS  I have since read of a case in New York City (trial on Jan 12, 1911) in which fingerprint evidence found at the site of a crime was used to identify suspects and when investigated, they were found in possession of the stolen goods.  However “The prisoners broke down…and pleaded to burglary in the third degree.”  The Sun Newspaper noted “It was the first conviction by the finger print method obtained in this country.” *

1972, the first scientific hand-held calculator (HP-35) was introduced for $395 by Hewlett-Packard. (Wikipedia gives this price as $795, either way, YIKES!) Its model number came from having 35 keys. It was the first hand-held calculator able to perform logarithmic and trigonometric functions with one keystroke. The red LED display could give scientific notation up to 10 digits mantissa and 2 digits exponent. The price was reduced several times, eventually to $195. By Feb 1975 (when production of the model was discontinued), 300,000 had been sold. The numbers and functions for calculations were entered in "Reverse Polish Notation" (RPN), which used an "ENTER" key but needed no parentheses or "=" key. Its size was 79 mm x 147 mm x 34 mm (3.1" x 5.8" x 1.4"), ran on rechargeable batteries, and its electronics used several integrated circuits.*TIS

1991 Sun Microsystems Starts JavaTM Technology.
Mike Sheridan, James Gosling, and Patrick Naughton of Sun Microsystems, Inc. start to develop JavaTM technology. It grew out of a Sun project in embedded control called *7 (Star Seven). Naughton focused on Aspen graphics system, Gosling on programming language ideas, Sheridan on business development.*CHM

2003 The seven-member crew of STS-107 died when the Columbia orbiter disintegrated during reentry into the Earth's atmosphere. STS-107 was the 113th flight of the Space Shuttle program, and the final flight of Space Shuttle Columbia. The mission launched from Kennedy Space Center on 16 January 2003, and during its 16 days in orbit conducted a multitude of international scientific investigations.
The Columbia Accident Investigation Board determined the failure was caused by a piece of foam that broke off during launch and damaged the thermal protection system components (reinforced carbon-carbon panels and thermal protection tiles) on the leading edge of the left wing of the orbiter. During re-entry the damaged wing slowly overheated and came apart, eventually leading to loss of control and disintegration of the vehicle.
2012 a fireball over central Texas wowed thousands of onlookers in the Dallas-Fort Worth area. *Wik
"It was brighter and long-lasting than anything I've seen before," reports eye-witness Daryn Morran. "The fireball took about 8 seconds to cross the sky. I could see the fireball start to slow down; then it exploded like a firecracker artillery shell into several pieces, flickered a few more times and then slowly burned out." Another observer in Coppell, Texas, reported a loud double boom as "the object broke into two major chunks with many smaller pieces." There would be over seven different "fireball" events in the month, NASA's Meteoroid Environment Office called that, "about normal".

1561 Henry Briggs (Feb ? 1561, 26 Jan 1630) English mathematician who constructed the decimal-based common (Briggsian) logarithms that use base 10, and popularized them in Europe. John Napier had already introduced “natural” logarithms (1614) that use the base e (2.71...) [I think this is an error. Napier's log tables were not base e, nor any other particular base as they produced smaller log values for larger numbers, with log(107=0.]. Briggs visited Napier in 1616, and they agreed on the merit of using base 10 {with log(1)=0}. By 1624, Briggs had calculated logarithm tables to 14 decimal places, published in Arithmetica Logarithmica. These tables vastly simplified the task of mathematicians, astronomers and other scientists making otherwise long and tedious calculations. Briggs was professor of astronomy at Oxford from 1619. He is also credited with developing the modern method of long division. Briggs was strongly opposed to astrology, at a time when it was otherwise widely accepted by many scholars, including Napier. *TIS
A story is told that when Briggs first journeyed to Scotland to meet Napier, after he was shown into the room they stood in silence for almost a quarter of an hour, "each beholding the other with admiration".

1840 William Allen Whitworth (1 February 1840 – 12 March 1905) was an English mathematician and a priest in the Church of England.
As an undergraduate, Whitworth became the founding editor in chief of the Messenger of Mathematics, and he continued as its editor until 1880. He published works about the logarithmic spiral and about trilinear coordinates, but his most famous mathematical publication is the book Choice and Chance: An Elementary Treatise on Permutations, Combinations, and Probability (first published in 1867 and extended over several later editions). The first edition of the book treated the subject primarily from the point of view of arithmetic calculations, but had an appendix on algebra, and was based on lectures he had given at Queen's College. Later editions added material on enumerative combinatorics (the numbers of ways of arranging items into groups with various constraints), derangements, frequentist probability, life expectancy, and the fairness of bets, among other topics.
Among the other contributions in this book, Whitworth was the first to use ordered Bell numbers to count the number of weak orderings of a set, in the 1886 edition. These numbers had been studied earlier by Arthur Cayley, but for a different problem. He was the first to publish Bertrand's ballot theorem, in 1878; the theorem is misnamed after Joseph Louis François Bertrand, who rediscovered the same result in 1887. He is the inventor of the E[X] notation for the expected value of a random variable X, still commonly in use, and he coined the name "subfactorial" for the number of derangements of n items.
Another of Whitworth's contributions, in geometry, concerns equable shapes, shapes whose area has the same numerical value (with a different set of units) as their perimeter. As Whitworth showed with D. Biddle in 1904, there are exactly five equable triangles with integer sides: the two right triangles with side lengths (5,12,13) and (6,8,10), and the three triangles with side lengths (6,25,29), (7,15,20), and (9,10,17). *Wik
1847 Eduardo Torroja Caballe (February 1, 1847 – June 1, 1918) was a Spaniard mathematician born in the city of Tarragona, Spain. His father was Juan Torroja, a Professor of Geography and History. He continued his studies at Complutense University, where he obtained the degrees of Bachelor of Science (1864), Masters of Science (1866), Architect (1869) and Doctor of Science (1873) in Mathematics.
Very early in his studies he became a disciple of Karl Georg Christian von Staudt, whose ideas of Geometry he embraced and promoted among his fellow mathematicians for the rest of his life. The strong presence of Geometry in Spain's mathematical curriculum, even to this day, can be traced back to Torroja's influence. *Wik

1890 Jovan Karamata (February 1, 1902–August 14, 1967) was one of the greatest Serbian mathematicians of the 20th century. He is remembered for contributions to analysis, in particular, the Tauberian theory and the theory of slowly varying functions. Karamata was one of the founders of the Mathematical Institute of the Serbian Academy of Sciences and Arts in 1946. *Wik

1900 John Charles Burkill FRS (1 February 1900 Holt, Norfolk, England – 6 April 1993 Sheffield, England) was an English mathematician who worked on analysis and introduced the Burkill integral. He was elected a fellow of the Royal Society in 1953*Wik

1905 Ernst Carl Gerlach Stueckelberg (February 1, 1905, September 4, 1984) was a Swiss mathematician and physicist. In 1938 he recognized that massive electrodynamics contains a hidden scalar, and formulated an affine version of what would become known as the Abelian Higgs mechanism. He also proposed the law of conservation of baryon number. In 1953 he and the mathematician Andre Petermann discovered the renormalization group.
He was awarded the Max Planck medal.*Wik

1905 Emilio Gino Segrè (1 Feb 1905; 22 Apr 1989) was an Italian-born American physicist who was cowinner, with Owen Chamberlain of the United States, of the Nobel Prize for Physics in 1959 for the discovery of the antiproton, an antiparticle having the same mass as a proton but opposite in electrical charge. He also created atoms of the man-made new element technetium (1937) and astatine (1940). Technetium occupied a hitherto unfilled space in the body of the Periodic Table, and was the first man-made element not found in nature. Astatine exists naturally only in exceedly small quantities because as a decay product of larger atoms, and having a half-life of only a few days, it quickly disappears by radioactively decay to become atoms of another element.*TIS

1905 Lloyd Viel Berkner (1 Feb 1905; 4 Jun 1967) American physicist and engineer who first measured the extent, including height and density, of the ionosphere (ionized layers of the Earth's atmosphere), leading to a complete understanding of radio wave propagation and he helped develop radar systems, especially the Distant Early Warning system. He later investigated the origin and development of the Earth's atmosphere. Early in his career, he worked on radio navigation beacons for the Airways division of the Bureau of Lighthouses (1927-28), as radio engineer on the Byrd Antarctic expedition (1928-30). Returning to the U.S. Bureau of Standards (1930-33) he studied the ionosphere using radio-pulse transmissions, then terrestial magnetism with the Carnegie Institution (1933-51). *TIS

1907 Melba Newell Phillips (February 1, 1907 - November 8, 2004) was an American physicist and science educator. She completed her doctoral studies under J. Robert Oppenheimer and was also known for refusing to testify before a U.S. Senate Judiciary Committee's subcommittee on internal security, her actions leading to her dismissal by Brooklyn College.
Melba Phillips was born in Hazleton, Indiana. She graduated from high school at the age of 15 and went on to study Mathematics at Oakland City College, Indiana graduating in 1926. She received a master's degree in physics from Battle Creek College of Michigan in 1928 and her doctorate in physics in 1933 at the University of California, Berkeley.
Phillips's supervisor at Berkeley was J. Robert Oppenheimer, who would later become scientific head of the Allied atomic bomb effort, the Manhattan Project. Together they described the Oppenheimer-Phillips effect explaining the behavior of accelerated nuclei of radioactive hydrogen atoms in 1935. *Wik

1916 George Whitelaw Mackey (February 1, 1916 in St. Louis, Missouri – March 15, 2006 in Belmont, Massachusetts) was an American mathematician.
Mackey's main areas of research were in the areas of representation theory, ergodic theory, and related parts of functional analysis. Earlier in his career Mackey did significant work in the duality theory of locally convex spaces, which provided tools for subsequent work in this area, including Alexander Grothendieck's work on topological tensor products.
He has written numerous survey articles connecting his research interests with a large body of mathematics and physics, particularly quantum mechanics and statistical mechanics. He was among the first five recipients of William Lowell Putnam fellowships in 1938.*Wik

1903 Sir George Gabriel Stokes (13 Aug 1819, 1 Feb 1903)(1st Baronet) British mathematical physicist who studied viscous fluids and formulated his law of viscosity for the speed of a solid sphere falling in a fluid. Other laws and mathematical work for which he is known includes Stokes's theorem, in the field of vector analysis. Stokes also worked in optics, the wave theory of light, diffraction (1849), the ultraviolet spectrum and other spectrum analysis. He coined the word fluorescence (1852) while studying that phenomenon and was a founder of the field of geodesy with his study of variations in gravity (1849). From 1849 until his death in 1903, he held the Lucasian Chair of Mathematics at Cambridge (held earlier by Isaac Newton, and currently by Stephen Hawking). He came from a family with generations of scientists, mathematicians and engineers. *TIS

1958 Clinton Joseph Davisson (22 Oct 1881, 1 Feb 1958) American experimental physicist who shared the Nobel Prize for Physics in 1937 with George P. Thomson of England for discovering that electrons can be diffracted like light waves, thus verifying the thesis of Louis de Broglie that electrons behave both as waves and as particles. Davisson studied the effect of electron bombardment on surfaces, and observed (1925) the angle of reflection could depend on crystal orientation. Following Louis de Broglie's theory of the wave nature of particles, he realized that his results could be due to diffraction of electrons by the pattern of atoms on the crystal surface. Davisson worked with Lester Germer in an experiment in which electrons bouncing off a nickel surface produced wave patterns similar to those formed by light reflected from a diffraction grating, and supporting de Broglie's electron wavelength = (h/p). This discovery has been applied to the study of nuclear, atomic, and molecular structure. Davisson helped develop the electron microscope which uses the wave nature of electrons to view details smaller than the wavelength of visible light.*TIS

1961 Émile Henriot (2 July 1885 - 1 February 1961) was a French chemist notable for being the first to show definitely that potassium and rubidium are naturally radioactive.
He investigated methods to generate extremely high angular velocities, and found that suitably placed air-jets can be used to spin tops at very high speeds - this technique was later used to construct ultracentrifuges.
He was a pioneer in the study of the electron microscope. He also studied birefringence and molecular vibrations.
He obtained his DSc in physics in 1912 the Sorbonne, Paris, under Marie Curie. *Wik

1970 Alfréd Rényi (20 March 1921 – 1 February 1970) was a Hungarian mathematician who made contributions in combinatorics, graph theory, number theory but mostly in probability theory. He proved, using the large sieve, that there is a number K such that every even number is the sum of a prime number and a number that can be written as the product of at most K primes. See also Goldbach conjecture.
In information theory, he introduced the spectrum of Rényi entropies of order α, giving an important generalisation of the Shannon entropy and the Kullback-Leibler divergence. The Rényi entropies give a spectrum of useful diversity indices, and lead to a spectrum of fractal dimensions. The Rényi–Ulam game is a guessing game where some of the answers may be wrong.
He wrote 32 joint papers with Paul Erdős, the most well-known of which are his papers introducing the Erdős–Rényi model of random graphs. Rényi, who was addicted to coffee, invented the quote: "A mathematician is a device for turning coffee into theorems.", which is generally ascribed to Erdős. The sentence was originally in German, being a wordplay on the double meaning of the word Satz (theorem or residue of coffee). *Wik

1976 Werner Karl Heisenberg (5 Dec 1901, 1 Feb 1976) was the German physicist and philosopher who discovered a way to formulate quantum mechanics in terms of matrices (1925). For that discovery, he was awarded the Nobel Prize for Physics for 1932. In 1927 he published his indeterminacy, or uncertainty, principle, upon which he built his philosophy and for which he is best known. He also made important contributions to the theories of the hydrodynamics of turbulence, the atomic nucleus, ferromagnetism, cosmic rays, and elementary particles, and he planned the first post-World War II German nuclear reactor, at Karlsruhe, then in West Germany. *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


.mau. said...

If I remember correctly, Napier's logarithms were in a base roughly equal to 1/e.

Since the base is negative, they went "the wrong way"...

Pat's Blog said...

I think this 1/e is also not correct. The best approximation between them I know of is

Napier's Log(x) appx = 9999999.5 (7 ln(10) - ln(x) )