Sunday 8 January 2023

On This Day in Math - January 8

For more about the analemma, above, see The Analemma is Gone

But I do not feel obliged to believe that that same God who has endowed us with senses, reason, and intellect has intended to forgo their use and by some other means to give us knowledge which we can attain by them.
~Galileo Galilei

The 8th day of the year; the well known Fibonacci sequence has only two cubes, one and eight

There are 8! minutes in four weeks, say February in a non leap year.

8 and 9  (${2}^{3},{3}^{2}$ are the only consecutive powers of integers. The result,  has only one solution for integers x, y both greater than 1) conjectured in 1842 by Eugène Catalan, was proved in 2002 by Preda Mihăilescu.

3 = 512 and 5+1+2 = 8; (Any other cubes with this property?)

I found a post by Ben Vitale that relates the number eight to the digital root of twin primes.

5 * 7 = 35, 3 + 5 = 8
11 * 13 = 143, 1 + 4 + 3 = 8
17 * 19 = 323, 3 + 2 + 3 = 8
29 * 31 = 899, 8 + 9 + 9 = 26, 2 + 6 = 8
41 * 43 = 1763 1 + 7 + 6 + 3 = 17, 1 + 7 = 8
59 * 61 = 3599, 3 + 5 + 9 + 9 = 26, 2 + 6 = 8
71 * 73 = 5183, 5 + 1 + 8 + 3 = 17, 1 + 7 = 8
101 * 103 = 10403, 1 + 0 + 4 + 0 + 3 = 8

Other than the pair three and five (3x5 = 15, 1+5 = 6), this seems to be true forever.

The only known number to appear 8 times in Pascal's Arithmetic Triangle, is the palindrome 3003.  It is conjectured that, a) no number can appear more than eight times and b) 3003 is the only number that will appear eight times.  *John D. Cook

According to a tweet from @HaggardHawks "cabbaged" is the longest dictionary word that can be spelled using musical notes.  (It's British slang for wasted, by alcohol or drug)

Eight was an unincorporated community located in McDowell County, West Virginia. (Six is an unincorporated community located in the same county. Six is known to be named for a mine. Anyone know about Eight?) The Eight post office closed in 1936.

EVENTS

1610 It is highly probable that Simon Marius (1573 – 1624) court astronomer in Ansbach Franconia used a telescope as an astronomical instrument before Galileo but it is not possible to determine when. On 7th January 1610: Galileo discovers the first three moons of Jupiter. On 8th January 1610: Marius discovers the first three moons of Jupiter independently of Galileo. It was Marius who seems to have first used the names Io, Europa, Ganymede and Calisto, suggested privately by Kepler for the four largest of Jupiter’s moons. Because of the difference between calendars used by Catholic and protestant areas, Marius dated his work on 28 December (Julian) which led to ugly charges of plagiarism. The story, and the eventual exoneration of Marius is well told by Thony Christie here. *Renaissance Mathematicus

1730 In a letter from Euler to Goldbach, Euler first presents an integral representation of the interpolating function of the factorials and explains the properties of a definite integral taken from 0 to 1, where the integrand depends from a further variable. Then he defines the interpolating function for the factorial in the form Z dx(−lx)n. Today we would write this as $n!={\int }_{0}^{1}\left(-ln\left(x{\right)}^{n}\right)dx$ *Detlef Gronau Why Is The Gamma Function So As It Is

On October 13, 1729 (Julian date, it was the 24th in most of the rest of the world using the Gregorian Calendar) Euler had mentioned the gamma function in a letter to Goldbach. In the letter Euler writes

1760 Charles Messier spotted the Great Comet on 8 January 1760 in Paris, by the sword of Orion. *Astronomy

1816 The public was disappointed that Sophie Germain did not appear at the awards ceremony for a prixe offered by the Institut de France on the mathematical theory of elastic surfaces. Germain received an honorable mention.
The competition question had be first set in 1811, and Germain was the only entry. In the reopened competitions of 1813 she was again the only entry, and she recieved an honorable mention. In the 1815 competition she was deemed worthy of the prize. *WM

1828 George S. Ohm conducts the experiments which will give him the result for the physics law which bears his name.  Using boiling water in one cup and ice in another he generates current with a bismuth-electric thermocouple.  He then measured current flow through different lengths of uniform wires by rotation of a torsion head.

*A history of physics in its elementary branches:  By Florian Cajori

1838. William Rowan Hamilton assumes the chair as President of the Royal Irish Academy. “SIR Wm. R. HAMILTON, A. M., President, in the Chair. The President, on taking the Chair, delivered an Address to the Academy. *Proceedings of the Royal Irish Academy (1836-1869), Vol. 1, (1836 - 1840), pp. 106-126

1868 The Newark Advertiser featured a story about a "A Remarkable Mechanical Invention — A Steam Man." The article continued:

Mr. Zadock Deddrick, a Newark machinist, has invented a man; one that, moved by steam, will perform some of the most important functions of humanity; that will, standing upright, walk or run as he is bid, in any direction, and at almost any rate of speed, drawing after him a load whose weight would tax the strength of three draught horses.
The man stands seven feet and nine inches high, the other dimensions of the body being correctly proportioned, making him a second Daniel Lambert, by which name he is facetiously spoken of among the workmen. He weighs five hundred pounds. Steam is generated in the body or trunk, which is nothing but a three-horse power engine, like those used in our steam fire engines. The legs which support it are complicated and wonderful. The steps are taken very naturally and quite easily. As the body is thrown forward upon the advanced foot the other is lifted from the ground with a spring and thrown forward by the steam. Each step or pace advances the body two feet, and every revolution of the engine produces four paces.

Although it did not meet all it's expectations, it did provide inspiration for many more "steam men" in the following years of the 19th Century.
It also inspired what is called the first U.S. science fiction dime novel, The Steam Man of the Prairies by Edward Sylvester Ellis. In the tale the steam-man was constructed by Johnny Brainerd, a teenaged boy, who uses the steam-man to carry him in a carriage on various adventures.

The earliest known steam automaton I am aware of was a Holy Water vending machine in the First Century AD, created by the famous Heron who created the school geometry formula for the Area of a triangle using the three sides. You can see more about that at Holy Cow, Holy Water, Heron invents a Vending Machine

1889 Dr. Herman Hollerith of New York City received patent #395,782 for the ﬁrst tabulating machine. It used punched cards and electrical counters operated by electromagnets. Its ﬁrst extensive use was in the compilation of the population statistics for the eleventh U.S. census in 1890. See 1 June 1890. *FFF
His system was designed to record separate statistical items by means of combinations of holes in a punched card to carry information about an individual. The information contained on numerous cards could then be tallied by passing the cards through electrical counters operated by electromagnets. The patent described its application in compilation of the statistics of the population for the U.S. Census. The first extensive application of this system was for the 1890 census counting data items such as age, sex, occupation, etc., of which tallies could be made in combinations such as how many males of certain ages.*TIS (These punched cards were once a principle element of writing computer programs)

1901, Another apportionment paradox brings angry letters about political mathematics.. John C Bell of Colorado, and Math vrs the State of Maine ..

In 1935, the first U.S. patent for a spectrophotometer was issued to Professor Arthur Cobb Hardy of Wellesley, Mass. (No. 1,987,441) which he called a "photometric apparatus." It could detect two million different shades of colour and make a permanent record chart of the results. The patent was assigned to the General Electric Company of Schenectady, N.Y. which sold the first machine on 24 May 1935. It used a photo-electric device to receive light alternately from a sample and from a standard for comparison. It eliminated any need for the two beams (from sample and from standard) to travel different optical paths which in previous designs could introduce inaccuracies if one path varied from the other*TIS

1947 Norbert Wiener refuses to address a Harvard symposium on computers because they are used “for war work” and announces he will not publish work “which may do damage in the hands of irresponsible militarists.” *VFR

1970 The Bangor Daily News contained this item with the headline “Had to Happen”: “Hell, Norway (UPI)–The water froze in Hell Wednesday when the temperature dropped to 6 degrees below zero.” *VFR

1996 Computer is Used in the Discovery of New Planets. Paul Butler and Geoffrey Marcy announced to the American Astronomical Society that they had discovered two new planets using an unconventional computer technique to analyze the movement of stars. Butler and Marcy let computers analyze spectrographic images of stars for eight years, looking for shifts in the light that would imply it is being pulled by the gravity of a planet. The first discovery, a planet orbiting the star 47 Ursae Majoris​, was announced in December 1995 and, since then, this team found 12 planets outside of our solar system. *CHM

BIRTHS

1587 Johannes Fabricius (8 Jan 1587; c. 1615) Dutch astronomer who was perhaps the first to Publish about sunspots (Thomas Harriot was first known to observe them). On 9 Mar 1611, at dawn, Johannes directed his telescope at the rising sun and saw several dark spots on it. He called his father to investigate this new phenomenon with him. The brightness of the Sun's center was very painful, and the two quickly switched to a projection method by means of a camera obscura. Johannes was the first to publish information on such observations. He did so in his Narratio de maculis in sole observatis et apparente earum cum sole conversione. ("Narration on Spots Observed on the Sun and their Apparent Rotation with the Sun"), the dedication of which was dated 13 Jun 1611. He died aged 29. *TIS Thony Christie has a nice post with a little more about this short life.

1829 Heinrich Eduard Schroeter (January 8th 1829 in Königsberg , January 3 1892 in Breslau ) was a German mathematician , who worked in synthetic geometry in the tradition of Jacob Steiner. *Wik

1852 Giovanni Frattini (January 8, 1852 Rome – July 21, 1925, Rome) was an Italian mathematician, noted for his contributions to group theory.
He entered the University of Rome in 1869, where he studied mathematics with Giuseppe Battaglini, Eugenio Beltrami, and Luigi Cremona, obtaining his PhD. in 1875.*Wik

1868 Sir Frank (Watson) Dyson (8 Jan 1868; 25 May 1939) was a Cambridge-educated, British astronomer, who spent his entire career (except for 5 years in Edinburgh) at the Royal Greenwich Observatory, where he was Astronomer Royal from 1910-33. He directed measurements of terrestrial magnetism, latitude, and time, and he initiated the radio broadcast of time. He determined proper motions of northern stars and completed his portion of the international Carte du Ciel project of photographing the entire sky. Dyson is best known for directing (with Eddington) the 1919 eclipse expedition which confirmed the bending of starlight by the sun's gravitational field. This bending of light, predicted by Einstein, was evidence supporting his general theory of relativity. *TIS

1888 Richard Courant (8 Jan 1888; 27 Jan 1972) German-born American mathematician, who upon joining the faculty of New York University in 1934, began to build the nucleus of a small research group based on the Göttingen model he had experienced as a student of David Hilbert in Germany. Courant's published papers were in variational problems, finite difference methods, minimal surfaces, and partial differential equations. He encouraged the publication of mathematical texts and high quality monographs, such as Methods of Mathematical Physics by Courant and Hilbert. His leadership was commemorated in 1964 when the institute he founded was named the Courant Institute of Mathematical Sciences at New York University.*TIS

1889 Percy John Daniell​ (9 January 1889 – 25 May 1946) was a pure and applied mathematician. In a series of papers published between 1918 and 1928, he developed and expanded a generalized theory of integration and differentiation, which is today known as the Daniell integral. In mathematics, the Daniell integral is a type of integration that generalizes the concept of more elementary versions such as the Riemann integral to which students are typically first introduced. One of the main difficulties with the traditional formulation of the Lebesgue integral is that it requires the initial development of a workable measure theory before any useful results for the integral can be obtained. However, an alternative approach is available, developed by Percy J. Daniell (1918) that does not suffer from this deficiency, and has a few significant advantages over the traditional formulation, especially as the integral is generalized into higher dimensional spaces and further generalizations such as the Stieltjes integral. The basic idea involves the axiomatization of the integral. *Wik

1891 Walther Wilhelm Georg Bothe (8 Jan 1891; 8 Feb 1957) was a German physicist who developed the coincidence method of detecting the emission of electrons by x-rays in which electrons passing through two adjacent Geiger tubes at almost the same time are registered as a coincidental event. He used it to show that momentum and energy are conserved at the atomic level. In 1929 he applied the method to the study of cosmic rays and was able to show that they consisted of massive particles rather than photons. This research brought him a share (with Max Born) in the Nobel Prize for 1954. In 1930, he observed a strange radiation emitted from beryllium when it was exposed to alpha particles, later identified by Chadwick as consisting of neutrons. He built Germany's first cyclotron (1943).*TIS

1923 Bryce Seligman DeWitt (January 8, 1923 – September 23, 2004) was a theoretical physicist who studied gravity and field theories.
He approached the quantization of general relativity, in particular, developed canonical quantum gravity and manifestly covariant methods that use the heat kernel. B. DeWitt formulated the Wheeler–DeWitt equation for the wavefunction of the Universe with John Archibald Wheeler and advanced the formulation of the Hugh Everett's many-worlds interpretation of quantum mechanics. With his student Larry Smarr he originated the field of numerical relativity.
He received his bachelor's, master's and doctoral degrees from Harvard University. His Ph.D. (1950) supervisor was Julian S. Schwinger. Afterwards he worked at the Institute for Advanced Study, the University of North Carolina at Chapel Hill and the University of Texas at Austin. He was awarded the Dirac Prize in 1987, the American Physical Society's Einstein Prize in 2005, and was a member of the National Academy of Sciences and the American Academy of Arts and Letters.
He was born Carl Bryce Seligman but he and his three brothers added "DeWitt" from their mother's side of the family, at the urging of their father, in 1950. This is similar to Spanish naming customs, where a person bears two surnames, one being from their father and the other from their mother. Twenty years later this change of name so angered Felix Bloch that he blocked DeWitt's appointment to Stanford University and DeWitt instead moved to Austin, Texas. He served in World War II as a naval aviator. He was married to mathematical physicist Cécile DeWitt-Morette. He died September 23, 2004 from pancreatic cancer at the age of 81. He is buried in France, and was survived by his wife and four daughters. *Wik

1924 Paul Moritz Cohn FRS (8 January 1924, Hamburg, Germany – 20 April 2006, London, England) was Astor Professor of Mathematics at University College London, 1986-9, and author of many textbooks on algebra. His work was mostly in the area of algebra, especially non-commutative rings.*Wik

1942 Stephen W. Hawking (8 Jan 1942, )English theoretical physicist who is one of the world's leaders in his field. His principal areas of research are theoretical cosmology and quantum gravity. Hawking is the Lucasian Professor of Mathematics at Cambridge University (formerly held by Sir Isaac Newton). Afflicted with Lou Gehrig's disease (amyotrophic lateral sclerosis; ALS), Hawking is confined to a wheelchair and is unable to speak without the aid of a computer voice synthesizer. However, despite his challenges, he has utilized his intelligence, knowledge and abilities to make remarkable contributions to the field of cosmology (the study of the universe as a whole). *TIS

DEATHS

1642 Galileo Galilei (15 Feb 1564, 8 Jan 1642) 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

1952 Antonia Coetana de Paiva Pereira Maury (21 Mar 1866; 8 Jan 1952 at age 85) was an American astronomer and ornithologist whose painstaking classifications of stars by their spectra included elaborate work on 681 bright stars of the northern skies published in Annals of Harvard College Observatory (1896), a significant early catalog. Yet she was unappreciated by her observatory director, Edward C. Pickering. Her work was important in Ejnar Hertzsprung's verification of the distinction between dwarf stars and giant stars, as now seen in the Hertzsprung-Russell diagram. After Pickering discovered the first spectroscopic binary star, Mizar, she was first to measure its period, 104 days. In 1889, she identified the second such star, Beta Aurigae, with a period of about 4 days. Antonia was the niece of astronomer Henry Draper, and the granddaughter of John William Draper who pioneered in the use of photography in astronomy.*TIS

1956 Greenleaf Whittier Pickard (14 Feb 1877, 8 Jan 1956) U.S. electrical engineer whose invention of the crystal detector was one of the first devices widely used for receiving radio broadcasts until superseded by the triode vacuum tube. His patent of 20 Nov 1906 described it as "a means for receiving intelligence communicated by electric waves." He was also one of the first scientists to demonstrate the wireless electromagnetic transmission of speech. Pickard conducted numerous experiments to determine the effect of the sun and sunspots on radio. In his study of the polarisation of radio waves, he contributed to development of the direction finder, and noted as early as 1908 that errors in reading radio compasses might be caused by buildings, trees and other objects.*TIS

1968 Charles Loewner (29 May 1893 Lány, Bohemia – 8 January 1968, Stanford, California) was an American mathematician. His name was Karel Löwner in Czech and Karl Löwner in German.
Loewner received his Ph.D. from the University of Prague in 1917 under supervision of Georg Pick. One of his central mathematical contributions is the proof of the Bieberbach conjecture in the first highly nontrivial case of the third coefficient. The technique he introduced, the Loewner differential equation, has had far-reaching implications in geometric function theory; it was used in the final solution of the Bieberbach conjecture by Louis de Branges in 1985.*Wik

1980 John W. Mauchly (30 Aug 1907, 8 Jan 1980) American physicist and engineer, who with John P. Eckert invented (1946) the Electronic Numerical Integrator and Computer (ENIAC), the first general-purpose electronic computer. Mauchly initially conceived of the computer's architecture, and Eckert possessed the engineering skills to bring the idea to life. ENIAC was developed (1946) for the US Army Ordnance Department as what was probably the first general-purpose electronic computer. It was a vast machine, consuming 100 kW of electric power and containing 18,000 electronic valves. Their successful UNIVAC computer (1951) was the first commercial computer, and introduced magnetic tape for programming.*TIS

2002 Aleksandr Mikhaylovich Prokhorov (11 Jul 1916, 8 Jan 2002) is the Soviet physicist who received, (with Nikolay G. Basov, USSR and Charles H. Townes, US), the Nobel Prize for Physics in 1964 "for fundamental work in the field of quantum electronics, which has led to the construction of oscillators and amplifiers based on the maser-laser principle." "Maser" stands for "microwave amplification by stimulated emission of radiation." An amplification can occur only if the stimulated emission is larger than the absorption, requiring that there should be more atoms in a high energy state than in a lower one. This state is called an inverted population. Prokhorov had researched the maser independently but simultaneously with the other prize recipients. *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