## Saturday 27 April 2024

### On This Day in Math - April 27

I believe that we do not know anything for certain,
but everything probably.
~ Christiaan Huygens

The 117th day of the year; 117 can be written as the difference of prime squares (112 - 22) or prime cubes (53 - 23). *Prime Curios (Can you find another number which can be expressed as both the difference of squared primes and cubed primes?)

117 is the smallest possible length for the longest side of a Heronian tetrahedron (one whose sides are all integers, and all surface areas and volume are rational). The other edges are 51, 52, 53, 80, & 84. (Are the areas / volume integral?)
 *Mathworld.Wolfram

An Euler brick, named after Leonhard Euler, is a cuboid whose edge and face diagonals all have integer lengths. A primitive Euler brick is an Euler brick whose edge lengths are relatively prime.The smallest Euler brick, discovered by Paul Halcke in 1719, has edges(a,b,c) = (44, 117, 240) and face diagonals 125, 244, and 267.

EVENTS

1521 In the Philippines, Magellan became involved in a tribal war in which he was killed. His remaining ships returned to Spain in September of 1522 without their leader. *VFR

1610 Martin Horky writes to Kepler saying that Galileo's telescope was admirable for terrestrial observations,but completely failed to show others what the latter claimed for the heavens. *John McCafferty

1657 Christiaan Huygens published De ratiociniis in ludo aleae. *VFR [Download of English version printed in London in pdf]
In 1655 he made his first visit to Paris. He informed the mathematicians in Paris including Boulliau of his discovery and in turn Huygens learnt of the work on probability carried out in a correspondence between Pascal and Fermat. On his return to Holland Huygens wrote a small work De Ratiociniis in Ludo Aleae on the calculus of probabilities, the first printed work on the subject.

1740 The French Academie des Sciences announced that their prize on the ebb and ﬂow of the tides would be shared between Leonhard Euler, Daniel Bernoulli, Antoine Cavalleri, one of the last of the Cartesians, and Colin Maclaurin, then Professor of Mathematics at the University of Edinburgh. [Niccol´o Guiciardini, The Development of Newtonian Calculus in Britain 1700–1800 (1989), p. 69.] *VFR

1783 In a letter to A. M. Lorgna, Gian Francesco Malfatti gave the polar equation concerning the squaring of the circle. [DSB 9, 55] Does this refer to the polar equation of the spiral of Archimedes, r = aθ? *VFR
Malfatti and Lorgna were two of the founders of the "Società Italiana delle Scienze" (1782) and Malfatti was active in academic reform, especially in the Napoleonic period.  He is remembered for the Malfetti problem, finding three circles in a triangle that include the largest area.  Malfatti applied the distinction that circles had to all be mutually tangent and tangent to two sides of the triangle.  Later this solution was chipped apart as better solutions were found by not having the three circles all be cotangent.
 *wik

In 1871, the American Museum of Natural History opened to the public in New York City. With a series of exhibits, the Museum's collection Went on view for the first time in the Central Park Arsenal, the Museum's original home, on the eastern side of Central Park. The museum began from the efforts of Albert Smith Bickmore, one-time student of Harvard zoologist Louis Agassiz, who was successful in his proposal to create a natural history museum in Central Park, New York City, with the support of William E. Dodge, Jr., Theodore Roosevelt, Sr., Joseph Choate, and J. Pierpont Morgan. The Governor of New York, John Thompson Hoffman, signed a bill officially creating the American Museum of Natural History on 6 Apr 1869. *TIS

1865 King George V of Hanover visited Gottingen and ordered a commemorative plate placed at the room in which Gauss had died ten years before.

In 1895, Professor Charles F. Marvin, a future chief of the Weather Bureau, began experimenting with kites for routine use in the Bureau. In 1896 he perfected his kite meteorograph, an instrument capable of measuring and recording temperature, pressure and humidity. These measurements were recorded by pens tracings on paper, or on a smoked copper sheet, which was attached to a clock rotated drum. i
n 1898, the first Weather Bureau kite was launched from Topeka, Kansas, and by the end of the year, 16 additional kite stations were attempting daily, early morning, simultaneous observations. The kites were large "box types" with dimensions of 8 feet long, 7 feet wide and 3 feet high. As many as seven kites would be attached to the kite wire during and observation. These kites were placed at regular intervals with the second 1500 feet behind the first, the third 2000 feet behind the second and from there on a spacing of 2500 feet.*TIS

1961 Patent issued for multilayer circuit boards. Hazeltyne, a US firm, patented hole technology and its use in multi-layer printed circuit board assemblies. The result was that component density increased, and the newly close-spaced electrical paths changed the design of printed circuit board assemblies dramatically.

1962 The Netherlands issued a stamp showing Christiaan Huygens’ Pendulum
Clock as pictured by van Ceulen. [Scott #B365] *VFR

1994 U.S. Companies Get Aid From Government   The Clinton administration unveils a multimillion-dollar program to aid U.S. companies that make flat-panel display screens as part of an effort to help the industry stay afloat in light of Japanese domination of 95 percent of the industry. The funding comes partly from the Defense Department, for use of flat screens on military equipment. The flat-panel display market had previously been limited to laptop computers. *CHM
 Japanese Assembly Plant

2002 The last successful reception of telemetry was received from Pioneer 10 on April 27, 2002; subsequent signals were barely strong enough to detect, and provided no usable data. Pioneer 10 was launched in 1972 . Pioneer 10 crossed the orbit of Saturn in 1976 and the orbit of Uranus in 1979.
On June 13, 1983, Pioneer 10 crossed the orbit of Neptune, the outermost planet at the time, and so became the first man-made object to leave the proximity of the major planets of the solar system. The final, very weak signal from Pioneer 10 was received on January 23, 2003 when it was 12 billion kilometers (80 AU) from Earth. *Wik
 Wave Goodby

BIRTHS

1791 Samuel Finley Breese Morse (27 Apr 1791; 2 Apr 1872 at age 81) was an American artist and inventor who is famous for developing the Morse Code (1838) and independently perfecting an electric telegraph (1832-35). He spent the first part of his life as a portrait artist, and did not turn to science until 1832, when he was past his 40th birthday. He was returning to America from a tour of Europe, when he met Charles T. Jackson on the boat, who inspired him about newly discovered electromagnets. From that point, Morse worked to develop apparatus for electrical communications. Backed by Congress, he erected a line spanning 40 miles between Baltimore, Maryland and Washington D.C. which had its first trial on 23 May 1843. It was ready for public use on 1 Apr 1845. *TIS

1837 Paul Albert Gordan,(27 April 1837 – 21 December 1912) king of the invariant theorists, (died: 1912). He found simpler proofs that π and e are transcendental. Emmy Noether, the ﬁrst woman to get a doctorate in Germany, was his student. *VFR
He was known as "the king of invariant theory". His most famous result is that the ring of invariants of binary forms of fixed degree is finitely generated. Clebsch–Gordan coefficients are named after him and

A famous quote attributed to Gordan about David Hilbert's proof of Hilbert's basis theorem, a result which vastly generalized his result on invariants, is "This is not mathematics; this is theology." The proof in question was the (non-constructive) existence of a finite basis for invariants. It is not clear if Gordan really said this since the earliest reference to it is 25 years after the events and after his death. Nor is it clear whether the quote was intended as criticism, or praise, or a subtle joke. Gordan himself encouraged Hilbert and used Hilbert's results and methods, and the widespread story that he opposed Hilbert's work on invariant theory is a myth (though he did correctly point out in a referee's report that some of the reasoning in Hilbert's paper was incomplete).

1843 Felix Muller He compiled the earliest mathematical calendar (that I know of)*VFR.His advisors were Weierstrass and Kummer.
In 1868 he entered Schellbach's mathematical-pedagogical seminar and in 1869 became an assistant teacher at the Friedrich-Wilhelm-Gymnasium and at a secondary school in Berlin and in 1870 a full teacher. Finally, in 1882 he became a senior teacher and in 1887 a professor at the Luisengymnasium in Berlin. He retired in 1897 and then lived as a private citizen in Oberloschwitz and on the Weißen Hirsch near Dresden . Around 1900 he lived briefly in Berlin-Steglitz .

In 1869, together with Carl Ohrtmann, he founded the Yearbook on the Advances in Mathematics based on the model of advances in physics , of which he was a member of the editorial board until 1906.

As a historian of mathematics, he was primarily concerned with the history of mathematical terminology and bibliographical work.

1875 (6th duke) (Louis-César-Victor-) Maurice de Broglie (27 Apr 1875; died 14 Jul 1960 at age 85.) a French physicist who made many contributions to the study of X rays. While in the navy (1895-1908), he first distinguished himself by installing the first French shipboard wireless. From 1912, his chief interest was X-ray spectroscopy. His “method of the rotating crystal” was an application of Bragg's “focussing effect” to eliminate spurious spectral lines. De Broglie discovered the third L absorption edge (1916), which led to the exploration of “corpuscular spectra.” During 1921-22, he worked with his brother Louis to refine Bohr's specification of the substructure of the various atomic shells. He also did pioneer work in nuclear physics and cosmic radiation.*TIS

1913 Philip Hauge Abelson (April 27, 1913 – August 1, 2004) was an American physicist, scientific editor and science writer. He proposed the gas diffusion process for separating uranium-235 from uranium-238 which was essential to the development of the atomic bomb. In collaboration with the U.S. physicist Edwin M. McMillan, he discovered a new element, later named neptunium, produced by irradiating uranium with neutrons. At the end WW II, his report on the feasibility of building a nuclear-powered submarine gave birth to the U.S. program in that field. In 1946, Abelson returned to the Carnegie Institution and pioneered in utilizing radioactive isotopes. As director of the Geophysics Laboratory of the Carnegie Institution (1953-71), he found amino acids in fossils, and fatty acids in rocks more than 1,000,000,000 years old. *TIS

1920 Mark Alexandrovich Krasnosel'skii (April 27, 1920, Starokostiantyniv – February 13, 1997, Moscow) was a Soviet, Russian and Ukrainian mathematician renowned for his work on nonlinear functional analysis and its applications. *Wik

1932 Gian-Carlo Rota Rota (April 27, 1932 – April 18, 1999) worked on functional analysis for his doctorate and, up to about 1960, he wrote a series of papers on operator theory. Two papers in 1959-60, although still in the area of operator theory, looked at ergodic theory which is an area which requires considerable combinatorial skills. These papers seem to have led Rota away from operator theory and into the area of combinatorics. His first major work on combinatorics, which was to change the direction of the whole subject, was On the Foundations of Combinatorial Theory which Rota published in 1964.
Rota received the Steele Prize from the American Mathematical Society in 1988. The Prize citation singles out the 1964 paper On the Foundations of Combinatorial Theory as:-... the single paper most responsible for the revolution that incorporated combinatorics into the mainstream of modern mathematics. *SAU

DEATHS

1936 Karl Pearson, (27 March 1857 in London, England - 27 April 1936 in Coldharbour, Surrey, England) English mathematician, one of the founders of modern statistics. Pearson's lectures as professor of geometry evolved into The Grammar of Science (1892), his most widely read book and a classic in the philosophy of science. Stimulated by the evolutionary writings of Francis Galton and a personal friendship with Walter F.R. Weldon, Pearson became immersed in the problem of applying statistics to biological problems of heredity and evolution. The methods he developed are essential to every serious application of statistics. From 1893 to 1912 he wrote a series of 18 papers entitled Mathematical Contributions to the Theory of Evolution, which contained much of his most valuable work, including the chi-square test of statistical significance. *TIS l There is a plaque in the church at Crambe in No. Yorkshire where he was born and many of his family are buried.

1978 Guido Stampacchia (March 26, 1922 - April 27, 1978) was a 20th century mathematician. Stampacchia was active in research and teaching throughout his career. He made key contributions to a number of fields, including calculus of variation and differential equations. In 1967 Stampacchia was elected President of the Unione Matematica Italiana. It was about this time that his research efforts shifted toward the emerging field of variational inequalities, which he modeled after boundary value problems for partial differential equations.
Stampacchia accepted the position of Professor Mathematical Analysis at the University of Rome in 1968 and returned to Pisa in 1970. He suffered a serious heart attack in early 1978 and died of heart arrest on April 27 of that year *Wik

Gerard Kitchen O'Neill (February 6, 1927 – April 27, 1992) was an American physicist and space activist. As a faculty member of Princeton University, he invented a device called the particle storage ring for high-energy physics experiments. Later, he invented a magnetic launcher called the mass driver. In the 1970s, he developed a plan to build human settlements in outer space, including a space habitat design known as the O'Neill cylinder. He founded the Space Studies Institute, an organization devoted to funding research into space manufacturing and colonization.*Wik

As a leading advocate of space colonization, he wrote in his book The High Frontier (1978), that space colonies could be the ultimate solution to such terrestrial problems as pollution, overpopulation, and the energy shortage. He designed a 1-km long sealed cylindrical space station to be built primarily of processed lunar materials and using solar energy. It would be capable of sustaining a human colony indefinitely in space between the Earth and the Moon. *TIS

1999 Rolf William Landauer (4 Feb 1927; 27 Apr 1999) German-born American physicist known for his formulation of Landauer's principle concerning the energy used during a computer's operation. Whenever the machine is resetting for another computation, bits are flushed from the computer's memory, and in that electronic operation, a certain amount of energy is lost. Thus, when information is erased, there is an inevitable "thermodynamic cost of forgetting," which governs the development of more energy-efficient computers. While engineers dealt with practical limitations of compacting ever more circuitry onto tiny chips, Landauer considered the theoretical limit, that if technology improved indefinitely, how soon will it run into the insuperable barriers set by nature?*TIS

1999 Mark David Weiser (23 Jul 1952, 27 Apr 1999 at age 46) American computer scientist and visionary who was the chief technology officer at XEROX PARC, and is remembered for developed the pioneering idea for what he referred to as “ubiquitous computing.” He coined that term in 1988 to describe a future in which personal computers will be replaced with tiny computers embedded in everyday “smart” devices (everyday items such as coffeepots and copy machines) and their connection via a network. He said, “First were mainframes, each shared by lots of people. Now we are in the personal computing era, person and machine staring uneasily at each other across the desktop. Next comes ubiquitous computing, or the age of calm technology, when technology recedes into the background of our lives.” He died at age 46, only six weeks after being diagnosed as having gastric cancer. *TIS

2002 Ruth Marianna Handler (née Mosko; November 4, 1916 – April 27, 2002) was an American inventor who created the Barbie Doll (1959), a teenage doll with a tiny waist and slender hips, and Ken, a boy doll (1961), which she named after her children. She co-founded the Mattel company in 1942. The business originally sold picture frames, and later dollhouse furniture which shortly led to specializing in toys. With a blonde ponytail and a zebra-striped swimsuit, the first "Barbie Teen-Age Fashion Model" sold over 350,000 the first year. The company soon made \$100m annually. After being diagnosed with breast cancer in 1970, resulting in a mastectomy, she founded Ruthton Corporation to manufacture and market a prosthetic breast for women with a similar need.  *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