## Friday 30 August 2024

### On This Day in Math - August 30

Frustra fit per plura, quod fieri potest per pauciora.

It is vain to do with more what can be done with less.

~William of Ockham

The 242nd day of the year; 242 has six divisors...but 243, 244, and 245 also each has six divisors. 242 is the smallest integer to begin a run of four consecutive integers all of which have the same number of divisors. (What is the smallest integer that begins a run of three consecutive integers with an equal number of divisors?)

242 is not only a palindrome in base ten, it is also a palindrome in base 3, ${22222}_{3}$ and base 7, ${464}_{7}$. (What palindrome in base ten is also a palindrome in the most other bases 2-9?)
242 = 2 x 11^2, it is divisible by 2, 11, 22, 121 all of which are also palindromes.

242 is the nth prime + n for n = 45.  197 + 45 = 242

See More Math Facts for every Year Day, here

EVENTS

In 1831, Charles Darwin replied to the letter from Revd. Henslow telling him of the offer to sail on the H.M.S. Beagle. Darwin's had learned natural history from Henslow, who had recommended him for the unpaid position as a naturalist. Darwin told Henslow that his father would not permit him to leave on such a voyage. Meanwhile, his father had written to his brother-in-law, Josiah Wedgwood II, about his concerns regarding the proposed two-year jaunt. This afternoon Darwin prepared to join the Wedgwoods for the next day's beginning of the shooting season by riding to Maer Hall, the Wedgwood home. The Darwin family was related to the Wedgwood family through the marriage of Darwin's father to the daughter of the first Josiah Wedgwood, the famous potter. *TIS

1791 Thomas Jefferson sends a letter to Benjamin Banneker after receiving his almanac and a letter announcing that, "Sir, I freely and cheerfully acknowledge, that I am of the African race, and in that color which is natural to them of the deepest dye". Jefferson responds that, " I thank you sincerely for your letter of the 19th. instant and for the Almanac it contained. no body wishes more than I do to see such proofs as you exhibit, that nature has given to our black brethren, talents equal to those of the other colours of men, that the appearance of a want of them is owing merely to the degraded condition of their existence both in Africa and America. I can add with truth that no body wishes more ardently to see a good system commenced for raising the condition both of their body & mind to what it ought to be, as fast as the imbecillity of their present existence, and other circumstance which cannot be neglected, will admit. I have taken the liberty of sending your almanac to Monsieur de Condorcet, Secretary of the Academy of sciences at Paris, and member of the Philanthropic society because I considered it as a document to which your whole colour had a right for their justification against the doubts which have been entertained of them. I am with great esteem, Sir, Your most obedt. humble servt. Th. Jefferson" *Mathematicians of the African Diaspora, SUNY at Buffalo

In 1831, Michael Faraday demonstrated the first electrical transformer.*TIS

1908 A committee appointed by the Swiss society of naturalists reported its willingness, provided sufficient ﬁnancial assistance could be secured, to publish the complete works of Euler in about 40 volumes. Today 80 volumes of Euler’s Opera Omnia have been published, and the end is hardly in sight.*VFR

1950 Harald Bohr  presented a Fields Medal to Lauren Schwartz, French mathematician who is best known for his work in the theory of distributions, at the International Congress of Mathematicians in Harvard  for his work on the theory of distributions. Harald Bohr  described Schwartz's 1948 paper as one:-

... which certainly will stand as one of the classical mathematical papers of our times. ... I think every reader of his cited paper, like myself, will have left a considerable amount of pleasant excitement, on seeing the wonderful harmony of the whole structure of the calculus to which the theory leads and on understanding how essential an advance its application may mean to many parts of higher analysis, such as spectral theory, potential theory, and indeed the whole theory of linear partial differential equations ...

Harald August Bohr (22 April 1887 – 22 January 1951) was a Danish mathematician and footballer. After receiving his doctorate in 1910, Bohr became an eminent mathematician, founding the field of almost periodic functions. His brother was the Nobel Prize-winning physicist Niels Bohr. He was a member of the Danish national football team for the 1908 Summer Olympics, where he won a silver medal.

In 1963, the "Hot Line" communications link between the White House, Washington D.C. and the Kremlin, Moscow, went into operation to provide a direct two-way communications channel between the American and Soviet governments in the event of an international crisis. This was one year after the Cuban Missile Crisis. It consisted of one full-time duplex wire telegraph circuit, routed Washington- London- Copenhagen- Stockholm- Helsinki- Moscow, used for the transmission of messages and one full-time duplex radiotelegraph circuit, routed Washington- Tangier- Moscow used for service communications and for coordination of operations between the two terminal points. Note, this was not a telephone voice link.*TIS

In 1979, Comet Howard-Koomen-Michels (SOLWIND I) collided with the Sun, the first recorded comet to collide with Sun and the first discovered by a spacecraft. The coronographs taken on 30 and 31 Aug 1979 from the satellite P78-1 used to monitor solar corona activity were not inspected until Sep 1981, by Russ Howard. The recording instruments were designed and operated by Martin Koomen and Don Michels. The remarkable series of images showed the comet heading around the Sun. Its perihelion distance was too small, and the head did not reappear from behind the Sun, presumably disintegrated by the heat of the sun. The decapitated comet's tail continued, becoming fan-like, brightening the corona, until dissipated and blown away from the Sun*TIS

1983   In 1967, a press conference announced four Air Force officers selected for training in the U.S. Air Force's Manned Orbital Laboratory (MOL) program, El Segundo, California. One of the four, Major Robert Lawrence, was the first African-American to qualify for training in the US space program. His career was cut short only a few months later, when he died on 8 Dec 1967 on a training flight in a Starfighter jet that crashed at Edwards Air Force Base, California. (Several years earlier, another African-American, Captain Ed Dwight, had been selected for the MOL program, on 31 Mar 1961, but not subsequently selected for training). It was not until 30 Aug 1983 that the first African-American entered space: Col. Guion S. Bluford, Jr.*TiS

2019  National Slinky Day  As its jingle once cheered: “A spring, a spring, a marvelous thing! Everyone knows it’s Slinky.” The coiled toy certainly is a marvelous, if simplistic, thing. In 1943, mechanical engineer Richard James was designing a device that the Navy could use to secure equipment and shipments on ships while they rocked at sea. As the story goes, he dropped the coiled wires he was tinkering with on the ground and watched them tumble end-over-end across the floor.

After dropping the coil, he could have gotten up, frustrated, and chased after it without a second thought. But he—as inventors often do—had a second thought: perhaps this would make a good toy.

Richard James went home and told his wife, Betty James, about his idea. In 1944, she scoured the dictionary for a fitting name, landing on “slinky,” which means “sleek and sinuous in movement or outline.” Together, with a \$500 loan, they co-founded James Industries in 1945, the year the Slinky hit store shelves.

On August 30, 2019  National Slinky Day, the Pennsylvania Historical and Museum Commission installed a historical marker to commemorate the invention of the toy in Clifton Heights, the Philadelphia suburb where it was first manufactured. *Smithsonian Mag

BIRTHS

1804 Ernst Wilhelm Grebe (30 August, 1804 - 14 January, 1874) is remembered only for a thoughtful paper that appeared in 1847 concerning some interesting properties of the triangle: If on each side of a given (arbitrary) triangle ABC one describes a square ( exterior to ABC ), then the extended outside sides of the squares, thus obtained, form a similar triangle A'B'C'. The center of similarity of both triangles is the meeting point of the straight lines AA', BB', CC'. In German this point was first called _Grebe'schen Punkt_ [Grebe's point], a TERM which seems to have been first referred to by E. Hain as early as 1875, in his paper "Ueber den Grebe'schen Punkt" [ _Archiv der Mathematik und Physik_ (= Grunert's _Archive_) volume LVIII (1876), pp. 84-89 ] *Julio Gonzalez Cabillon , Posting to the Historia Matematica discussion group
He also named the Vecten point.  (The Greeb Point is also called the Lemoine Point, and the Symmedian {medians reflected at the associated angle bisectors}
point)   The French mathematician Émile Lemoine proved the existence of the symmedian point in 1873,
The symmedian point of a triangle with side lengths a, b and c has homogeneous trilinear coordinates [a : b : c].
Ross Honsberger called its existence "one of the crown jewels of modern geometry"

### Martin Lukarevski informed me that, " Grebe was 26 years ahead of Lemoine, but in fact the symmedian point had already been noted in 1809 by the Swiss geometer Simon L'Huilier. "  My Thanks!

Image:  A triangle with medians (black), angle bisectors (dotted) and symmedians (red). The symmedians intersect in the symmedian point L, the angle bisectors in the incenter I and the medians in the centroid G.

1819 Joseph Alfred Serret (30 Aug 1819 in Paris, France - 2 March 1885 in Versailles, France) He was a French mathematician best remembered for the Serret-Frenet formulas for a space-curve. In 1860 Serret succeeded Poinsot in the Académie des Sciences. In 1871 he retired to Versailles as his health began to deteriorate.
Serret also worked in number theory, calculus and mechanics. He edited the works of Lagrange which were published in 14 volumes between 1867 and 1892. He also edited the 5th edition of Monge in 1850.*SAU

The Frenet–Serret formulas are: where d/ds is the derivative with respect to arclength, κ is the curvature, and τ is the torsion of the curve. The two scalars κ and τ effectively define the curvature and torsion of a space curve.

 *Wik

1856 Carl David Tolmé Runge ( 30 August 1856 – 3 January 1927) was a German mathematician, physicist, and spectroscopist.  He was co-developer and co-eponym of the Runge–Kutta method in the field of what is today known as numerical analysis. He worked on a procedure for the numerical solution of algebraic equations and later studied the wavelengths of the spectral lines of elements. *SAU

In numerical analysis, the Runge–Kutta methods that are named for him are an important family of implicit and explicit iterative methods for the approximation of solutions of ordinary differential equations. These techniques were developed around 1900  Runge and M.W. Kutta.*Wik When  your regular walking partners include Felix Klein, David Hilbert, and Hermann Minkowski, you can't count on easily impressing them with your mental math skills, but it seems that Runge did so frequently.  Once on their regular walks Klein brought up some departmental event that required them to know what date Easter would occur the next year.  The group immediately turned to the idea of where they might acquire a calendar for the following year along the walk; all that is, except Runge who fell silent for a few yards, and then announced the date.

1871 Sir Ernest Rutherford (30 Aug 1871; 19 Oct 1937). (baron) New Zealand-born British physicist who laid the groundwork for the development of nuclear physics. He worked under Sir J. J. Thomson at Cambridge University (1895-98). Then he collaborated with Frederick Soddy in studying radioactivity. In 1899 he discovered alpha particles and beta particles, followed by the discovery of gamma radiation the following year. In 1905, with Soddy, he announced that radioactive decay involves a series of transformations. In 1907, with Hans Geiger and Ernest Marsden, he devised the alpha-particle scattering experiment that led in 1911 to the discovery of the atomic nucleus. In 1919 he achieved the artificial splitting of light atoms. In 1908 he was awarded the Nobel Prize for Chemistry. *TIS A story is told by A.. V. Hill that Rutherford had told him once, "I've just been reading some of my early papers, and when I had read them for a bit I said to myself, "Ernest my boy, you used to be a darn clever fellow.'" *Walter Gratzer, Eurekas and Euphorias, pg 27
[I love this quote from a few years before his death. "The energy produced by the breaking down of the atom is a very poor kind of thing. Anyone who expects a source of power from the transformation of these atoms is talking moonshine."]

1906 Olga Taussky-Todd (August 30, 1906 – October 7, 1995) was an Austrian and later Czech-American mathematician She received her Ph.D. in 1930 under Philip Furtwangler at Vienna in number theory. Her ﬁrst job involved editing Hilbert’s papers on number theory.*VFR

According to Gian-Carlo Rota, as a young mathematician she was hired by a group of German mathematicians to find and correct the many mathematical errors in the works of David Hilbert, so that they could be collected into a volume to be presented to him on his birthday. There was only one paper, on the continuum hypothesis, that she was unable to repair.

She published more than 300 research papers on algebraic number theory, integral matrices, and matrices in algebra and analysis.

1907 John 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

1907 Gordon Stanley Brown (August 30, 1907 in Australia – August 23, 1996 in Tucson, Arizona) was a professor of electrical engineering at MIT. He originated many of the concepts behind automatic-feedback control systems and the numerical control of machine tools.[1] From 1959 to 1968, he served as the dean of MIT's engineering school. With his former student Donald P. Campbell, he wrote Principles of Servomechanisms in 1948, which is still a standard reference in the field.

1912 E.M. Purcell (30 Aug 1912; 7 Mar 1997) American physicist who shared, with Felix Bloch of the United States, the Nobel Prize for Physics in 1952 for his independent discovery (1946) of nuclear magnetic resonance in liquids and in solids. Nuclear magnetic resonance (NMR) has become widely used to study the molecular structure of pure materials and the composition of mixtures. The method detects and measures the magnetic fields of atomic nuclei. *TIS

DEATHS

1621 Baha' ad-Din al-Amili (27 Feb 1547 in Baalbek, now in Lebanon - 30 Aug 1621 in Isfahan, Iran) was a Lebanese-born mathematician who wrote influential works on arithmetic, astronomy and grammar. Perhaps his most famous mathematical work was Quintessence of Calculation which was a treatise in ten sections, strongly influenced by The Key to Arithmetic (1427) by Jamshid al-Kashi. *SAU

1844 Francis Baily   (28 Apr 1774, 30 Aug 1844)English astronomer who detected the phenomenon called "Baily's beads" during an annular eclipse of the Sun on 15 May 1836. His vivid description aroused new interest in the study of eclipses. After retiring in 1825 from a successful business career, Baily turned to science. Baily revised several star catalogs, repeated Henry Cavendish's experiments to determine the density of the Earth, and measured its elliptical shape. His protests regarding the British Nautical Almanac, then notorious for its errors, were instrumental in bringing about its reform.*TIS  A really nice discussion of the many contributions of Baily is in this post at The Renaissance Mathematicus, To whet your appetite, " Baily’s Flamsteed memoir had a major influence on the history and the  historiography of science; he had succeeded in pricking Newton’s  hagiographic bubble. St Isaac had been taken down a peg or two. Baily’s  work marks a turning point in our understanding of Newton moving him  along the road from plastic saint to real, if somewhat unpleasant, human  being. Sometimes editing star catalogues can lead to unexpected results  for the history of science."

1901 Biquard Pierre, (30 August 1901 in Paris - 28 April 1992 in Paris)In 1932, He discovered light diffraction by ultrasonic waves:  friend of Frédéric Joliot Curie *Arjen Dijksman ‏@materion

1928 Wilhelm Wien  (13 Jan 1864, 30 Aug 1928)German physicist who received the Nobel Prize for Physics in 1911 for his displacement law concerning the radiation emitted by the perfectly efficient blackbody (a surface that absorbs all radiant energy falling on it). While studying streams of ionized gas Wien, in 1898, identified a positive particle equal in mass to the hydrogen atom. Wien, with this work, laid the foundation of mass spectroscopy. J J Thomson refined Wien's apparatus and conducted further experiments in 1913 then, after work by E Rutherford in 1919, Wien's particle was accepted and named the proton. Wien also made important contributions to the study of cathode rays, X-rays and canal rays.*TIS [I find it curiously interesting that all three of  the  great physicists mentioned here either were born or died this day]

1940 Sir J(oseph) J(ohn) Thomson (born 18 Dec 1856, 30 Aug 1940 )was an English physicist who helped revolutionize the knowledge of atomic structure by his discovery of the electron (1897). He received the Nobel Prize for Physics in 1906 and was knighted in 1908. Thomson experimented with currents of  electricity inside empty glass tubes, investigating a long-standing puzzle known as "cathode rays." His experiments prompted him to make a bold proposal: these mysterious rays are streams of particles much smaller than atoms. He called these particles "corpuscles," and suggested that they might make up all of the matter in atoms. It was startling to imagine a particles inside the atom at a time when most people thought that the atom was indivisible, the most fundamental unit of matter.*TIS

1995 Fischer Sheffey Black (January 11, 1938, August 30, 1995) was an American economist, best known as one of the authors of the famous Black–Scholes equation.In 1973, Black, along with Myron Scholes, published the paper 'The Pricing of Options and Corporate Liabilities' in 'The Journal of Political Economy'. This was his most famous work and included the Black–Scholes equation. The Nobel Prize is not given posthumously, so it was not awarded to Black in 1997 when his co-author Myron Scholes received the honor for their landmark work on option pricing along with Robert C. Merton, another pioneer in the development of valuation of stock options. In the announcement of the award that year, the Nobel committee prominently mentioned Black's key role.*Wik

1998 Irving Ezra Segal (Sept 13, 1918–Aug 30, 1998) was an American mathematician known for work on theoretical quantum mechanics. He shares credit for what is often referred to as the Segal–Shale–Weil representation. Early in his career Segal became known for his developments in quantum field theory and in functional and harmonic analysis, in particular his innovation of the algebraic axioms known as C*-algebra.

Segal provided an alternative to the Big Bang theory of expansion of the universe. The cosmological redshift that motivates the expanding universe theory is due to curvature of the cosmos, according to Segal. Spacetime symmetry is expressed by the Lorentz group and its extension the Poincaré group. “The inclusion of the Einstein temporal evolution among the fundamental symmetries gives rise to the conformal group...” But conformal compactification introduces closed timelike curves so Segal portrayed the spatial part of the cosmos as a large 3-sphere with an auxiliary real line for time. Spacetime cannot turn back on itself. At each point in the cosmos there is a convex future direction, meaning, "the future can never merge into the past", no spacetime curvature can close or loop.

Segal reviewed redshift data to verify his cosmology. He claimed confirmation, but generally his chronometric cosmology has not found favor. For instance, Abraham H. Taub reviewed Mathematical Cosmology and Extragalactic Astronomy, saying,  "The chronometric theory as described in this book is not a theory concerning the nature of the universe nor the behaviour of objects in it. Rather it ignores the effect of gravitational forces on these objects, postulates that astronomical bodies in it are at rest without explaining how this happens and ascribes the redshift to a particular description of methods of measurement which is at variance with that used in theories such as general relativity."

2004 Fred Lawrence Whipple  (5 Nov 1906, 30 Aug 2004) was an American astronomer who proposed the "dirty snowball" model for comet nuclei. In the 1930s, using a new, two-station method of photography, he determined meteor trajectories and found that nearly all visible meteors are made up of fragile material from comets, and that none come from beyond the solar system. Whipple suggested (1950) that comets have icy cores inside thin insulating layers of dirt, and that jets of material ejected as a result of solar heating were the cause of orbital changes. This model was confirmed in 1986 when spacecraft flew past comet Halley. Whipple’s work on tracking artificial satellites led to improved knowledge of the shape of the earth and greatly improved positions on earth. *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