## Sunday 25 June 2023

### On This Day in Math - June 25

Astronomy was the cradle of the natural sciences and the starting point of geometrical theories.

~Cornelius Lanczos

The 176th day of the year; 176 and its reversal 671 are both divisible by 11. ( Students should confirm that the reverse of  any number that is divisible by 11 will also be divisible by 11.)

176 is a happy number, repeatedly iterating the sum of the squares of the digits will lead to 1, 12 + 72 + 62= 86, 82 + 62 = 100 and 12 + 02 + 02 = 1

The number 15 can be partitioned in 176 ways. For younger students, imagine all the different ways of making fifteen cents with US coins, 1 cent, 5 cents, and 10 cents.... now imagine there were also coins worth 2, 3, 4, 6, 7, 8, 9, 11, 12, 13, 14, and 15 cents. There would be 176 different collections of coins that would total exactly 15 cents.

176 is a Self number, it can't be written by any other number plus the sum of its digits. 21 for instance, is not a self number because 15+1+5 = 21.

8*20 + 16 = 176 so 176 = 24^2 - 20 ^2  (try this on 192 also ) and it is divisible by 16 with quotient 11, so 15^2 - 7^2 = 176.

EVENTS

1641 John Pell begins the work of expanding Walter Warner's table of anti-logarithms from 10,000 to 100,000 entries. Warner felt he was too old to complete the laborious task he had set for  himself, and offered Pell 40 GBPounds (appx. worth 5,000 pounds today) to complete the tables and make them ready for printing.  *Thomas Harriot's Doctrine of Triangular Numbers, Beery & Stedall, pg 39

1665 René Descartes died on 11 February 1650 in Stockholm, Sweden, where he had been invited as a teacher for Queen Christina of Sweden. The cause of death was said to be pneumonia—accustomed to working in bed until noon, he may have suffered a detrimental effect on his health due to Christina's demands for early morning study (the lack of sleep could have severely compromised his immune system). Others believe that Descartes may have contracted pneumonia as a result of nursing a French ambassador, Dejion A. Nopeleen, ill with the aforementioned disease, back to health. In his recent book, Der rätselhafte Tod des René Descartes (The Mysterious Death of René Descartes), the German philosopher Theodor Ebert asserts that Descartes died not through natural causes, but from an arsenic-laced communion wafer given to him by a Catholic priest. He believes that Jacques Viogué, a missionary working in Stockholm, administered the poison because he feared Descartes's radical theological ideas would derail an expected conversion to Roman Catholicism by the monarch of Protestant Lutheran Sweden.*Wik

After his death in Stockholm, his body was returned to Paris, arriving on 25 Jun 1665 , though the coffin had been looted by his followers for relics in Stockholm.  Supposedly, the coffin was shipped overland from Copenhagen to avoid piracy by English admirers!  The remains were in Ste. Geneviève, then in Lenoir's Museum of French Monuments, and then finally moved to St‑Germain-des-Prés in 1819. His headstone (or gravestone) is in St‑Germain‑des‑Prés, in the second chapel on the right of the apse.   Stephen Jay Gould says the (purported) skull of Descartes is in the Musée de l'Homme, apparently on display.  Arjen Dijksman recently advised me that the Musee de l'Homme is closed for another year, and there have been efforts to move the skull to the Pantheon.
Église St-Germain-des-Prés, at 3 Place St-Germain-des-Prés, is the oldest church in Paris. Part of it dates to the 6th century, when a Benedictine abbey was founded on the site by King Childebert, son of Clovis. The church was originally built to house a relic of the True Cross brought from Spain in 542. The Normans destroyed the abbey on multiple occasions and only the marble columns in the triforium remain from the original structure. The carved capitals on the pillars are copies of the originals, which are kept in the Musée National du Moyen-Age. The church was enlarged and reconsecrated by Pope Alexander III in 1163. The abbey was completely destroyed during the Revolution, but the church was spared. The present building is a fine example of Romanesque architecture, with gothic interior elements. The square tower dating from the early 11th century, is topped by a landmark spire, which dates to the 19th century. For a time, the abbey served as a pantheon for Merovingian kings. The Chapelle Saint Symphorien, built during the Middle Ages and restored in 1981, served as the necropolis mérovingienne (crypt of the Merovingians). This is the presumed site of first tomb of Saint Germain, Bishop of Paris, who died in 576. Among the others interred here are King Jean-Casimir of Poland

1712 Brook Taylor suggested that if two glass plates which are clamped together into a “V” are placed into a pan of water then capillary action will draw water up into the shape of a rectangular hyperbola with asymptotes the surface of the water and the point of the “V.” This and several similar experiments performed by Francis Hauksbee before the Royal Society caused Newton to rethink his ideas on capillary force. *VFR

1730 Euler observes in a letter to Goldbach that 104 + 1 is divisible by 37, and that
38 +2 8 is divisible by 17. Euler cannot prove that any number is the sum of four squares. He has found another result by Fermat, namely that 1 is the only triangular number that is a fourth power (Several years earlier, Goldbach had sent an erroneous proof of this claim to D. Bernoulli) *Lemmemeyer, EULER, GOLDBACH, AND “FERMAT’S THEOREM"

1776 Captain Cook sails from Deptford on his third voyage, in the 'Resolution' with the 'Discovery' *Nat. Maritime Museum ‏@NMMGreenwich

1783  Antonie Lavoisier announced to the French Academy of Sciences that water was the product formed by the combination of hydrogen and oxygen. However, this discovery had been made earlier by the English chemist Henry Cavendish *TIS

1795 The Bureau des Longitudes is a French scientific institution, founded by decree of 25 June 1795 and charged with the improvement of nautical navigation, standardization of time-keeping, geodesy and astronomical observation. During the 19th century, it was responsible for synchronizing clocks across the world. It was headed during this time by François Arago and Henri Poincaré. The Bureau now functions as an academy and still meets monthly to discuss topics related to astronomy.
The Bureau was founded by the National Convention after it heard a report drawn up jointly by the Committee of Navy, the Committee of Finances and the Committee of State education. Henri Grégoire had brought to the attention of the National Convention France's failing maritime power and the naval mastery of England, proposing that improvements in navigation would lay the foundations for a renaissance in naval strength. As a result, the Bureau was established with authority over the Paris Observatory and all other astronomical establishments throughout France. The Bureau was charged with taking control of the seas away from the English and improving accuracy when tracking the longitudes of ships through astronomical observations and reliable clocks.
The ten original members of its founding board were:
Geometers:
Joseph-Louis Lagrange;
Pierre-Simon Laplace;
Astronomers:
Joseph Jérôme Lefrançais de Lalande;
Pierre Méchain;
Jean Baptiste Joseph Delambre;
Dominique, comte de Cassini;
Jean-Charles de Borda, who carried out work related to the mechanics of fluids and precursor of Carnot because of his insights on thermodynamics;
Jean-Nicolas Buache, geographer;
Louis Antoine de Bougainville, celebrated navigator; and
Noël Simon Caroché, manufacturer of telescopes.
*Wik

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1903 Marie Skłodowska Curie defended her doctoral thesis on radioactive substances at Université de la Sorbonne in Paris on 25 June 1903 – becoming the first woman in France to receive a doctoral degree.

The examination committee expressed the opinion that Curie's findings, including the determination of radium’s atomic weight, represented the greatest scientific contribution ever made in a doctoral thesis.

In the committee’s three members were two future Nobel Prize laureates: Gabriel Lippmann (Physics 1908) and Henri Moissan (Chemistry 1906).

*The Noble Prize

1973 Last total solar eclipse with a maximum duration of totality longer than 7 minutes between year 0 and 4000 was June 30, 1973. The eclipse was visible in Africa. The next total solar eclipse with a duration of totality longer than 7 minutes will be on 25 June 2150 in the Pacific Ocean. Thereafter it will be 5 July 2168 in the Indian Ocean. Ref. More Mathematical AstronomicalMorsels by Jean Meeus; Willmann-Bell, 2002. *NSEC

BIRTHS

1864 Walther Hermann Nernst (25 June 1864 – 18 November 1941) German who was one of the founders of modern physical chemistry. In 1889, he devised his theory of electric potential and conduction of electrolytic solutions (the Nernst Equation) and introduced the solubility product to explain precipitation reactions. In 1906, Nernst showed that it is possible to determine the equilibrium constant for a chemical reaction from thermal data, and in so doing he formulated what he himself called the third law of thermodynamics. This states that the entropy, (a thermodynamic measure of disorder in a system), approaches zero as the temperature goes towards absolute zero. For this, he was awarded the 1920 Nobel Prize in Chemistry. In 1918, he explained the H2-Cl2 explosion on exposure to light as an atom chain reaction. *TIS

1905 Rupert Wildt (/ˈvɪlt/; June 25, 1905 – January 9, 1976) was a German-American astronomer.
He was born in Munich, Germany, and grew up in that country during World War I and its aftermath. In 1927 he was awarded a Ph.D. from the University of Berlin. He joined the University of Göttingen, specializing in the properties of atmospheres.
In 1932 he studied the spectra of Jupiter, and other outer planets, and identified certain absorption bands as belonging to the hydrogen-rich compounds of methane and ammonia. The composition appeared consistent with a composition similar to the sun and other stars.
Assuming that the atmosphere was composed of these gases, during the 1940s and 1950s he constructed a model of the structure of these planets. He believed the core of the planets is solid and composed of a mixture of rock and metal, covered by a thick outer shell of ice, overlaid by a dense atmosphere. His model is still widely accepted.
In 1934 he emigrated to the United States, and became a research assistant at Princeton University from 1937 until 1942. He then became an assistant professor at the University of Virginia until 1947, before joining the faculty of the Yale University.
In 1939 he demonstrated that the major source of optical opacity in the Sun's atmosphere is the H- ion, and thus the main source of visible light for the Sun and stars.
From 1965 until 1968 he was president of the Association of Universities for Research in Astronomy. In the period 1966-1968 he also held the post of the chairman of the department of astronomy at Yale, and from 1973 until his death he was professor emeritus. He died in Orleans, Massachusetts.
His awards include the Eddington Medal in 1966. The Asteroid 1953 Rupertwildt is named after him and the crater Wildt on the Moon is also. *Wik

1928 Alexei Alexeyevich Abrikosov (June 25, 1928; ) is a Soviet and Russian theoretical physicist whose main contributions are in the field of condensed matter physics. He was awarded the Nobel Prize in Physics in 2003.
In two works in 1952 and 1957, Abrikosov explained how magnetic flux can penetrate a class of superconductors. This class of materials is known as type-II superconductors. The accompanying arrangement of magnetic flux lines is called the Abrikosov vortex lattice.
Abrikosov was awarded the Lenin Prize in 1966, the Fritz London Memorial Prize in 1972, and the USSR State Prize in 1982. In 1989 he received the Landau Prize from the Academy of Sciences, Russia. Two years later, in 1991, Abrikosov was awarded the Sony Corporation’s John Bardeen Award. The same year he was elected a Foreign Honorary Member of the American Academy of Arts and Sciences.[1] He is also a member of the Royal Academy of London, a fellow of the American Physical Society, and in 2000 was elected to the prestigious National Academy of Sciences. He was the co-recipient of the 2003 Nobel Prize in Physics, with Vitaly Ginzburg and Anthony James Leggett, for theories about how matter can behave at extremely low temperatures. *Wik

DEATHS

1671 Giovanni Riccioli (17 April 1598 – 25 June 1671) Italian astronomer who was the first to observe (1650) a double star (two stars so close together that they appear to be one) -  Mizar in Ursa Major, the middle star in the handle of the Big Dipper. He also discovered satellite shadows on Jupiter. In 1651, he assigned the majority of the lunar feature names in current use. He named the more prominent features after famous astronomers, scientists and philosophers, while the large dark and smooth areas he called "seas" or "maria". The lunar seas were named after moods (Seas of Tranquillity, Serenity) or terrestrial phenomena (Sea of Rains, Ocean or Storms) His map was published in Almagestum Novum in1651.*TIS
Riccioli studied seventy-seven objections to the Copernican thesis and after studying them Riccioli said that the weight of argument favored a “geo-heliocentric” hypothesis such as that advocated by the great Danish astronomer Tycho Brahe. Riccioli's preference for Tycho's model illustrates something important about how science is done. While today anti-Copernicans are often portrayed as Einstein characterized them (opposed to rational thinking, opposed to science), Riccioli, perhaps the most prominent of the anti-Copernicans, examined the available evidence diligently and rationally. The conclusion he reached was indeed wrong, but wrong because at that time neither the diffraction of light and the Airy disk, nor the details of the Coriolis effect, were understood. Riccioli's anti-Copernican arguments were so solid that they would become subjects of further investigation in physics, long after the Copernican theory had triumphed over the Tychonic theory.*Christopher M. Graney, Teaching Galileo, Physics Teacher V50,1

1879 Sir William Fothergill Cooke (4 May 1806 – 25 June 1879) English inventor who worked with Charles Wheatstone in developing electric telegraphy. Of the pair, Cooke contributed a superior business ability, whereas Wheatstone is generally considered the more important of the two in the history of the telegraph. After Cooke attended a demonstration of the use of wire in transmitting messages, he began his own experiments with telegraphy (1836) and formed a partnership with Wheatstone. Their first patent (1837) was impractical because of cost. They demonstrated their five-needle telegraph on 24 July 1837 when they ran a telegraph line along the railway track from Euston to Camden Town able to transmit and successfully receive a message. In 1845, they patented a single-needle electric telegraph. *TIS

1941 Alfred Pringsheim (2 September 1850 – 25 June 1941). His work in Fourier series, analytic function theory, and continued fractions was a model of the Weierstrassian approach, although he was not a student of Weier­strass. *VFR
In mathematical analysis, Pringsheim studied real and complex functions, following the power-series-approach of the Weierstrass school. Pringsheim published numerous works on the subject of complex analysis, with a focus on the summability theory of infinite series and the boundary behavior of analytic functions.
Pringsheim's theorem concerns the convergence of a power series with non-negative real coefficients. However, Pringsheim's original proof had a flaw (related to uniform convergence), and a correct proof was provided by Ralph P. Boas. Pringsheim's theorem is used in analytic combinatorics and the Perron–Frobenius theory of positive operators on ordered vector spaces.
Besides his research in analysis, Pringsheim also wrote articles for the Encyclopedia of Mathematical Sciences on the fundamentals of arithmetic and on number theory. He published papers in the Annals of Mathematics. As an officer of the Bavarian Academy of Sciences, he recorded the minutes of its scientific meetings.
Pringsheim and Ivan Śleszyński, working separately, proved what is now called the Śleszyński–Pringsheim theorem on convergence of certain continued fractions.*Wik

1960 Walter Baade (24 Mar 1893; 25 Jun 1960 at age 67) German-American astronomer who, with Fritz Zwicky, proposed that supernovae could produce cosmic rays and neutron stars (1934), and Baade made extensive studies of the Crab Nebula and its central star. During WW II blackouts of the Los Angeles area Baade used the 100-inch Hooker telescope to resolve stars in the central region of the Andromeda Galaxy for the first time. This led to his definition of two stellar populations, to the realization that there were two kinds of Cepheid variable stars, and from there to a doubling of the assumed scale of the universe. Baade and Rudolph Minkowski identified and took spectrograms of optical counterparts of many of the first-discovered radio sources, including Cygnus A and Cassiopeia A. *TIS

1974 Cornelius Lanczos (2 Feb 1893 - 25 June 1974) worked on relativity and mathematical physics and invented what is now called the Fast Fourier Transform. *SAU Lanczos served as assistant to Albert Einstein during the period of 1928–29.*Wik

1978 Hsien Chung Wang (April 18, 1918 — June 25, 1978.)worked on algebraic topology and discovered the 'Wang sequence', an exact sequence involving homology groups associated with fibre bundles over spheres. These discoveries were made while he worked with Newman in Manchester. Wang also solved, at that time, an important open problem in determining the closed subgroups of maximal rank in a compact Lie group *SAU

1997 Jacques-Yves Cousteau (11 June 1910 – 25 June 1997) French naval officer, oceanographer, marine biologist and ocean explorer, known for his extensive underseas investigations. He was co-inventor of the aqualung which made SCUBA diving possible (1943). Cousteau developed the Conshelf series of manned habitats, the Diving Saucer, a process of underwater television and numerous other platforms and specialized instruments of ocean science. In 1945 he founded the French Navy's Undersea Research Group. He modified a WWII wooden hull minesweeper into the research vessel Calypso, in 1950. An observation dome added to the foot of Calypso's bow was found to increase the ship's stability, speed and fuel efficiency. *TIS

2006 Irving "Kap" Kaplansky (March 22, 1917, Toronto – June 25, 2006, Los Angeles) was born in Toronto, Ontario, Canada after his parents emigrated from Poland and attended the University of Toronto as an undergraduate. After receiving his Ph.D  from Harvard in 1941 as Saunders Mac Lane's first student, Kaplansky was professor of mathematics at the University of Chicago from 1945 to 1984. He was chair of the department from 1962 to 1967.
"Kap," as his friends and colleagues called him, made major contributions to group theory, ring theory, the theory of operator algebras and field theory. He published over 150 papers with over 20 co-authors. He was a member of the National Academy of Sciences and the American Academy of Arts and Sciences. He was the Director of the Mathematical Sciences Research Institute from 1984 to 1992, and the President of the American Mathematical Society from 1985 to 1986.
Kaplansky also was a noted pianist known to take part in Chicago performances of Gilbert and Sullivan productions. He often composed music based on mathematical themes. One of those compositions, A Song About Pi, is a melody based on assigning notes to the first 14 decimal places of pi.
Kaplansky was the father of singer-songwriter Lucy Kaplansky, who occasionally performs A Song About Pi in her act.
He was among the first five recipients of William Lowell Putnam fellowships in 1938.*Wik

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