Sunday 28 July 2024

On This Day in Math - July 28

It appears to me that if one wishes to make progress in mathematics
one should study the masters and not the pupils.

Quoted in O Ore's, Niels Abel, Mathematician Extraordinary

The 209th day of the year; 209=16+25+34+43+52+61.

Also 209 is a "Self number" A self number, Colombian number or Devlali number (after the town where he lived) is an integer which, in a given base, cannot be generated by any other integer added to the sum of that other integer's digits. For example, 21 is not a self number, since it can be generated by the sum of 15 and the digits comprising 15, that is, 21 = 15 + 1 + 5. No such sum will generate the integer 209, hence it is a self number. These numbers were first described in 1949 by the Indian mathematician D. R. Kaprekar. students might want to explore self numbers for patterns
[The earliest use of Colombian number I can find is by B. Recaman (1974). "Problem E2408". Amer. Math. Monthly 81. Would love to know if there are earlier uses.]

209 is the maximum number of pieces that can be made by cutting an annulus with 19 straight cuts.

The curve 42x^2 - y^2 = 209 contains the 'prime points' (3, 13), (5, 29), (7, 43), and (13, 83). *Prime Curios

There is an infinity of pairs x,y where x^2 - y^2 - xy = 209 for x, y integers *Prime Curios

As far as I know, there are only two three digit numbers so that abc^2 = uvwxyz and uvw+xyz = abc.  These are called three digit Kaprekar numbers.  209 is involved in each case.  The two numbers are 297^2 = 88209, with 88 + 209 = 297 and 703^2 = 494209 where 494 + 209 = 703

See More Math Facts for every Year Day here

EVENTS

1619 Kepler wrote Napier expressing his enthusiasm for Napier’s invention of logarithms. *VFR
Napier who used logarithm tables extensively to compile his Ephemeris and therefore dedicated it to Napier, remarked:

... the accent in calculation led Justus Byrgius [Joost Bürgi] on the way to these very logarithms many years before Napier's system appeared; but ... instead of rearing up his child for the public benefit he deserted it in the birth.

— Johannes Kepler, Rudolphine Tables (1627)

1851  First American eclipse expedition to Europe when George Phillips Bond (1825 - 1865) led a team to Scandinavia. *NSEC   In the transcription of his notes he wrote:

1851 A total solar eclipse was photographed for the ﬁrst time. *VFR The first correctly-exposed photograph of the solar corona was made during the total phase of the solar eclipse of 28 July 1851 at Königsberg (now Kaliningrad) by a local daguerreotypist named Berkowski at the Royal Observatory in Königsberg, Prussia (now Kalinigrad in Russia). Berkowski, whose first name was never published, observed at the Royal Observatory. A small 6-cm refracting telescope was attached to the 15.8-cm Fraunhofer heliometer and a 84-second exposure was taken shortly after the beginning of totality.
United Kingdom astronomers, Robert Grant and William Swan, and Austrian astronomer Karl Ludwig von Littrow observed this eclipse and determined that prominences are part of the Sun because the Moon is seen to cover and uncover them as it moves in front of the Sun.*Wik

In 1858, fingerprints were used as a means of identification for the first time.*TIS The English first began using fingerprints in July of 1858, when Sir William James Herschel, Chief Magistrate of the Hooghly district in Jungipoor, India, first used fingerprints on native contracts. On a whim, and without thought toward personal identification, Herschel had Rajyadhar Konai, a local businessman, impress his hand print on a contract.
The idea was merely "... to frighten [him] out of all thought of repudiating his signature." The native was suitably impressed, and Herschel made a habit of requiring palm prints--and later, simply the prints of the right Index and Middle fingers--on every contract made with the locals. Personal contact with the document, they believed, made the contract more binding than if they simply signed it. Thus, the first wide-scale, modern-day use of fingerprints was predicated, not upon scientific evidence, but upon superstitious beliefs.
As his fingerprint collection grew, however, Herschel began to note that the inked impressions could, indeed, prove or disprove identity. While his experience with fingerprinting was admittedly limited, Sir William Herschel's private conviction that all fingerprints were unique to the individual, as well as permanent throughout that individual's life, inspired him to expand their use. *History of Fingerprints, Onin.com
 *Wik

I was reminded by Douglas W Boone that Mark Twain uses fingerprint identification in his book Pudd'nhead Wilson.
"As we see most clearly in the trial scene at the end of the book, fingers turn out to be Tom's deadliest enemy when his fingerprints turn up on the murder weapon, revealing his identity. Referring to fingerprints, Pudd'nhead explains:

Every human being carries with him from his cradle to his grave certain physical marks which do not change their character, and by which he can always be identified—and that without shade of doubt or question. " *SHMOOP

1866 The ﬁrst act (in the USA) legalizing the employment of the metric system was approved (14 Stat. L. 339). The act provided that it “shall be lawful throughout the United States of America to employ the weights and measures of the metric system.” *VFR

1882 The Institute of Accountants and Bookkeepers was organized in New York City. It was the first accounting society in the United States. *FFF

1883 On the 28th of July, about nine o"clock in the morning, Jack Ferry pedaled across the English Channel on a floating tricycle. He started from Dover about nine o’clock in the morning, and arrived at Calais in less than eight hours. The distance as the crow flies was twenty miles, but on account of the currents, the effort required was considerably increased. The construction of his vehicle was illustrated in La Nature. Bulky paddlewheels (probably needing more displacement than shown) replace wheels of a land tricycle. The small wheel behind acted as a rudder. The event was reported in Science, 14 Dec 1883. *TiS

1899 Cantor asks Dedekind whether the set of all cardinal numbers is itself a set, because if it is it would have a cardinal number larger than any other cardinal. *VFR

1948 Allen Turing writes to Jack Good with an estimate of the number of neurons in the human brain. "I have repeatedly looked in books on  I looked up an estimate neurology ... and never found any numbers offered. My own estimate is 3x108 to 3x109. " *Turing Archives
I looked up an estimate in 2024 and it gave, "Approximately 86 billion neurons in the human brain. "about 9 x 10^10, pretty close for an estimate 80 years out.

1984 The town of Eighty-four Pennsylvania celebrated it's centennial on this day.

1997  Dell Computer Corp. announced its entry into the workstation market with the Dell Workstation 400. The move to the more powerful desktop computers, most commonly used for engineering, followed Dell's entry into the network server industry as it expanded from personal desktop computers and laptops in order to grab a larger part of the market. Dell offered its workstations for $3,000 to$8,000. (Yikes!!!) *CHM

 *CHM

2061 Halley's comet will next reach perihelion. The comet last reached perihelion on 9 February 1986, and will reach it again on 28 July 2061 *Wik

BIRTHS
1849 Robert Scott studied at Cambridge and was elected to a fellowship. After a short time teaching he studied to be a barrister. He spent most of his career as Bursar and Master of St John's College Cambridge. He published a book on Determinants. *SAU

1867 Charles Dillon Perrine (July 28, 1867; Steubenville, Ohio, – June 21, 1951) U.S. astronomer who discovered the sixth and seventh moons of Jupiter in 1904 and 1905, respectively. In 1904 he published a calculation of the solar parallax (a measure of the Earth-Sun distance) based on observations of the minor planet Eros during one of its close approaches to the Earth. *TIS  He was an American astronomer at the Lick Observatory in California (1893-1909) who moved to Cordoba, Argentina to accept the position of Director of the Argentine National Observatory (1909-1936). The Cordoba Observatory under Perrine's direction made the first attempts to prove Einstein's theory of relativity by astronomical observation of the deflection of starlight near the Sun during the solar eclipse of October 10, 1912 in Cristina (Brazil), and the solar eclipse of August 21, 1914 at Feodosia, Crimea, Russian Empire.[1] Rain in 1912 and clouds in 1914 prevented results.*Wik

 maser components at amhistorymuseum HT toBen Gross ‏@bhgross144
1915 Charles Hard Townes (July 28, 1915 – January 27, 2015) was an American Nobel Prize-winning physicist and educator. Townes was known for his work on the theory and application of the maser, on which he got the fundamental patent, and other work in quantum electronics connected with both maser and laser devices. He shared the Nobel Prize in Physics in 1964 with Nikolay Basov and Alexander Prokhorov.
In a career that spanned six decades, Dr. Townes developed radar bombing systems and navigation devices during World War II, advised presidents and government commissions on lunar landings and the MX missile system, verified Einstein’s cosmological theories, discovered ammonia molecules at the center of the Milky Way, and created an atomic clock that measured time to within one second in 300 years. He died at the age of 99 in Berkeley, California*Wik *NY Times

1928 John Bell (28 June 1928 – 1 October 1990)   his great achievement was that during the 1960s he was able to breathe new and exciting life into the foundations of quantum theory, a topic seemingly exhausted by the outcome of the Bohr-Einstein debate thirty years earlier, and ignored by virtually all those who used quantum theory in the intervening period. Bell was able to show that discussion of such concepts as 'realism', 'determinism' and 'locality' could be sharpened into a rigorous mathematical statement, 'Bell's inequality', which is capable of experimental test. Such tests, steadily increasing in power and precision, have been carried out over the last thirty years. *SAU

1954 Gerd Faltings (July 28, 1954 - ) was born in Gelsenkirchen-Buer, West Germany. In 1986 he received a Fields Medal for solving Mordell’s Conjecture using arithmetic algebraic geometry. *VFR He has also been closely linked with the work leading to the final proof of Fermat's Last Theorem by Andrew Wiles. In 1983 Faltings proved that for every n greater than 2 there are at most a finite number of coprime integers x, y, z with xn + yn = zn. This was a major step but a proof that the finite number was 0 in all cases did not seem likely to follow by extending Falting's arguments.
However, Faltings was the natural person that Wiles turned to when he wanted an opinion on the correctness of his repair of his proof of Fermat's Last Theorem in 1994.*TIS

DEATHS

1818 Gaspard Monge (9 May 1746 – 28 July 1818) died in disgrace in Bourbon Paris, having been stripped of his place in the reorganized Acad´emie of 1816. Although he contributed to diﬀerential equations and the geom¬etry of surfaces, his special interest was descriptive geometry. Employed as a teacher, he made signiﬁcant contributions to educational reform. [Ivor Grattan-Guiness, Convolutions in French Mathematics, 1800–1840, p. 616]
On the fall of Napoleon he was deprived of all his honors, and even excluded from the list of members of the reconstituted Institute. Monge died at Paris on 28 July 1818 and was interred in Le Père Lachaise Cemetery, in Paris, in a mausoleum. He was later transferred to the Panthéon. The mausoleum and Monge's bust remain in Le Père Lachaise Cemetery.
A statue portraying him was erected in his home town of Beaune, Côte-d'Ors in 1849. His name is one of the 72 names inscribed on the Eiffel Tower.

1944 Sir Ralph Fowler (17 January 1889 – 28 July 1944) a brilliant physicist. But it may be for his influence upon others that he is best known. In fact, no less than fifteen Fellows of the Royal Society and three Nobel Laureates were supervised by Fowler between 1922 and 1939. The total number supervised during this time was a staggering sixty-four giving him an average of eleven research students at any given time. One might be led to believe that this did not allow for any depth of relationship to form between him and his students. However, this was far from the truth of the matter. Those who studied under Fowler had a tremendous admiration for him. In particular, E A Milne [1] was especially taken by the man whom he fondly referred to as "the kind of man you can still remain friendly with, even when he has sold you a motor-bike; it is not possible to say more" and whom he called a "prince amongst men".
Aside from Milne, on whom he had a profound impact, he also had the opportunity of influencing the likes of Sir Arthur Eddington, Subramanian Chandrasekhar, Paul Dirac, Sir William McCrea, Lady Jeffreys and others either directly through supervision or indirectly through collaboration. Even in his personal life he was intimately connected with brilliant people having married Eileen, the only daughter of Lord Rutherford whom he met through Rutherford's Cavendish Laboratory at Cambridge. Sometimes his influence was simply the fact that he was known to so many people. It was Fowler who ultimately introduced Paul Dirac to the burgeoning field of quantum theory in 1923 leading Dirac to the forefront of its ultimate discovery in 1925. Fowler also put Dirac and Werner Heisenberg in touch with each other through Niels Bohr. As Sir William McCrea simply put it: "he was the right man in the right place at the right time." *SAU
1968 Otto Hahn (8 Mar 1879; 28 Jul 1968 at age 89) German physical chemist who, with the radiochemist Fritz Strassmann, is credited with the discovery of nuclear fission. He was awarded the Nobel Prize for Chemistry in 1944 and shared the Enrico Fermi Award in 1966 with Strassmann and Lise Meitner. Element 105 carries the name hahnium in recognition of his work.*TIS

1968 Otto Hahn (8 Mar 1879; 28 Jul 1968 at age 89) German physical chemist who, with the radiochemist Fritz Strassmann, is credited with the discovery of nuclear fission. He was awarded the Nobel Prize for Chemistry in 1944 and shared the Enrico Fermi Award in 1966 with Strassmann and Lise Meitner. Element 105 carries the name hahnium in recognition of his work.*TIS

"For the rest of his life, Hahn provided a standard explanation: fission was a discovery that relied on chemistry only and took place after Meitner left Berlin; she and physics had nothing to do with it, except to prevent it from happening sooner." *Lise Meitner by  Ruth Lewin Sime

The prize-winning science-fiction writer, Frederik Pohl, talking about Szilard's epiphany in Chasing Science (pg 25), ".. we know the exact spot where Leo Szilard got the idea that led to the atomic bomb.  There isn't even a plaque to mark it, but it happened in 1938, while he was waiting for a traffic light to change on London's Southampton Row.  Szilard had been remembering H. G. Well's old science-fiction novel about atomic power, The World Set Free and had been reading about the nuclear-fission experiment of Otto Hahn and Lise Meitner, and the lightbulb went on over his head." (Maybe she had a little idea?)

in 1939 during the Fifth Washington Conference on Theoretical Physics at the George Washington University, Nobel Laureate Niels Bohr publicly announced the splitting of the uranium atom. The resulting “fission,” with its release of two hundred million electron volts of energy, heralded the beginning of the atomic age.

The announcement came just weeks after Otto Hahn and Fritz Strassmann, two of Bohr’s colleagues at Copenhagen, reported that they had discovered the element barium after bombarding uranium with neutrons. After receiving the news in a letter, physicist Lise Meitner and her cousin, Otto Frisch, correctly interpreted the results as evidence of nuclear fission. Frisch confirmed this experimentally on January 13, 1939. *atomicheritage.org

Niels Bohr was planning a trip to America to discuss other problems with Einstein who had found a haven at Princeton's Institute for Advanced Studies. Bohr came to America, but the principal item he discussed with Einstein was the report of Meitner and Frisch. Bohr arrived at Princeton on January 16, 1939. He talked to Einstein and J. A. Wheeler who had once been his student. From Princeton the news spread by word of mouth to neighboring physicists, including Enrico Fermi at Columbia. Fermi and his associates immediately began work to find the heavy pulse of ionization which could be expected from the fission and consequent release of energy. *Atomic Archive

1982 Graciela Beatriz Salicrup López (México City, México, April 7, 1935 – July 29, 1982) was a Mexican architect, archaeologist, and mathematician. In the 1970s and 1980s, she was a pioneer in the field of categorical topology. Most of her work was published in Spanish, and her original contributions were not widely recognized until after her premature death.
A professor at Colegio Alemán originally encouraged her, inciting an interest in mathematics that her family did not understand or support, even sending her to see a psychiatrist for "extravagance, disorientation, and a bit of madness," according to her friend Claudia Gomez Wulschner.
When asked how the story ends, Salicrup López states that she married him. She married the psychiatrist Armando Hinojosa Cavazos. They had three children: Ariel who pursued music, David who became an architect like his mother; and Mariana who studied ballet.

Salicrup Lopez had many interests and passions, especially for music and art. She loved the opera and visiting art exhibits. She also enjoyed literature and history.
Salicrup Lopez still wanted to become a mathematician, and finally enrolled in the Faculty of Sciences in 1964 to study mathematics. Between 1966 and 1968 she taught mathematics at the UNAM Faculty of Architecture. Her thesis, accepted in 1969, was on the Jiang Boju subgroup.

After graduating in 1969 Graciela began teaching in the UNAM Faculty of Sciences. In 1970 she was given a position as a researcher in the UNAM Mathematics Institute, where she worked with Dr. Roberto Vázquez, her mentor. That same year she published her first work along with her mentor.

Her work was concerned with the structure of the Top category of topological spaces and with continuous functions. Her work related concepts such as reflexivity or coreflexivity to those of connection and coexistence, both in Top and in certain subcategories of Top (and in some more general concrete categories). The publications she co-authored with Vázquez were always in Spanish, so many mathematicians were not aware of her work.
Shortly before her death, Graciela fell out with her mentor Roberto Vázquez and they stopped collaborating. In the summer of 1982, she was visited by Lamar Bentley and Horst Herrlich, with whom she planned to collaborate. Soon after this Graciela suffered a fall that hurt her badly. She did not recover and died on July 29, 1982.

1988 Caleb Gattegno (1911–1988) was an educator, psychologist, and mathematician. He is considered one of the most influential and prolific mathematics educators of the twentieth century. He is best known for introducing new approaches to teaching and learning mathematics (Visible & Tangible Math), foreign languages (The Silent Way) and reading (Words in Color). Gattegno also developed pedagogical materials for each of these approaches, and was the author of more than 120 books and hundreds of articles largely on the topics of education and human development.
Gattegno's pedagogical approach is characterised by propositions based on the observation of human learning in many and varied situations. This is a description of three of these propositions. He was also influenced by the works of Jean Piaget and worked on introducing the implications of the latter's cognitive theory on education.
In his approach to teaching mathematics, manipulatives, such as Geoboards which he invented and Cuisenaire Rods which he popularized, are part of a way of systematically developing students' mathematical thinking through the exploration of clear and tangible problems. *Wik

2000 Abraham Pais (May 19, 1918 – July 28, 2000) Dutch-American physicist and science historian whose research became the building blocks of the theory of elemental particles. He wrote Subtle Is the Lord: The Science and Life of Albert Einstein, which is considered the definitive Einstein biography. In Holland, his Ph.D. in physics was awarded on 9 Jul 1941, five days before a Nazi deadline banning Jews from receiving degrees. Later, during WW II, while in hiding to evade the Gestapo, he worked out ideas in quantum electrodynamics that he later shared when working with Niels Bohr (Jan - Aug 1946). In Sep 1946, he went to the U.S. to work with Robert Oppenheimer at Princeton, where Pais contributed to the foundations of the modern theory of particle physics.*TIS

2004 Francis Harry Compton Crick (8 June 1916 – 28 July 2004) was a British biophysicist, who, with James Watson and Maurice Wilkins, received the 1962 Nobel Prize for Physiology or Medicine for their determination of the molecular structure of deoxyribonucleic acid (DNA), the chemical substance ultimately responsible for hereditary control of life functions. Crick and Watson began their collaboration in 1951, and published their paper on the double helix structure on 2 Apr 1953 in Nature. This accomplishment became a cornerstone of genetics and was widely regarded as one of the most important discoveries of 20th-century biology. *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