## Wednesday 19 June 2024

### On This Day in Math - June 19

The more I see of men, the better I like my dog.
Blaise Pascal (over 350 years before Carrie Underwood)

The 170th day of the year; the start of a record-breaking run of consecutive integers (170-176) with an odd number of prime factors.

170 is the smallest number that can be written as the sum of the squares of 2 distinct primes, where each of these primes is the square of a prime added to another prime (170 = (22 + 3)2 + (32 + 2)2).
*Prime Curios

170 is the largest integer for which its factorial can be stored in double-precision floating-point format. This is probably why it is also the largest factorial that Google's built-in calculator will calculate, returning the answer as 170! = 7.25741562 × 10306. (For 171! it returns "infinity".)

170 is the smallest number n for which phi(n)(the number of integers relatively prime to 170=64=82) and sigma(n) (the sum of the divisors of 170=324=182) are both square.

EVENTS

In 240 BC, Eratosthenes, a Greek astronomer and mathematician, estimated the circumference of the earth. As the director of the great library of Alexandria, he read in a papyrus book that in Syene, approaching noon on the summer solstice, the longest day of the year, shadows of temple columns grew shorter. At noon, they were gone. The sun was directly overhead. However, a stick in Alexandria, far to the north, could cast a pronounced shadow. Thus, he realized that the surface of the Earth could not be flat. It must be curved. Not only that, but the greater the curvature, the greater the difference in the shadow lengths. By measurement on the ground and application of geometry, he calculated the circumference of the earth. *TIS  He estimated that the meridian has a length of 252,000 stadia (39,060 to 40,320 kilometres (24,270 to 25,050 mi)), with an error on the real value between −2.4% and +0.8%

 *Wik

325 The early Christian church opened the council of Nicaea, which decided the rules for computing the date of Easter: The ﬁrst Sunday after the ﬁrst full moon on or after the vernal equinox *VFR

1934 Jerzy Neyman's paper before the Royal Statistical Society entitled "On the Two Different Aspects of the Representative Method: The Method of Stratified Sampling and the Method of Purposive Selection. This paper was the one first presenting the concept of a "confidence interval" (interval estimate). *David Bee

1934 1st motion picture of the solar surface was made using the McMath-Hulbert Spectroheliokinematograph (repeat three times real fast):
K8MHO is the club radio station for the McMath-Hulbert Astronomical Society. The station is housed in the McGregor administration building of the McMath-Hulbert Solar Observatory which at one time was the second largest solar observatory in the world. The Observatory is located in Lake Angelus, Oakland County, Michigan,
The station is currently manned by Tom Hagen, NE9Y, and Dave Benham, K8TRF. Members of this radio club have a mutual interest in astronomy, ham radio and the preservation of the McMath-Hulbert Solar Observatory.
The McMath-Hulbert Solar Observatory was founded in 1929 by Francis McMath, his son Robert McMath and Henry Hulbert, neighbors who just had a mutual interest in astronomy. The first tower at this site was built with a 16 foot dome in 1930 and originally had a 10.5” equatorial telescope. As they gained more interest in observing the sun, this building became more exclusively devoted to solar observing. On June 19, 1934, they released the first ever motion picture film of the surface of the sun. *QRZ.Com with hat tip to David Dickinson ‏@Astroguyz

1951 In 1951, a little girl named Monique wrote to Einstein about her fears regarding the end of the world. Einstein reassured her that earth has been around for a little more than a billion years [sic], so she needn't worry:

*Paul Halpern

In 1963, Soviet cosmonaut Valentina Tereshkova returned to Earth after spending nearly three days as the first woman in space. She had been interested in parachute jumping when she was young, and that expertise was one of the reasons she was picked for the cosmonaut program. She became the first person to be recruited without experience as a test pilot. On 16 Jun 1963, Tereshkova was launched into space aboard Vostok 6, and became the first woman to travel in space. Her radio name was "Chaika," Russian for "seagull." Her flight made 48 orbits of Earth. Tereshkova never made a second trip into space. She became an important member of the Communist Party and a representative of the Soviet government.*TIS

 *NASA

BIRTHS

1623 Blaise Pascal ( 19 June 1623 – 19 August 1662) born in Ferrand, Auvergne, France.  He laid the foundation for the modern theory of probabilities. In hydrodynamics he formulated what came to be known as Pascal's law of pressure, and invented the syringe and hydraulic press. Pascal invented the first digital calculator to help his father with his work collecting taxes. He worked on it for three years (1642-45). The device, called the Pascaline, resembled a mechanical calculator of the 1940s. This, almost certainly, makes Pascal the second person to invent a mechanical calculator for Schickard had manufactured one in 1624. He died at the young age of 39 having been sickly and physically weak through life. Autopsy showed he had been born with a deformed skull.*TIS
 Me considering Pascal considering the Roulette at at the Louvre

1669 Leonty Magnitsky (born Telyatin, June 9, 1669, Ostashkov – October 19, 1739, Moscow) was a Russian teacher who wrote the first guide to mathematics published in Russia.*SAU
ccounts, he graduated from the Slavic Greek Latin Academy in Moscow. From 1701 and until his death, he taught arithmetic, geometry and trigonometry at the Moscow School of Mathematics and Navigation, becoming its director in 1716.

In 1703, Magnitsky wrote his famous Arithmetic (Арифметика; 2,400 copies), which was used as the principal textbook on mathematics in Russia until the middle of the 18th century. Mikhail Lomonosov was himself taught by this book, which he called the "gates to his own erudition". In 1703, Magnitsky also produced a Russian edition of Adriaan Vlacq's log tables called Таблицы логарифмов и синусов, тангенсов и секансов (Tables of logarithms, sines, tangents, and secants).

Legend has it that Leonty Magnitsky was nicknamed Magnitsky by Peter the Great, who considered him a "people's magnet" (магнит, or "magnit" in Russian). For his educatorial achievements he was ennobled in 1704, and was given numerous awards and gifts by the Tsar.

1771 Joseph Gergonne born. (19 June 1771 Nancy, France—4 May 1859 Montpellier, France)  He came under the influence of Gaspard Monge, the Director of the new École Polytechnique in Paris. In 1810, in response to difficulties he encountered in trying to publish his work, Gergonne founded his own mathematics journal, officially named the Annales de mathématiques pures et appliquées but generally referred to as the Annales de Gergonne. The most common subject of articles in his journal was geometry, Gergonne's specialty. Over a period of 22 years, the Annales de Gergonne published about 200 articles by Gergonne himself, and other articles by many distinguished mathematicians, including Poncelet, Servois, Bobillier, Steiner, Plücker, Chasles, Brianchon, Dupin, Lamé, even Galois.
Gergonne was appointed to the chair of astronomy at the University of Montpellier in 1816. In 1830, he was appointed Rector of the University of Montpellier, at which time he ceased publishing his journal. He retired in 1844.
Gergonne was the first mathematician to employ the word polar. In a series of papers beginning in 1810, he discovered the principle of duality in projective geometry, by noticing that every theorem in the plane connecting points and lines corresponds to another theorem in which points and lines are interchanged, provided that the theorem embodied no metrical notions. In 1816, he devised an elegant solution to the problem of Apollonius: find a circle which touches three given circles.
In 1813, Gergonne wrote the prize-winning essay for the Bordeaux Academy, Methods of synthesis and analysis in mathematics, unpublished to this day and known only via a summary. The essay is very revealing of Gergonne's philosophical ideas. He called for the abandonment of the words analysis and synthesis, claiming they lacked clear meanings. Surprisingly for a geometer, he suggested that algebra is more important than geometry, at a time when algebra consisted almost entirely of the elementary algebra of the real field. He predicted that one day quasi-mechanical methods would be used to discover new results.
In 1815, Gergonne wrote the first paper on the optimal design of experiments for polynomial regression. According to S. M. Stigler, Gergonne is the pioneer of optimal design as well as response surface methodology.
The Gergonne Point, so named after the French mathematician Joseph Gergonne, is the point of concurrency which results from connecting the vertices of a triangle to the opposite points of tangency of the triangle's incircle.The Gergonne point Ge, triangle centroid G, and mittenpunkt M are collinear, with GeG:GM=2:1.
 *Mark Cowart

1846 Antonio Abetti (19 Jun 1846, 20 Feb 1928 at age 81) Italian astronomer who was an authority on minor planets. At first a civil engineer, he became an astronomer at the University of Padua (1868-93), with an interest in positional astronomy and made many observations of small planets, comets and star occultations. In 1874, Abetti went to Muddapur, Bengal, to observe the transit of Venus across the sun's disk where his use of a spectroscope was the first use of this kind. Later, he became director at the Arcetri Observatory and Professor of astronomy at the University of Florence (1894-1921). The observatory had been founded by G. B. Donati in 1872, and Abetti equipped it with a new telescope that he had built in the workshops at Padua. He was active after retirement, until his death, and was followed by his son Giorgio.*TIS

1851 Silvanus P. Thompson (19 June 1851 – 12 June 1916) In 1910 he published Calculus Made Easy, which was published anonymously until after his death in 1916. It is still in print. *VFR He was a noted physicist and engineer, and a celebrated teacher and writer on electricity and magnetism. He also wrote popular biographies of Faraday and Lord Kelvin. At his death he was professor at City and Guilds Technical College at Finsbury (London). Thompson’s particular gift was in his ability to communicate difficult scientific concepts in a clear and interesting manner. He attended and lectured at the Royal Institution giving the Christmas lectures in 1896 on Light, Visible and Invisible with an account of Röntgen Light. He was an impressive lecturer and the radiologist AE Barclay said that: “None who heard him could forget the vividness of the word-pictures he placed before them.”

1901 Raj Chandra Bose (or Basu) (19 June 1901 – 31 October 1987) was an Indian American mathematician and statistician best known for his work in design theory, finite geometry and the theory of error-correcting codes in which the class of BCH codes is partly named after him. He also invented the notions of partial geometry, association scheme, and strongly regular graph and started a systematic study of difference sets to construct symmetric block designs. He was notable for his work along with S. S. Shrikhande and E. T. Parker in their disproof of the famous conjecture made by Leonhard Euler dated 1782 that for no n do there exist two mutually orthogonal Latin squares of order 4n + 2.*Wik

1907 Børge Christian Jessen (19 June 1907 – 20 March 1993) was a Danish mathematician best known for his work in analysis, specifically on the Riemann zeta function, and in geometry, specifically on Hilbert's third problem.Jessen was a professor of descriptive geometry at the Technical University of Denmark from 1935 till 1942, when he moved back to the University of Copenhagen where he was professor from 1942 to 1977 when he retired. He was the president of the Carlsberg Foundation in 1955-1963 and one of the founders of the Hans Christian Ørsted Institute. He was the Secretary of the Interim Executive Committee of the International Mathematical Union (1950–1952), and in September 1951 he officially declared the founding of the Union, with its first domicile in Copenhagen. He was also active in the Danish Mathematical Society. After his death, the society named an award in his honor (Børge Jessen Diploma Award).*Wik

1922 Aage Niels Bohr (19 June 1922 – 8 September 2009) was a Danish nuclear physicist who shared the Nobel Prize in Physics in 1975 with Ben Roy Mottelson and James Rainwater "for the discovery of the connection between collective motion and particle motion in atomic nuclei and the development of the theory of the structure of the atomic nucleus based on this connection". His father was Niels Bohr.

Starting from Rainwater's concept of an irregular-shaped liquid drop model of the nucleus, Bohr and Mottelson developed a detailed theory that was in close agreement with experiments.

Since his father, Niels Bohr, had won the prize in 1922, he and his father are one of the six pairs of fathers and sons who have both won the Nobel Prize and one of the four pairs who have both won the Nobel Prize in Physics.

DEATHS

1504 Bernhard Walther
(1430 – June 19, 1504) was a German merchant, humanist and astronomer based in Nuremberg, Germany.
Walther was born in Memmingen, and was a man of large means, which he devoted to scientific pursuits. When Regiomontanus settled in Nuremberg in 1471, they worked in collaboration to build an observatory and a printing press. After the death of Regiomontanus in 1476 at Rome, Walther bought his instruments, after Hans von Dorn, commissioned by the Hungarian king, had tried in vain about it with the council of Nuremberg. Thenceforward, he continued the observation of planets till his death in Nuremberg. His house, purchased in 1509 by Albrecht Dürer, is now a museum

1770 Diego de Torres Villarroel (?17 Nov 1693 – 19 June 1770) was a Spanish writer, poet, dramatist, doctor, mathematician, priest and professor of the University of Salamanca.
Spanish mathematician and writer, famous in his own time as the great maker of almanacs that delighted the Spanish public, now remembered for his Vida, picaresque memoirs that are among the best sources for information on life in 18th-century Spain. While young, his career encompassed being a dancer, musician, bullfighter, poet, lock picker, and seller of patent medicines. Later, upon reading a book on solid geometry, he turned to mathematics. In 1721 he wrote his first almanac, and in 1726 he was made professor of mathematics at the University of Salamanca.

1945 Stefan Mazurkiewicz (25 September 1888 – 19 June 1945) was a Polish mathematician who worked in mathematical analysis, topology, and probability. He was a student of Wacław Sierpiński and a member of the Polish Academy of Learning (PAU). His students included Karol Borsuk, Bronisław Knaster, Kazimierz Kuratowski, Stanisław Saks, and Antoni Zygmund. For a time Mazurkiewicz was a professor at the University of Paris; however, he spent most of his career as a professor at the University of Warsaw.

The Hahn–Mazurkiewicz theorem, a basic result on curves prompted by the phenomenon of space-filling curves, is named for Mazurkiewicz and Hans Hahn. His 1935 paper Sur l'existence des continus indécomposables is generally considered the most elegant piece of work in point-set topology.

The Hahn–Mazurkiewicz theorem is the following characterization of spaces that are the continuous image of curves: A non-empty Hausdorff topological space is a continuous image of the unit interval if and only if it is a compact, connected, locally connected, second-countable space.
Spaces that are the continuous image of a unit interval are sometimes called Peano spaces.

During the Polish–Soviet War (1919–21), Mazurkiewicz as early as 1919 broke the most common Russian cipher for the Polish General Staff's cryptological agency. Thanks to this, orders issued by Soviet commander Mikhail Tukhachevsky's staff were known to Polish Army leaders. This contributed substantially, perhaps decisively, to Polish victory at the critical Battle of Warsaw and possibly to Poland's survival as an independent country.

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