## Monday, 21 August 2017

### On This Day in Math - August 21

As for methods I have sought to give them all the rigour that one requires in geometry, so as never to have recourse to the reasons drawn from the generality of algebra.
~Augustin-Louis Cauchy

The 233rd day of the year; 233 is the only three digit prime that is also a Fibonacci number. (Are there any four digit ones?)

233 is also the last day of the year that is the sum of the squares of consecutive Fibonacci numbers.  (A pretty mathematical fact for the day: the sum of the squares of two consecutive Fibonacci numbers is always a Fibonacci number, Students can show that the converse is not true.)

There are exactly 233 maximal planar graphs with ten vertices, and 233 connected topological spaces with four points.

And 233 is the last year day that will solve the Markov Equation; $x^2 + y^2 + z^2 =3xyz$

EVENTS

1560 The occurrence at the predicted time of a solar eclipse in Copenhagen turned Tycho Brahe toward a life of observational astronomy. *VFR Thony Christie has stated that it was the failure to occur at the predicted time that inspired Tycho. At any rate, he would be able to predict them himself within a few years: A total lunar eclipse occurred on December 8, 1573. It was predicted and then observed by a young Tycho Brahe (assisted by his sister Sophia) at Knutstorp Castle. He said "I cannot but be very surprised that even at this youthful age of 26 years, I was able to get such accurate results." *Wik

1609 Galileo demonstrates his telescope to the aristocrats of Venice. *Renaissance Mathematicus,

1706 Jakob Hermann writes to Leibniz about proof that Machin's series converges to pi. In 1706 William Jones published a work Synopsis palmariorum matheseos or, A New Introduction to the Mathematics, Containing the Principles of Arithmetic and Geometry Demonstrated in a Short and Easie Method ... Designed for ... Beginners. (This is the book in which Jones first uses Pi in the mathematical sense it is now used)  This contains on page 243 the following passage:-
There are various other ways of finding the lengths or areas of particular curve lines, or planes, which may very much facilitate the practice; as for instance, in the circle, the diameter is to the circumference as 1 to (16/5- 4/239) - 1/3(16/53- 4/2393) &c. = 3.14159 &c. = π. This series (among others for the same purpose, and drawn from the same principle) I received from the excellent analyst, and my much esteemed friend Mr John Machin; and by means thereof, van Ceulen's number, or that in Art. 64.38 may be examined with all desirable ease and dispatch.
Jones also reports that this formula allows π be calculated, "... to above 100 places; as computed by the accurate and ready pen of the truly ingenious Mr John Machin."
No indication is given in Jones's work, however, as to how Machin discovered his series expansion for π so when de Moivre wrote to Johann Bernoulli on 8 July 1706 telling him about Machin's series for π he suggested that Johann Bernoulli might tell Jakob Hermann about Machin's unproved result. He did so and Hermann quickly discovered a proof that Machin's series converges to π. He produced techniques that show other similar series also converge rapidly to π and he wrote on 21 August 1706 to Leibniz giving details. Two years later, on 6 July 1708, de Moivre wrote again to Johann Bernoulli about Machin's series, on this occasion giving two different proofs that it converged to π.  *VFR

1776 First recorded use of dollar symbol \$. Ezra l'Hommedieu, a member of the New York Provencial Assembly had over a dozen different symbols in his diary beginning with a single vertical bar and proceeding to two vertical bars. *F Carjori (Notes on the term "dollar" and the symbol here.)
The image of l'Hommedieu's diary from Cajori's History of Mathematical Notations

1888 William Seward Burroughs of St. Louis obtained a patent for his adding machine, the ﬁrst successfully marketed. In January, 1886, he incorporated as the American Arithmometer Corporation. *VFR He received patents on four adding machine applications (No. 388,116-388,119), the first U.S. patents for a "Calculating-Machine" that the inventor would continue to improve and successfully market. One year after making his first patent application on 10 Jan 1885, he incorporated his business as the American Arithmometer Corporation of St. Louis, in Jan 1886, with an authorized capitalization of $100,000$. After Burrough's early death in 1898, after moving from St. Louis to Detroit, Michigan, that company reorganized as the Burroughs Adding Machine Co., incorporated in Jan 1905, with a capital of $5,000,000$. The new name was in tribute to the inventor.*TIS
 Records of the Patent and Trademark Office, 1836 - 1978

1893 The zeroeth International Mathematical Congress with representatives of seven countries was held in conjunction with the Chicago World’s Fair on August 21–25. William E. Story of Clark University was president of the Congress. Felix Klein of Germany came at Kaiser Wilhelm’s personal request. Klein brought nearly all of the mathematical papers published by his countrymen and a superb collection of mathematic models. [AMS Semicentennial Publishers, vol 1, p. 74]. *VFR I have read that Klein's models led to more frequent use of them in American Education.
 Felix Klein's curious collection of geometric wonders, displayed by Goettingen mathematics department *@phalpern

1945 Harry Daghlian is exposed to radiation after an accident late in the evening while "Tickling the dragon's tail". This was a coined term for the criticality experiments to determine the amount of fissionable material needed for a sustained chain reaction. He died 25 days later at the hospital in Los Alamos. *atomicheritage.org

1949 John Mauchly and J. Presper Eckert, Jr. demonstrate BINAC, a computer capable of calculating 12,000 times faster than a human being.*VFR (I wonder how they decided how fast a human being could calculate?)

1959 With the admission of Hawaii as a U S State on Aug. 21, 1959, a new executive order called for the creation of a new U S Flag.
"This is a truly historic occasion because for the second time within a year, a new state has been admitted to the union," Eisenhower said to assembled guests in a White House Cabinet Room ceremony. "It had been a long time since any state had been admitted, so to have this 49th and 50th membership of our Union in such a short space is truly a unique experience."

The new flag's design began as a history project for Robert G. Heft, who was a 17-year-old high school student in Lancaster, Ohio, in 1958.

Heft had an idea that Alaska and Hawaii would one day be states, and he set out to design a 50-star flag.

Using his mother's sewing machine, Heft had spent 12 hours using a yardstick while applying his new design of 100 hand-cut stars on each side of the blue canton of an old 48-star flag.

His teacher, who had given him a "B-" for the project, promised he'd change the grade if his flag was accepted by Congress.

Eisenhower made a personal phone call to the shocked Heft to tell him that his flag design had been accepted.

With Executive Order No. 10834, signed on Aug. 21, 1959, Eisenhower selected Heft's flag out of 1,500 designs that had been submitted for consideration.

Heft's teacher made good on his promise and awarded him the coveted "A."

"I never thought when I designed the flag that it would outlast the 48-star flag," said Heft, who later became a teacher and mayor of Napoleon, Ohio, in a 2007 interview with the Grand Rapids Press in Michigan. "I think of all the things it stood for in the past, the things we've done as a nation that we're proud of. It's not a perfect country, but where else would I like to live?" Heft added in the newspaper interview. He died in 2009. * Frederick N. Rasmussen, The Baltimore Sun
Math teachers might point out to students that this is a very mathematical starfield

1972 Peru issued a Air Post Stamp picturing a Quipu. [Scott #C341]. *VFR

2015 The AAS Division For Planetary Sciences announced Dr. Dan Durda (Southwest Research Institute) as winner of the Carl Sagan Medal for outstanding communication by an active planetary scientist to the general public, Over 30 years ago in my first full year of teaching, Dan was one of the first of the many bright, kind, and conscientious students who made my years in the classroom wonderful. Congratulations to a great scientist, and scientific communicator.

2017 Next total solar eclipse in the USA. The southern part of Illinois will have 2 total solar eclipses in a time span of only 7 years. Maximum duration will be occur near Hopkinsville, Ky. It will last two minutes and 40 seconds.
The next total solar eclipse after 2017 will be on 8 April 2024. Thereafter the next total solar eclipse is on 30 March 2033. Ref. More Mathematical Astronomical Morsels by Jean Meeus; Willmann-Bell, 2002. *NSEC

BIRTHS

1665 Giacomo Filippo Maraldi (August 21, 1665 – December 1, 1729) was a French-Italian astronomer and mathematician. His name is also given as Jacques Philippe Maraldi. Born in Perinaldo (modern Liguria) he was the nephew of Giovanni Cassini, and worked most of his life at the Paris Observatory (1687 – 1718). He also is the uncle of Jean-Dominique Maraldi.
From 1700 until 1718 he worked on a catalog of fixed stars, and from 1672 until 1719 he studied Mars extensively. His most famous astronomical discovery was that the ice caps on Mars are not exactly on the rotational poles of that body. He also recognized (in May 1724) that the corona visible during a solar eclipse belongs to the Sun not to the Moon, and he discovered R Hydrae as a variable star. He also helped with the survey based on the Paris Meridian.
He is also credited for the first observation (1723) of what is usually referred to as Poisson's spot, an observation that was unrecognized until its rediscovery in the early 19th century by Dominique Arago. At the time of Arago's discovery, Poisson's spot gave convincing evidence for the contested wave nature of light.
In mathematics he is most known for obtaining the angle in the rhombic dodecahedron shape in 1712, which is still called the Maraldi angle. *Wik A rhombic face of a dodecahedron has diagonals in the proportion of 2:sqrt(2); making the acute angle appx. 109.5o. This is also the angle between two segments from the center to the vertices of a tetrahedron. Four soap bubbles intersect at this same angle according to Joseph Plateau's work, and Kepler noticed the shape at the closed ends of honeycombs.*PB NOTES

1757 Josiah Meigs (August 21, 1757 – September 4, 1822) was an American academic, journalist and government official meteorologist and mathematician, born.*Wik This freethinking Democrat left his professorship at Yale for political reasons and became president of the University of Georgia. He applied Galileo’s formula for fallen bodies to the nine day’s fall of Lucifer and his angels, to determine that Hell was 1,832,308,363 miles deep. [Struik, Origins of American Science, p. 370] *VFR

1789 Augustin-Louis Cauchy (21 Aug 1789;23 May 1857) French mathematician who pioneered in analysis and the theory of substitution groups (groups whose elements are ordered sequences of a set of things). He was one of the greatest of modern mathematicians. *TIS

1901 Edward Copson (21 Aug 1901; 16 Feb 1980) English mathematician known for his studies in classical analysis, differential and integral equations, and their use in mathematical physics. After graduating from Oxford University with a B.A. degree in 1922, he moved to Scotland where he spent the nearly all of his career. His first book, The Theory of Functions of a Complex Variable (1935) was immediately successful. He was a co-author for his next book, The Mathematical Theory of Huygens' Principle (1939). By 1975, he had published four more books, on asymptotic expansions, metric spaces and partial differential equations. Many of the papers he wrote bridged mathematics and physics, of which his last showed his interest in astrophysics, Electrostatics in a Gravitational Field (1978) which was relevant to Black Holes.*TIS

1932 Louis de Branges de Bourcia (born August 21, 1932) is a French-American mathematician. He is the Edward C. Elliott Distinguished Professor of Mathematics at Purdue University in West Lafayette, Indiana. He is best known for proving the long-standing Bieberbach conjecture in 1984, now called de Branges' theorem. He claims to have proved several important conjectures in mathematics, including the generalized Riemann hypothesis.*SAU

1940 Endre Szemerédi (August 21, 1940, ) is a Hungarian mathematician, working in the field of combinatorics and theoretical computer science. He is the State of New Jersey Professor of computer science at Rutgers University since 1986. He received his PhD from Moscow State University. His adviser was the late mathematician Israel Gelfand. He has published over 200 scientific articles in the fields of Discrete Mathematics, Theoretical Computer Science, Arithmetic Combinatorics and Discrete Geometry. He is best known for his proof from 1975 of an old conjecture of Paul Erdős and Paul Turán: if a sequence of natural numbers has positive upper density then it contains arbitrarily long arithmetic progressions. This is now known as Szemerédi's theorem. One of the key tools introduced in his proof is now known as the Szemerédi regularity lemma, which has become a very important tool in combinatorics, being used for instance in property testing for graphs and in the theory of graph limits.
He is also known for the Szemerédi-Trotter theorem in incidence geometry and the Hajnal-Szemerédi theorem in graph theory. Ajtai and Szemerédi proved the corners theorem, an important step toward higher dimensional generalizations of the Szemerédi theorem. With Ajtai and Komlós he proved the ct2 /log t upper bound for the Ramsey number R(3,t), and constructed a sorting network of optimal depth. With Ajtai, Chvátal, and M. M. Newborn, Szemerédi proved the famous Crossing Lemma, that a graph with n vertices and m edges, where m greater than 4n has at least m3 / 64n2 crossings. With Paul Erdős, he proved the Erdős-Szemerédi theorem on the number of sums and products in a finite set. With Wolfgang Paul, Nick Pippenger, and William Trotter, he established a separation between nondeterministic linear time and deterministic linear time, in the spirit of the infamous P versus NP problem. With William Trotter, he established the Szemerédi–Trotter theorem obtaining an optimal bound on the number of incidences between finite collections of points and lines in the plane.*Wik

DEATHS

1757 Samuel König (July 31, 1712, Büdingen – August 21, 1757, Zuilenstein near Amerongen) was a German mathematician who is best remembered for his part in a dispute with Euler over the Principle of Least Action.*SAU In the 17th century Pierre de Fermat postulated that "light travels between two given points along the path of shortest time," which is known as the principle of least time or Fermat's principle.
Credit for the formulation of the principle of least action is commonly given to Pierre Louis Maupertuis, who wrote about it in 1744 and 1746. Maupertuis felt that "Nature is thrifty in all its actions", and applied the principle broadly. Johann Bernoulli instructed both König and Pierre Louis Maupertuis as pupils during the same period. Konig is also remembered as a tutor to Émilie du Châtelet, one of the few female physicists of the 18th century. *Wik

1814 Count Benjamin Thompson Rumford (26 Mar 1753, 21 Aug 1814) American-born British physicist, government administrator, and a founder of the Royal Institution of Great Britain, London. Because he was a Redcoat officer and an English spy during the American revolution, he moved into exile in England. Through his investigations of heat he became one of the first scientists to declare that heat is a form of motion rather than a material substance, as was popularly believed until the mid-19th century. Among his numerous scientific contributions are the development of a calorimeter and a photometer. He invented a double boiler, a kitchen stove and a drip coffee pot. *TIS

1836 Claude-Louis Navier (10 February 1785 – 21 August 1836) was a French mathematician best known for the Navier-Stokes equations describing the behaviour of a incompressible fluid. *SAU Navier also formulated the general theory of elasticity in a mathematically usable form (1821), making it available to the field of construction with sufficient accuracy for the first time. In 1819 he succeeded in determining the zero line of mechanical stress, finally correcting Galileo Galilei's incorrect results, and in 1826 he established the elastic modulus as a property of materials independent of the second moment of area. Navier is therefore often considered to be the founder of modern structural analysis. *Wik

1927 William Burnside (2 July 1852 – 21 August 1927) wrote the first treatise on groups in English and was the first to develop the theory of groups from a modern abstract point of view. *SAU
Burnside is also remembered for the formulation of Burnside's problem (which concerns the question of bounding the size of a group if there are fixed bounds both on the order of all of its elements and the number of elements needed to generate it) and for Burnside's lemma (a formula relating the number of orbits of a permutation group acting on a set with the number of fixed points of each of its elements) though the latter had been discovered earlier and independently by Frobenius and Cauchy.
In addition to his mathematical work, Burnside was a noted rower; while he was a lecturer at Cambridge he also coached the crew team. In fact, his obituary in The Times took more interest in his athletic career, calling him "one of the best known Cambridge athletes of his day". *Wik

1957 Harald Ulrik Sverdrup ( 15 Nov 1888; 21 Aug 1957)was a Norwegian meteorologist and oceanographer known for his studies of the physics, chemistry, and biology of the oceans. He explained the equatorial countercurrents and helped develop the method of predicting surf and breakers. As scientific director of Roald Amundsen's polar expedition on Maud (1918-1925), Sverdrup worked extensively on meteorology, magnetics, atmospheric electricity, physical oceanography, and tidal dynamics on the Siberian shelf, and even on the anthropology of Chukchi natives. In 1953, Sverdrup quantified the concept of "critical depth", explaining the onset of the spring phytoplankton bloom in newly stratified water columns.*TIS

1995 Subrahmanyan Chandrasekhar (19 Oct 1910, 21 Aug 1995) Indian-born U.S. astrophysicist who shared with William A. Fowler the 1983 Nobel Prize for Physics for formulating the currently accepted theory on the later evolutionary stages of massive stars, work that subsequently led to the discovery of neutron stars and black holes. *TIS

2012 William Paul Thurston (October 30, 1946 – August 21, 2012) was an American mathematician. He was a pioneer in the field of low-dimensional topology. In 1982, he was awarded the Fields Medal for his contributions to the study of 3-manifolds. He was last a professor of mathematics and computer science at Cornell University (since 2003). *Wik His AMS obituary begins:
William P. Thurston, whose geometric vision revolutionized topology, died August 21 at the age of 65. Within a short span of just a few years at the beginning of his career, Thurston proved so many outstanding results in foliation theory, that the whole area seemed to be finished because he had answered most of the important open problems. Then, in the mid-1970s, he turned his attention to low-dimensional topology, to which he brought a whole new set of geometric tools, most notably from hyperbolic geometry.

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

## Sunday, 20 August 2017

### On This Day in Math - August 20

Mathematics is a form of poetry which transcends poetry in that it proclaims a truth; a form of reasoning which transcends reasoning in that it wants to bring about the truth it proclaims; a form of action, of ritual behavior, which does not find fulfillment in the act but must proclaim and elaborate a poetic form of truth.
~Salomon Bochner

The 232nd day of the year; 232 is the maximum number of regions that the plane can be divided into with 21 lines (how many of the regions would be of infinite area?)

And from Derek Orr
232 is sum of the cubes of the factorials of its digits,
232 = (2!)3 + (3!)3 + (2!)3
and the sum of the first 11 Fibonacci numbers
232 = 1+1+2+3+5+8+13+21+34+55+89

If you add up all the proper divisors of a number, n, they can be less than n(deficient), equal to n (perfect, like 6 or 28) or abundant. 12 is the smallest abundant number. Nicomachus wrote only of even numbers because he thought all odd numbers were deficient, but he was wrong. The 232nd abundant number is odd, 945.

EVENTS

1601 Piere Fermat, the child of Claire de Long is baptized in the town of Beaumont de Lomange near Toulouse. almost thirty years later he would marry his mother's distant cousin. *André Weil, Number Theory: An Approach Through History from Hammurapi to Legendre

1638 William Oughtred writes to instrument maker Elias Allen with instructions for the first physical pair of slide rules using his method. Oughtred had invented the rules as early as 1620, and definitely written about them by 1633, but as he says in the opening of his letter, he had never made one before: “I have here sent you directions (as you requested me being at Twickenham) about the making of the two rulers”. He would continue, “would gladly see one of [the two parts of the instrument] when it is finished: wch yet I never have done”. The slide rule that Allen created seems no longer to exist, but a reverse image printed from the rule, perhaps to show to Oughtred still remains.
*Boris Jardine, Cambridge University Library Special Collections
Oughtred's method used two rules with logarithmic scales that were positioned so that one slid against the other. Within two decades, the first slide rule with the scales bound together was created by Robert Bissaker. This is the oldest slide rule still existing today and is in the Science Museum, London.

1699 Newton's name introduced outside the Cambridge area. In 1669 Barrow had brought Newton a copy of Nicholas Mercator's Logarithmotechnia, which included the infinite series for ln(1+x). Newton recognized this as a simple example of his more general work on infinite series during his annus mirabilis in Woolsthorpe. Newton began to share some of his work with Barrow, who talked him into allowing him to send some of it, anonymously, to John Collins, which he did. When Collins highly favorable responses were received, Newton allowed Barrow to identify him to Collins. Barrow's letter to Collins on this date was the first time Newton became known to the mathematical community outside Cambridge. *James Gleick, Isaac Newton

1858 The Darwin-Wallace paper was read before the Linnean Society July 1st, 1858 and published in their Proceedings Vol 3 1858. pp 45-62. on this day.
"On the Tendency of Species to form Varieties; and on the Perpetuation of Varieties and Species by Natural Means of Selection" ; By Charles Darwin, Esq., F.R.S., F.L.S.., & F.G.S., and Alfred Wallace​, Esq. Communicated by Sir Charles Lyell, F.R.S., F.L.S., and J.D. Hooker, Esq., M.D., V.P.R.S., F.L.S., &c. *Linnean Society

1910 Florence Nightengale was buried on 20 August in the family plot at East Wellow, Hampshire. An offer of burial in Westminster Abbey was refused by her relatives. She died one week earlier. *Victorian Web Org

1955 Observances were held on the Island of Samos commemorating the 2500th anniversary of the founding of the ﬁrst school of philosophy by Pythagoras. Four postage stamps were issued by Greece. Naturally one of them illustrated the celebrated 47th proposition of Euclid, the Pythagorean Theorem, by a 3–4–5 triangle with squares erected on its sides.

1960 Two mongrel dogs, Belka(Little Squirrel) and Strelka(Little Arrow) became the first living creatures to perform a space flight and return safely to Earth. Korabl-Sputnik-2 (Spaceship Satellite-2), also known as Sputnik 5, was launched on August 19, 1960. Also on board were 40 mice, 2 rats and a variety of plants.
After a day in orbit, the spacecraft's retrorocket was fired and the landing capsule and the dogs were safely recovered. They were the first living animals to survive orbital flight. *Space Today Online

BIRTHS

1710 Thomas Simpson born (20 August 1710 – 14 May 1761). Best known to elementary calculus students for Simpson's rule, a method to approximate definite integrals. (this rule had been found 100 years earlier by Johannes Kepler, and in German is the so-called Keplersche Fassregel.) The method actually uses a method of fitting parabolas to the function (a word not in use when Simpson lived) but is exact for polynomials up to a cubic. Apparently, the method that became known as Simpson's rule was well known and used earlier by Bonaventura Cavalieri (a student of Galileo) in 1639, later rediscovered by James Gregory (who Simpson succeeded as Regius Professor of Mathematics at the University of St Andrews) and was only attributed to Simpson because of the popularity of his math books in which it was included. *Wik

1862 Paul Gustav Samuel Stäckel (20 August 1862, Berlin — 12 December 1919, Heidelberg) was a German mathematician, active in the areas of differential geometry, number theory, and non-Euclidean geometry. In the area of prime number theory, he used the term twin prime (Primzahlzwillinge i.e. "prime number twins")for the first time. *Wik

1863 Corrado Segre (20 August 1863, 18 May 1924) was an Italian mathematician who is remembered today as a major contributor to the early development of algebraic geometry.
Segre spent his entire career at the University of Turin, first as a student of Enrico D'Ovidio. In 1883 he published a dissertation on quadrics in projective space and was named as assistant to professors in algebra and analytic geometry. In 1885 he also assisted in descriptive geometry. He began to instruct in projective geometry, as stand-in for Giuseppe Bruno, from 1885 to 88. Then for 36 years he had the chair in higher geometry following D'Ovidio. Segre and Giuseppe Peano made Turin known in geometry.*Wik

1898 Leopold Infeld born (20 August 1898, Kraków – 15 January 1968, Warsaw), He was a Polish theoretical physicist. In 1948 he published Whom the Gods Love, a biographical novel about Evariste Galois. *VFR
He was awarded a doctorate at the Jagiellonian University (1921), worked as an assistant and a docent at the University of Lwów (1930–1933) and then as a professor at the University of Toronto between 1939 and 1950. In 1939 he married Helen Schlauch, an American mathematician and a graduate of Cornell.
He worked together with Albert Einstein at Princeton University (1936–1938). The two scientists co-formulated the equation describing star movements as well as co-wrote a popular science book The Evolution of Physics.
Infeld was one of the 11 signatories to the Russell–Einstein Manifesto in 1955, and is the only signatory never to receive a Nobel Prize. *Wik

1899 Salomon Bochner (20 Aug 1899; 2 May 1982) Galician-born American mathematician and educator responsible for the development of the Bochner theorem of positive-definite functions and the Bochner integral.*TIS

1957 Sir Simon Kirwan Donaldson FRS (born 20 August 1957 Cambridge, England - ) In 1986 he received a Fields Medal for his work on the topology of four-manifolds. *VFR Remarkably, Donaldson has solved problems of mathematics by using ideas from physics. From the Yang-Mills generalizations of James Clerk Maxwell's electromagnetic equations, Donaldson used special solutions to these equations, called instantons, to look at general four-manifolds. After being awarded the Fields Medal, Donaldson continued his exploitation of ideas from physics with applications to mathematics. *TIS

DEATHS

1622 Baha ad-din Muhammad ibn Husayn al-Amili (20 Mar 1546; 20 Aug 1622 at age 76) A Syrian-Iranian theologian, mathematician and astronomer, a.k.a. Shaykh Baha'i). He became a very learned Muslim whose genius touched every field of knowledge from mathematics and philosophy to architecture and landscape design. He revived the study of mathematics in Iran. His treatise on the subject, Khulasat al-hisab (“The Essentials of Arithmetic”), and translations from the original Arabic was in use as a textbook until the end of the 19th century. His treatise in astronomy, Tashrihu'l-aflak ("Anatomy of the Heavens") summarised the works of earlier masters. He was born within a year of William Gilbert in England and Tycho Brahe in Denmark, and was still a child when his family left Syria to escape religious persecution.*TIS

1672 Jan de Witt (September 24, 1625, Dordrecht - August 20, 1672) murdered by a mob from the (William of) Orange faction. For the previous twenty years he served as grand pensionary in Holland, essentially the prime minister of the Netherlands. Consequently this talented mathematician had little time to devote to mathematics. He wrote the ﬁrst systematic account of the analytic geometry of the straight line and conics. It was published in Van Schooten’s second Latin edition of Descartes’ Geometrie *VFR de Witt and his brother were both killed by a mob which was probably supported by William III of Orange. At the very least, as the Wikipedia articles states, "he protected and rewarded the killers." After a previous attempt on his life, he was lured by a forged letter to the cell where his brother was held, and both were hanged and then their bodies were mutilated. The story of their deaths are a critical element in the plot of Alexander Dumas' "The Black Tulip". *Wik

1677 Pierre Petit (8 Dec 1594 in Montluçon, France - 20 Aug 1677 in Lagny-sur-Marne, France) was a French scientist who had a strong influence on the French government. He was one of Mersenne's collaborators. Petit was an influential figure with important government positions which enabled him to try to influence national science policy. A firm believer, as were the other members of Mersenne's group, of the experimental method rather than the philosophical approach advocated by Descartes, Petit argued strongly for better astronomical facilities in France. He wanted the King to establish a Royal Observatory to allow France to again take a leading role in astronomy. Petit argued that France had fallen behind some other European countries and was relying on observations made in other countries. Petit himself had a fine collection of astronomical instruments and several of these were of his own invention. In particular, late in his life, Petit devised a filar micrometer to measure the diameters of celestial objects such as the Sun, Moon and planets.*SAU

1791 Jacques Charles,(probably 1752, August 20, 1791) Mathematician, born in Cluny, France. He is often confused with the Jacques A. C. Charles who is credited (or mis-credited) with Charles' Law and much of the work of this Jacques Charles. During the Late 18th Century both were active in Paris scientific circles and both were members of the Paris Scientific Academy. They were often distinguished by calling this one Charles the Geometer, and the other Charles the Balloonist since JAC Charles was active in promoting the use of hydrogen balloons and had designed the first balloon that is known to have been used.
This Jacques Charles is also frequently referred to by the historians who are aware of the confusion between them as Charles the Obscure.
Jacques Charles first contact with the Paris Acad of Sci was in a 1770 letter in which he submitted an article on a problem in Algebra at about the age of 18. It was turned down by the academy due to it's elementary level. The address shows that he was living in Cluny at the time. But two years later a second correspondence to the academy is read to the Academy, and Lavosier's minutes list his position as a professor of Mathematics as the school at Nanterre, on the outskirts of Paris. It is suspected that this was a preparatory school for young nobles who were training to become engineers that had been located there since the 1760's.
Between 1779 and 1785 Jacques Charles submitted seven articles to the Paris Academy, all of which were deemed worthy of publication, but only the last seemed to merit his admittance to this esteemed group. Condorcet, who was then perpetual secretary of the Academy said that this, as well as his prior papers certainly warranted his admission. It seems that Laplace, who had a conflict with Charles' mentor/sponsor, Bossut, and had been blocking his entry. With some behind the scenes effort by Lavosier had created a new geometry section, he was voted into the Academy on May 11 (often given as May 12).
By 1792 due to the confusion of their names, much of the mathematical work of Charles the Geometer would be credited to Charles the Balloonist and the "Geometer" would become the "obscure". Even the energetic J. C. Poggendorf would miscredit eight papers by the geometer to the other, and in biographies of J. A. C. Charles written even in the 20th century, you will see him credited as a "mathematician" and statements that suggest that "most of his writings were in mathematics." J. B. Gough, writing in an article in Isis in 1979 describes the ballooning Charles as, "nearly a mathematical illiterate."
The confusion between the two men of common names was exacerbated by the timing of this Charles' death. The year 1791 and the problems related to the Revolution made this the Academy of Sciences did not publish a Memoires, and as a result, no eloge's for the members who died in that year. Strangely, this was still four years before the better remembered Charles was admitted to the Academy.
He was buried (according to an old note to Cvomptes Rendes) at St. Germain l'auxerrois, but this seems hard to confirm in the church records. (*J. B. Gough)
Charles was also the Royal Professor of Hydrodynamics, and as such was also inducted into The Academy of Architecture. *Roger Hahn, More Light on Charles the Obscure, Isis, Vol. 72, No. 1 (Mar., 1981), pp. 83-86

1923 Vilfredo Pareto (15 Jul 1848, 20 Aug 1923) Italian economist and sociologist, known for his application of mathematics to economic analysis and for his theory of the 'circulation of elites'. His initial five-year course in civil engineering, graduating in 1870, gave him a grounding in mathematics. While working as an engineer, he studied philosophy and politics and wrote many periodical articles in which he was one of the first to analyse economic problems with mathematical tools. Pareto's first work, Cours d'economie politique (1896-97), included his famous 'law' of income distribution, a complicated mathematical formulation attempting to prove the distribution of incomes and wealth in society is not random and that a consistent pattern appears throughout history, in all parts of the world and in all societies. *TIS Pareto's Law was not created by him, but named in honor of him. The Pareto principle (also known as the 80-20 rule, the law of the vital few, and the principle of factor sparsity) states that, for many events, roughly 80% of the effects come from 20% of the causes.
Business-management consultant Joseph M. Juran suggested the principle and named it after Pareto, who had observed in 1906 that 80% of the land in Italy was owned by 20% of the population; he developed the principle by observing that 20% of the pea pods in his garden contained 80% of the peas. *Wik

1930 Herbert Hall Turner (13 Aug 1861, 20 Aug 1930) English astronomer who pioneered many of the procedures now universally employed in determining stellar positions from astronomical photographs. After serving as chief assistant at the Royal Greenwich Observatory for nine years, he spent most of his career as Savilian professor of astronomy at Oxford University. One of the leaders in the worldwide effort to produce an astrographic chart of the sky, he developed improved methods for obtaining both positions and magnitudes from photographic plates. Most of his later work was in seismology; he compiled and published worldwide earthquake data starting in 1918, and he discovered the existence of deep-focus earthquakes in 1922. *TIS

1972 Carol (Vander Velde)Karp (10 August 1926, Forest Grove, Ottawa County, Michigan – 20 August 1972, Maryland) died of breast cancer. At the time she was at the height of her career in logic. She received her Ph.D. in 1959 from Southern California under the direction of Leon Henkin. She created the ﬁeld of Inﬁnitary Logics which studies logics such as Lω,ω which allowed for the conjunction and disjunction of countably many formulas. This work has become very important in modern logic. *VFR

2001 Sir Fred Hoyle (24 June 1915, 20 Aug 2001) English mathematician and astronomer, best known as the foremost proponent and defender of the steady-state theory of the universe. This theory holds both that the universe is expanding and that matter is being continuously created to keep the mean density of matter in space constant. He became Britain's best-known astronomer in 1950 with his broadcast lectures on The Nature of the Universe, and he recalled coining the term "Big Bang" in the last of those talks. Although over time, belief in a "steady state" universe as Hoyle had proposed was shared by fewer and fewer scientists because of new discoveries, Hoyle never accepted the now most popular "Big Bang" theory for the origin of the universe. *TIS

2006 Professor William (Bill) Parry FRS (3 July 1934–20 August 2006) was an English mathematician. During his research career, he was highly active in the study of dynamical systems, and, in particular, ergodic theory, and made significant contributions to these fields. He is considered to have been at the forefront of the introduction of ergodic theory to the United Kingdom. He played a founding role in the study of subshifts of finite type, and his work on nilflows was highly regarded.*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

## Saturday, 19 August 2017

### On This Day in Math - August 19

Let us weigh the gain and the loss in wagering that God is. Let us consider the two possibilities. If you gain, you gain all; if you lose, you lose nothing. Hesitate not, then, to wager that He is.

Blaise Pascal,Pensees (1670)

The 231st day of the year; there are 231 cubic inches in a US Gallon, (admit it, you did NOT know that.) Ok, and it's also the sum of the squares of four distinct primes, 231 = 22 + 32 + 72 + 132.

$(3!)^3 + (2!)^4 - (1!)^5$

231 = 12 + 23 + 34 + 45 + 56 + 61 (loop 1-2-3-4-5-6-1)

231 = 98 + 76 + 54 + 3

*Derek Orr

EVENTS
1577 " On August 19, his new book is put to printing (one hundred copies) at John Day's press in Aldersgate. " The printing of John Dee's 'General and rare memorials...' begins.
ht  ‏@RCPmuseum

1758 Etienne Montucla received the approval from the censors for his Histoire des mathematiques. Often called the first true history of mathematics. *VFR

1791 "On this day in 1791, Benjamin Banneker (free African American scientist & almanac author) published his 1st Almanac."
*Bibliophilia ‏@Libroantiguo

1819 the first bicycle in the U.S. were seen in New York City. Such bicycle velocipedes or "swift walkers" had been imported that same year. Shortly thereafter, on 19 Aug 1819, the city's Common Council passed a law to "prevent the use of velocipedes in the public places and on the sidewalks of the city of New York."*TIS (Skateborders take note, you are not the first to be banned from the sidewalks)

In 1887, Dmitri Ivanovich Mendeleev (1834-1907) used a balloon to ascend above the cloud cover to an altitude of 11,500 feet (3.5 km) to observe an eclipse in Russia. He made the solo ascent above Klin without any prior experience. While his family was rather concerned, he paid no attention to controlling the balloon until after he had completed his observations, at which time he worked out how to land it. Mendeleev is the Russian chemist known for the ordering of the Periodic Table of the Elements. Yet, he was interested in many fields of science. He studied problems associated with Russia's natural resources, such as coal, salt, metals, and the petroleum industry. In 1876, he visited the U.S. to observe the Pennsylvania oil fields. *TIS

1888 Irving Stringham, after a few years at the newly formed University of California at Berkeley, writes Felix Klein, his old professor, to complain that, "I impatiently await the time when it will be possible to bring some important researchers in the field of mathematics to the California coast." *Karen Hunger Parshall, David E. Rowe; The Emergence of the American Mathematical Research Community, 1876-1900

BIRTHS

1584 Pierre Vernier born (19 August 1580 at Ornans, Franche-Comté, Spanish Habsburgs (now France) – 14 September 1637 same location). He developed an accurate scale for the astrolabe. The Vernier scale that he invented in 1631 is still common on precision instruments. First described in English by John Barrow in 1750 in his Navigatio Britannica. It is sometimes called a nonius after Pedro Nunes, the Portuguese mathematician and instrument maker, who designed a precursor to the vernier scale in 1542. A nice illustration of how the Vernier alignment method works is at this Wikipedia site. *Wik
Clavius originated a way of dividing a scale for precise measurements. His idea was adopted by Vernier 42 years later.

1646 John Flamsteed (19 Aug 1646; 31 Dec 1719)English astronomer who established the Greenwich Observatory. Science Historian/blogger Thony Christie writes
"the observational astronomer John Flamsteed Observational astronomy only produced three significant star catalogues in the two thousand years leading up to the 18th century. The first, the Greek catalogue from Hipparchus and Ptolemaeus published by Ptolemaeus in the 2nd century CE, which contained just over 1000 stars mapped with an accuracy that was astounding for the conditions under which it was produced. The second, containing somewhat more that 700 stars plus another 300 borrowed from the Ptolemaeus catalogue, was produced by the Danish astronomer Tycho Brahe in the last quarter of the 16th century, with an accuracy many factors better than his Greek predecessors. Both of these catalogues were produced with naked eye observations. The first catalogue to be produced using telescopic sights on the measuring instruments was that of John Flamsteed published posthumously in 1725, which contains more than 3000 stars measured to a much higher degree of accuracy than that of Tycho."
He then goes on to correct some misconceptions about Flamsteed's life that are commonly repeated, (he did NOT take part in talking Charles II into creating the observatory) and gives a nice description of a complex man. *Renaissance Mathematicus

1739 Georg Simon Klügel (August 19, 1739 – August 4, 1812) made an exceptional contribution to trigonometry, unifying formulae and introducing the concept of trigonometric function, in his Analytische Trigonometrie. Euler, who studied similar problems 9 years later, in some respects achieved less than Klügel in this area. Folta writes:"Klügel's trigonometry was very modern for its time and was exceptional among the contemporary textbooks. "
It was his mathematical dictionary, however, which led to his fame. This was a three volume work which appeared between 1803 and 1808. In 1808 Klügel became seriously ill and could do no further work on the project. Another three volumes were added between 1823 and 1836 by Mollweide and Grunert and the dictionary was widely used for several generations making Klügel's name widely known. *SAU

1790 Edward John Dent (19 Aug 1790 - 8 Mar 1853).English clockmaker and inventor whose chronometers were noted for high accuracy. His patents in this field included compasses for navigation and surveying. He experimented with springs made of steel, gold and glass, and devices for counteracting the effects of temperature change upon timepiece mechanisms. As clockmaker to Queen Victoria, he was commissioned to build the Great Clock for the clock tower of the Houses of Parliament (known as Big Ben, although that is actually the nickname of its hour bell) which he began in the year he died. His son, Frederick Dent, completed the work the following year and it was installed in the tower in 1859. It continues to be recognised for its great accuracy of 4 seconds in a year.*TIS

1830 (Julius) Lothar Meyer (19 Aug 1830; 12 Apr 1895) was a German chemist who discovered the Periodic Law, independently of Dmitry Mendeleyev, at about the same time (1869). However, he did not develop the periodic classification of the chemical elements as thoroughly as Mendeleyev. Meyer trained originally in medicine and chemistry. He examined the effect of carbon monoxide on blood. In 1879, Meyer compared atomic volume to atomic weight. Plotted on a graph, the curve showed the periodicity of the elements. He also established the concept of valency by indicating that a given element combined with a characteristic number of hydrogen atoms, and coined the terms like univalent, bivalent, and trivalent, based on that number.*TIS

1872 Théophile Ernest de Donder (19 August 1872 – 11 May 1957) was a Belgian mathematician and physicist famous for his 1923 work in developing correlations between the Newtonian concept of chemical affinity and the Gibbsian concept of free energy.
He received his doctorate in physics and mathematics from the Université Libre de Bruxelles in 1899, for a thesis entitled Sur la Théorie des Invariants Intégraux (On the Theory of Integral Invariants).
He was professor between 1911 and 1942, at the Université Libre de Bruxelles. Initially he continued the work of Henri Poincaré and Élie Cartan. As from 1914 he was influenced by the work of Albert Einstein and was an enthusiastic proponent of the theory of relativity. He gained significant reputation in 1923, when he developed his definition of chemical affinity. He pointed out a connection between the chemical affinity and the Gibbs free energy.
He is considered the father of thermodynamics of irreversible processes. De Donder’s work was later developed further by Ilya Prigogine. De Donder was an associate and friend of Albert Einstein. *Wik

1934 Gordon Bell (August 19, 1934 - ) is born Digital Equipment Corporation​ (DEC) innovator . In his 23 years at DEC, Bell developed several of the company's most successful minicomputers as well as its well-known VAX machine. One the world's top computer architects, Bell is considered by many to be the father of the minicomputer and is also an authority on supercomputing. The author of several books, Bell's awards include the National Medal of Technology and the IEEE Von Neumann Medal. *CHM

1939 Alan Baker born in London (19 August 1939 - ). In 1970 he received a Fields Medal for his work on Hilbert’s seventh problem which dealt with transcendental numbers. *VFR In mathematics, a transcendental number is a number (possibly a complex number) that is not algebraic—that is, it is not a root of a non-constant polynomial equation with rational coefficients. The most prominent examples of transcendental numbers are π and e. The word transcendental seems to have been created by Liebniz. In 1900, David Hilbert posed an influential question about transcendental numbers, Hilbert's seventh problem: If a is an algebraic number, that is not zero or one, and b is an irrational algebraic number, is ab necessarily transcendental? The affirmative answer was provided in 1934 by the Gelfond–Schneider theorem. This work was extended by Alan Baker in the 1960s in his work on lower bounds for linear forms in any number of logarithms (of algebraic numbers). *Wik

1973 Olga Holtz (August 19, 1973 - ) is a Russian mathematician specializing in numerical analysis. She received the Sofia Kovalevskaya Award in 2006 and the European Mathematical Society Prize (2008). Since 2008, she is a member of the Young Academy of Germany.

Holtz's early mathematical development was largely due to her parents, who were both programmers.

After winning a €1,000,000 Sofia Kovalevskaya Award in 2006, Holtz built her research group at the Technical University Berlin, [ where she became a Professor of applied mathematics while concurrently serving as an Associate, then Full Professor of Mathematics at University of California, Berkeley. Since then, Holtz has garnered additional honors. The European Mathematical Society awarded her its 2008 prize, and the European Research Council awarded her €880,000 Starting Grant in August 2010. In 2015 she was elected as a fellow of the American Mathematical Society "for contributions to numerical linear algebra, numerical analysis, approximation theory, theoretical computer science, and algebra".

Holtz, who considered a career in music before deciding on mathematics, performs with the Berlin Philharmonic Choir and practices ballroom dancing, (in her spare time????)*Wik

DEATHS

1662 Blaise Pascal died (19 June 1623 – 19 August 1662). I can not be brief about a life that contained so much in such a short time, so I mention his death. Sickly for most of his life (autopsies showed he had a deformed skull), he grew much worse in 1662. Pascal was also in a severe depression after his sister's death the year. On the night before his death he went into convulsions and received the sacraments. His last words were "May God never abandon me." He was thirty-nine years old at the time of his death. He is buried in the cemetery of Saint-Étienne, the little church where he worshiped regularly in the fifth district of Paris, near the Parthenon. There is a simple small marker near the front of the church. While frequently overlooked today, it was a prestigious church during Pascal's life. *Wik Among Pascal's lesser known inventions, it seems that he may have established the first commercial bus line in Paris.  The profits were all to go to the monastery in Port Royal.*Peter L. Bernstein, Against the Gods

1703 John Wallis (23 Nov 1616, 19 Aug 1703) British mathematician who introduced the infinity math symbol. Wallis was skilled in cryptography and decoded Royalist messages for the Parliamentarians during the Civil War. Subsequently, he was appointed to the Savilian Chair of geometry at Oxford in 1649, a position he held until his death more than 50 years later. Wallis was part of a group interested in natural and experimental science which became the Royal Society, so Wallis is a founder member of the Royal Society and one of its first Fellows. Wallis contributed substantially to the origins of calculus and was the most influential English mathematician before Newton. *TIS In addition to the infinity sign, and the use of it's reciprocal for infinitesimals, he also is credited with the idea of number line. He also probably originated the terms "mantissa" and "continued fraction". The commonly repeated idea that he refused to believe negative numbers were "less than zero" is dispelled by his use of the number line to show 5 - 8 = -3 in his "Treatise on Algebra", in 1685. *personal correspondence from Professor Phillip Beeley, Wallis Project, Oxford Univ.

1822 Jean Baptiste Joseph chevalier Delambre (19 September 1749, Amiens – 19 August 1822, Paris) was a French mathematician and astronomer. He was also director of the Paris Observatory, and author of well-known books on the history of astronomy from ancient times to the 18th century. Delambre was one of the first astronomers to derive astronomical equations from analytical formulas. His name is also one of the 72 names inscribed on the Eiffel tower. Delambre died in 1822 and was interred in the Père Lachaise Cemetery in Paris.

1887 Alvan Clark (8 Mar 1804, 19 Aug 1887)American astronomer whose family became the first significant manufacturers of astronomical instruments in the U.S. His company manufactured apparatus for most American observatories of the era, including Lick and Pulkovo, and others in Europe. In 1862, while testing a telescope, Clark discovered the companion star to Sirius, which had previously been predicted but until then never sighted. The 18½-in objective telescope he used was subsequently delivered to the Dearborn Observatory, Chicago. His sons, Alvan Graham Clark and George Bassett Clark, continued the business. The unexcelled 40-in refractor telescopes for the 40-in Yerkes observatory was made by Alvan Graham Clark*TIS

1910 Eugène Rouché (18 August 1832 at Sommières, Hérault, France - 19 August 1910 at Lunel, Hérault) died on the day following his seventy-eighth birthday. A French Geometer who edited Laguerre's "Collected Works". He also is known for Rouche's Theorem on Complex functions. *SAU

1957 Maurice Kraitchik (April 21, 1882, Minsk - August 19, 1957, Bruxelles) was a Belgian mathematician, author, and game designer. His main interests were the theory of numbers and recreational mathematics.
He is famous for having inspired the two envelopes problem in 1953, with the following puzzle in La mathématique des jeux:
Two people, equally rich, meet to compare the contents of their wallets. Each is ignorant of the contents of the two wallets. The game is as follows: whoever has the least money receives the contents of the wallet of the other (in the case where the amounts are equal, nothing happens). One of the two men can reason: "Suppose that I have the amount A in my wallet. That's the maximum that I could lose. If I win (probability 0.5), the amount that I'll have in my possession at the end of the game will be more than 2A. Therefore the game is favorable to me." The other man can reason in exactly the same way. In fact, by symmetry, the game is fair. Where is the mistake in the reasoning of each man?

Kraitchik wrote several books on number theory during 1922-1930 and after the war, and from 1931 to 1939 edited Sphinx, a periodical devoted to recreational mathematics.

During World War II, Kraïtchik emigrated to the United States, where he taught a course at the New School for Social Research in New York City on the general topic of "mathematical recreations." *Wik

1951 Michael H. Freedman (21 April 1951 in Los Angeles, California, ). In 1986 he received a Fields Medal for his proof of the four-dimensional Poincar´e conjecture. *VFR [The Poincaré conjecture, one of the famous problems of 20th-century mathematics, asserts that a simply connected closed 3-dimensional manifold is a 3-dimensional sphere. The higher dimensional Poincaré conjecture claims that any closed n-manifold which is homotopy equivalent to the n-sphere must be the n-sphere. When n = 3 this is equivalent to the Poincaré conjecture. Smale proved the higher dimensional Poincaré conjecture in 1961 for n at least 5. Freedman proved the conjecture for n = 4 in 1982 but the original conjecture remained open until settled by G Perelman who was offered the 2006 Fields medal for his proof. ] *Wik

1957 Carl-Gustaf Arvid Rossby (28 Dec 1898, 19 Aug 1957) Swedish-U.S. meteorologist who first explained the large-scale motions of the atmosphere in terms of fluid mechanics. His work contributed to developing meteorology as a science. Rossby first theorized about the existence of the jet stream in 1939, and that it governs the easterly movement of most weather. U.S. Army Air Corps pilots flying B-29 bombing missions across the Pacific Ocean during World War II proved the jet stream's existence. The pilots found that when they flew from east to west, they experienced slower arrival times and fuel shortage problems. When flying from west to east, however, they found the opposite to be true. Rossby created mathematical models (Rossby equations) for computerized weather prediction (1950).*TIS

1964 Hugo Gernsback (August 16, 1884 – August 19, 1967), born Hugo Gernsbacher, was a Luxembourgish-American inventor, writer, editor, and magazine publisher, best known for publications including the first science fiction magazine. His contributions to the genre as publisher were so significant that, along with the novelists H. G. Wells and Jules Verne, he is sometimes called "The Father of Science Fiction". In his honour, annual awards presented at the World Science Fiction Convention are named the "Hugos" *Wik

1968 George Gamow (4 Mar 1904,19 Aug 1968) Russian-born American nuclear physicist, cosmologist and writer who was one of the foremost advocates of the big-bang theory, which desribes the origin of the universe as a colossal explosion that took place billions of years ago. In 1954, he expanded his interests into biochemistry and his work on deoxyribonucleic acid (DNA) made a basic contribution to modern genetic theory. *TIS
Einstein is often quoted as saying that his use of a "cosmological constant" in his equations for the General Theory of Relativity was his "greatest blunder".  Recently (2013) I read that Mario Livio suspected that the quote had been made up by Gamow and first appears in a Scientific American article in 1956.  He quotes Gamow's history of "antics" and a quote from his wife that  ""In more than twenty years together, Geo has never been happier than when perpetuating a practical joke." *Rebecca J Rosen, The Atlantic

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

## Friday, 18 August 2017

### On This Day in Math - August 18

The total number of Dirichlet's publications is not large: jewels are not weighed on a grocery scale.
~Karl F. Gauss

The 230th day of the year; 230 is the smallest number such that it and the next number are both sphenic numbers, the product of three distinct primes (230 = 2*5*23 and 231 = 3*7*11). *Prime Curios (can there be three consecutive numbers that are the product of three (or n) distinct primes

Their are 230 possible crystal shapes that can tile space (this counts the chiral reflections as separate). This is the analogy of the better known 17 "wallpaper groups" which tile the plane. Interestingly, both were proved by the same man, Evgraf Fedorov, in 1891. He did the plane problem the hard way, he proved the case for space first, then worked backwards to the plane.

EVENTS

1709 Cotes writes to Newton in hopes of prompting the revision of the Principia which Newton had promised to deliver in "a fortnights time.". The revised papers (through Prop XXXIII) would be delivered by Cotes neighbor Whiston in September when he returned from London. *Correspondence of Sir Isaac Newton and Professor Cotes, pg 3

1783 The 1783 Great Meteor was an unusually bright Bolide observed on August 18, 1783, from the British Isles at a time when such phenomena were not well understood. The meteor was the subject of much discussion in the Philosophical Transactions of the Royal Society and was the subject of a detailed study by Charles Blagden. *Wik Christopher Goulding reproduced this Paul Sandby watercolor of the meteor as seen from the terrace of Windsor Castle on 18 August 1783. Goulding lists the observers as James Lind, the Italian physicist Dr Tiberio Cavallo (1749-1809), Dr. Lockman (the Canon of St George's, Windsor), Thomas Sandby (the brother of the artist), and two unknown women.*GeoCosmo History

1813 On August 18, 1913, at the famous Monte Carlo casino, black came up 26 times in a row. Supposedly the house made a fortune against people betting that the long overdue red HAD to show up. *PB Personal notes

In 1868, Pierre Janssan discovered helium in the solar spectrum during eclipse, but did not recognize it as a new element. The first evidence of helium was observed on August 18, 1868 as a bright yellow line with a wavelength of 587.49 nanometers in the spectrum of the chromosphere of the Sun. The line was detected by French astronomer Janssen during a total solar eclipse in Guntur, India. This line was initially assumed to be sodium. English astronomer Norman Lockyer observed a yellow line in the solar spectrum during the same eclipse, which he named the D3 Fraunhofer line because it was near the known D1 and D2 lines of sodium. He concluded that it was caused by an element in the Sun unknown on Earth. Lockyer and English chemist Edward Frankland named the element with the Greek word for the Sun, Helios. Terrestrial helium was found about 10 years later by William Ramsay. *Wik

1877 Asaph Hall discovered Phobos, a satellite of Mars. The two moons of Mars, Phobos and Deimos, were found when American astronomer Hall identified them after a long search, although their existence had been a source of speculation before. The possibility of Martian moons had been speculated long before Hall's discovery. The astronomer Johannes Kepler (1571–1630) even predicted their number correctly, although with faulty logic: he wrote that since Jupiter had four known moons and Earth had one, it was only natural that Mars should have two.
Perhaps inspired by Kepler (and quoting Kepler's third law), Jonathan Swift's satire Gulliver's Travels (1726) refers to two moons in Part 3, Chapter 3 (the "Voyage to Laputa"), in which the astronomers of Laputa are described as having discovered two satellites of Mars orbiting at distances of 3 and 5 Martian diameters, and periods of 10 and 21.5 hours, respectively. The actual orbital distances and periods of Phobos and Deimos of 1.4 and 3.5 Martian diameters, and 7.6 and 30.3 hours, respectively.
Hall discovered Deimos on August 12, 1877 at about 07:48 UTC and Phobos on August 18, 1877, at the US Naval Observatory in Washington, D.C., at about 09:14 GMT (contemporary sources, using the pre-1925 astronomical convention that began the day at noon, give the time of discovery as August 11, 14:40 and August 17 16:06 Washington mean time respectively)*Wik In the words of Asaph Hall, "Of the various names that have been proposed for these satellites, I have chosen those suggested by Mr Madan of Eton, England, viz: Deimos for the outer satellite; Phobos for the inner satellite. These are generally the names of the horses that draw the chariot of Mars.”

1881 “The matter is so perfectly clear that we cannot be amazed enough how the mathematicians so stubbornly insist on mystifying it.” Comment of Friedrich Engels on a manuscript of Karl Marx on the differential calculus. *VFR

1913 On August 18, 1913, at the famous Monte Carlo casino, black came up 26 times in a row. Supposedly the house made a fortune against people betting that the long overdue red HAD to show up. *PB Personal notes

1978 Henri Cohen gives lecture to confirm Roger Apery's proof that Apéry's constant ζ(3) is irrational. In June 1978 Roger Apéry gave a talk entitled "Sur l'irrationalité de ζ(3)." During the course of the talk he outlined proofs that ζ(3) and ζ(2) were irrational, the latter using methods simplified from those used to tackle the former rather than relying on the expression in terms of π. Due to the wholly unexpected nature of the result and Apéry's blasé and very sketchy approach to the subject many of the mathematicians in the audience dismissed the proof as flawed. Three of the audience members suspected Apéry was onto something, though, and set out to confirm his proof.
Two months later these three—Henri Cohen, Hendrik Lenstra, and Alfred van der Poorten—finished their work, and on August 18 Cohen delivered a lecture giving full details of Apéry's proof. Following the talk Apéry himself took to the podium to explain the source of some of his ideas. *Wik

BIRTHS

 *@sciencemuseum
1685 Brook Taylor born (18 August 1685 – 29 December 1731). Remembered in introductory Calculus classes for Taylor's Theorem and Taylor series. His 1713 "Methodus.." was the first book published on the calculus of finite differences and also the first use of Taylor's Theorem.
In his 1715 essay Linear Perspective, Taylor set forth the true principles of the art in an original and more general form than any of his predecessors; but the work suffered from the brevity and obscurity which affected most of his writings, and needed the elucidation bestowed on it in the treatises of John Joshua Kirby (1754) and Daniel Fournier. *Wik

1832 Eugène Rouché (18 August 1832 at Sommières, Hérault, France, -19 August 1910 at Lunel, Hérault) French Geometer who edited Laguerre's "Collected Works". He also is known for Rouche's Theorem on Complex functions. *SAU

1861 William J Greenstreet (18 Aug 1861 in Milton, Kent, England
- 28 June 1930 in Burghfield Common, Reading, England) graduated from Cambridge and became headmaster of Marling School Stroud. He is best-known as the long-running editor of the Mathematical Gazette. *SAU

1897 Bern Dibner (18 Aug 1897; 6 Jan 1988 ) Ukrainian-American engineer and science historian. Dibner worked as an engineer during the electrification of Cuba. Realizing the need for improved methods of connecting electrical conductors, in 1924, he founded the Burndy Engineering Company. A few years later, he became interested in the history of Renaissance science. Subsequently, he began collecting books and everything he could find that was related to the history of science. This became a second career as a scholar that would run parallel with his life as a businessman. He wrote many books and pamphlets, on topics from the transport of ancient obelisks, to authorative biographies of many scientific pioneers, including Volta, inventor of the electric battery, and Roentgen, discoverer of the X ray. *TIS

1910 Paul Turán (18 Aug 1910,26 Sept 1976) Paul Erdos, who co-authored many papers with Turan wrote:
Probably the most important, most enduring and most original of Turán's results are in his power sum method and its applications. I was there when it originated in 1938. Turán mentioned these problems and told me that they were not only interesting in themselves but their positive solution would have many applications. Their importance first of all is that they lead to interesting deep problems of a completely new type; they have quite unexpectedly surprising consequences in many branches of mathematics - differential equations, numerical algebra, and various branches of function theory.
In fact Turán invented the power sum method while investigating the zeta function and he first used the method to prove results about the zeros of the zeta function.*SAU

DEATHS

1652 Florimond DeBeaune died (7 October 1601, Blois – 18 August 1652, Blois). His name is attached to one of the ﬁrst problems ever posed in diﬀerential equations. *VFR DeBeaune was a friend of Descartes, and helped van Schooten write the Latin Translation of Descartes "Geometrie". De Beaune asked to find a curve for which the subtangent had a fixed length. De Beaune did not give this curve a name, but it has come to be called by his name. Leibniz solve De Beaune's question in his first paper on calculus in 1684. *Ed Sandifer, How Euler Did It. (Oct 2008)
In a 1638 letter to Descartes, de Beaune posed the problem of solving the differential equation

$\frac{\operatorname{d}y}{\operatorname{d}x}=\frac{\alpha}{y-x}$

now seen as the first example of the inverse tangent method of deducing properties of a curve from its tangents.
His Tractatus de limitibus aequationum was reprinted in England in 1807; in it, he finds upper and lower bounds for the solutions to quadratic equations and cubic equations, as simple functions of the coefficients of these equations. His Doctrine de l'angle solide and Inventaire de sa bibliothèque were also reprinted, in Paris in 1975. Another of his writings was Notae breves, the introduction to a 1649 edition of Descartes' La Géométrie. *Wik

1823 André-Jacques Garnerin (31 Jan 1769, 18 Aug 1823) French aeronaut, the first person to use a parachute regularly and successfully. He perfected the parachute and made jumps from greater altitudes than had been possible before. On 22 October 1797, at age 28, Garnerin made his first jump above the Parc Monceau in Paris. He dropped from a hot-air balloon at 3000 feet. His parachute, with 36 ribs and lines, was semi-rigid, somewhat resembling an umbrella. The descent was a success, except that he shook back and forth violently while falling. The physicist Lalande, who attended the event, suggested improving air flow with a small opening at the top of the canopy. Garnerin died aged 41. While preparing balloon equipment, a beam struck his head inflicting a mortal wound. *TIS

1960 Carlo Emilio Bonferroni (28 Jan 1892 in Bergamo, Italy - 18 Aug 1960 in Florence, Italy) His articles are more of a contribution to probability theory than to simultaneous statistical inference. He also had interests in the foundations of probability. He developed a strongly frequentist view of probability denying that subjectivist views can even be the subject of mathematical probability. *SAU He is best known for the Bonferroni inequalities, and gives his name to (but did not devise) the Bonferroni correction in statistics. *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