## Wednesday, 23 August 2017

### On This Day in Math - August 23

The laws of nature are but the mathematical thoughts of God.
~Euclid

The 235th day of the year; 235 is the number of trees with 11 vertices.
(Counting the number of unlabeled free trees is still an open problem in math. No closed formula for the number of trees with n vertices up to graph isomorphism is known.)

If you build an equilateral triangle with nine matchsticks on each side, then subdivide into additional equilateral triangles, there will be a total of 235 triangles of several different sizes. The image shows the subdivision of a equilateral triangle with three matchsticks on a side. Can you find the thirteen triangles in it?

EVENTS

1638 Descartes, in a letter to Mersenne, proposed his folium (x3 + y3 = 2axy) as a test case to challenge Fermat’s differentiation techniques. To Descartes’ embarrassment, Fermat’s method worked better than his own. *VFR

1735 Abraham deMoivre elected to the Berlin Academy after Philipp Naud´e (1684–1747) presented a copy of deMoivre’s Miscellanea analytica of 1730. Among other things this book contains work on the Fibonacci sequence. See “Abraham deMoivre” by Helen M. Walker, Scripta Mathematica, 2(1933), 316–333. *VFR

1811 The aged Thomas Jefferson, confined to his room due to rhumatism, amuses him self with mathematical pursuits by calculating the lines for a sun-dial, as he reports in a letter to Charles Clay, "I have amused myself with calculating the hour lines of an horizontal dial for the latitude of this place, which I find to be 37o 22' 26". The calculations are for every five minutes of time, and are always exact to within less than half a second of a degree. " *John Fauval, From a lecture at the Univ of Va.

In 1966, the Lunar Orbiter 1 took the first photograph of the Earth from the Moon.*TIS

1977 Dr. Paul MacCready’s Gossamer Condor, powered only by the pilot, Bryan Allen, completed a 800-yard ﬁgure-8 ﬂight to win the Kremer Prize. See July 12, 1979. [Air & Space] *VFR

BIRTHS

1683 Giovanni Poleni ( 23 Aug, 1683;Venice,- 14 Nov, 1761; Padua) was an Italian mathematician who worked on hydraulics, physics, astronomy and archaeology *SAU He was the son of Marquess Jacopo Poleni and studied the classics, philosophy, theology, mathematics, and physics at the School of the Padri Somaschi, Venice. He was appointed, at the age of twenty-five, professor of astronomy at Padua. In 1715 he was assigned to the chair of physics, and in 1719 he succeeded Nicholas II Bernoulli as professor of mathematics. As an expert in hydraulic engineering he was charged by the Venetian Senate with the care of the waters of lower Lombardy and with the constructions necessary to prevent floods. He was also repeatedly called in to decide cases between sovereigns whose states were bordered by waterways.
Poleni was the first to build a calculator that used a pinwheel design. Made of wood, his calculating clock was built in 1709; he destroyed it after hearing that Antonius Braun had received 10,000 Guldens for dedicating a pinwheel machine of his own design to the emperor Charles VI of Vienna. Poleni described his machine in his Miscellanea in 1709, but it was also described by Jacob Leupold in his Theatrum Machinarum Generale ("The General Theory of Machines") which was published in 1727. In 1729, he also built a tractional device that enabled logarithmic functions to be drawn.
Poleni's observations on the impact of falling weights (similar to William 's Gravesande's) led to a controversy with Samuel Clarke and other Newtonians that became a part of the so-called "vis viva dispute" in the history of classical mechanics.
His knowledge of architecture caused Benedict XIV to call him to Rome in 1748 to examine the cupola of St. Peter's, which was rapidly disintegrating. He promptly indicated the repairs necessary. He also wrote a number of antiquarian dissertations. In 1710 he was elected a Fellow of the Royal Society,[4] in 1739 the French Academy of Sciences made him a member and later the societies of Berlin and St. Petersburg did the same. The city of Padua elected him as magistrate, and after his death erected his statue by Canova. Venice also honoured him by striking a medal.
He married Orsola Roberti of Bassano della Grappa. *Wik

1778 Josef-Maria Hoëné de Wronski wrote on the philosophy of mathematics. *SAU He wrote exclusively in French, desirous that his ideas, of whose immortality he was convinced, should be accessible to all; he worked, he said, "through France for Poland." He published over a hundred works, and left many more in manuscript. When dying in the seventy-fifth year of his life, he exclaimed: "God Almighty, there's still so much more I wanted to say!"
In science, Hoene-Wroński set himself maximal tasks: the complete reform of philosophy and of mathematics, astronomy, technology. He not only elaborated a system of philosophy, but applications to politics, history, economics, law, psychology, music, pedagogy. It was his aspiration to reform human knowledge in an "absolute, that is, ultimate" manner.
Though during his lifetime nearly all his work was dismissed as nonsense, some of it has come in later years to be seen in a more favorable light. Although nearly all his grandiose claims were in fact unfounded, his mathematical work contains flashes of deep insight and many important intermediary results. Most significant was his work on series. He had strongly criticized Lagrange's use of infinite series, introducing instead a novel series expansion for a function. His criticisms of Lagrange were for the most part unfounded, but the coefficients in Wroński's new series were found to be important after his death, forming the determinants now known as the Wronskians (the name was given them by Thomas Muir in 1882).
The level of Wroński's scientific and scholarly accomplishments, and the amplitude of his objectives, placed Wroński in the first rank of European metaphysicians in the early 19th century. But the abstractness, formalism and obscurity of his thought, the difficulty of his language, his boundless self-assurance, his uncompromising judgments of others—alienated. He was perhaps the most original of the Polish metaphysicians, but others were more representative of the Polish outlook. *Wik

1797 Adhémar Jean Claude Barré de Saint-Venant (August 23, 1797, Villiers-en-Bière, Seine-et-Marne – January 1886, Saint-Ouen, Loir-et-Cher) was a mechanician and mathematician who contributed to early stress analysis and also developed the one-dimensional unsteady open channel flow shallow water equations or Saint-Venant equations that are a fundamental set of equations used in modern hydraulic engineering. Although his surname was Barré de Saint-Venant in non-French mathematical literature he is known simply as Saint-Venant. His name is also associated with Saint-Venant's principle of statically equivalent systems of load, Saint-Venant's theorem and for Saint-Venant's compatibility condition, the integrability conditions for a symmetric tensor field to be a strain.
In 1843 he published the correct derivation of the Navier-Stokes equations for a viscous flow and was the first to "properly identify the coefficient of viscosity and its role as a multiplying factor for the velocity gradients in the flow". Although he published before Stokes the equations do not bear his name.
Barré de Saint-Venant developed a version of vector calculus similar to that of Grassmann (now understood as exterior differential forms) which he published in 1845.[3] A dispute arose between Saint-Venant and Grassmann over priority for this invention. Grassmann had published his results in 1844, but Barré de Saint-Venant claimed he had developed the method in 1832. *Wik

1811 Auguste Bravais (23 Aug 1811;30 Mar 1863) French physicist and mineralogist, best remembered for his work on the lattice theory of crystals. Bravais lattices are named for him. In 1850, he showed that crystals could be divided into 14 unit cells for which: (a) the unit cell is the simplest repeating unit in the crystal; (b) opposite faces of a unit cell are parallel; and (c) the edge of the unit cell connects equivalent points. These unit cells fall into seven geometrical categories, which differ in their relative edge lengths and internal angles. In 1866, he elaborated the relationships between the ideal lattice and the material crystal. Sixty years later, Bravais' work provided the mathematical and conceptual basis for the determination of crystal structures after Laue's discovery of X-ray diffraction in 1911. *TIS Auguste Bravais is best known for pointing out that there are in total 14 types of crystallographic lattices. His ordering and denomination of lattices is still in use today. *Arjen Dijksman, commonsensequantum.blogspot.fr

1817 Sarah Frances Whiting (August 23, 1847 – September 12, 1927), American physicist and astronomer, was the instructor to several astronomers, including Annie Jump Cannon.
Whiting graduated from Ingham University in 1865.
She was appointed by Wellesley College president Henry Fowle Durant, one year after the College's 1875 opening, as its first professor of physics. She established its physics department and the undergraduate experimental physics lab at Wellesley, the second of its kind to be started in the country. At the request of Durant, she attended lectures at MIT given by Edward Charles Pickering.[1] He invited Whiting to observe some of the new techniques being applied to astronomy, such as spectroscopy. In 1880, Whiting started teaching a course on Practical Astronomy at Wellesley.
In 1895, as told by biographer Annie Jump Cannon,
An especially exciting moment came when the Boston morning papers reported the discovery of the Rontgen or X-rays in 1895. The advanced students in physics of those days will always remember the zeal with which Miss Whiting immediately set up an old Crookes tube and the delight when she actually obtained some of the very first photographs taken in this country of coins within a purse and bones within the flesh.
Between 1896 and 1900, Whiting helped Wellesley College trustee Sarah Elizabeth Whitin to establish the Whitin Observatory, of which Whiting became the first director.
Tufts College bestowed an honorary doctorate on Whiting in 1905. She was also known for supporting prohibition.
Whiting retired from Wellesley in 1916 and was a Professor Emeritus until her death in 1927. She is buried in Machpelah Cemetery in Le Roy, New York, near her now-defunct alma mater.*Wik

1829 Birthdate of Moritz Cantor, (23 Aug 1829;10 Apr 1920)
German historian of mathematics, one of the greatest of the 19th century. He is best remembered for the four volume work Vorlesungen über Geschichte der Mathematik which traces the history of mathematics up to 1799. The first volume (published 1880) traces the general history of mathematics up to 1200. The second volume traces the history up to 1668 (the year Newton and Leibniz were just about to embark on their mathematicalresearches). The third volume continues up to 1758 (Lagrange's work began shortly after this date). Cantor then, at the age of 69, as editor-in-chief, organised a team with nine further contributors to collaborate on the fourth volume (published 1908), continuing to 1799, the year of Gauss's doctoral thesis. *TIS

1842 Osborne Reynolds (23 Aug 1842; 21 Feb 1912) British engineer, physicist, and educator best known for his work in hydraulics and hydrodynamics. He introduced the Reynolds number classifying fluid flow.*TIS

1875 William Henry Eccles (23 Aug 1875; 29 Apr 1966); British physicist who pioneered in the development of radio communication. Eccles was an early proponent of Oliver Heaviside's theory that an upper layer of the atmosphere reflects radio waves, thus enabling their transmission over long distances. He also suggested in 1912 that solar radiation accounted for the differences in wave propagation during the day and night. He experimented with detectors and amplifiers for radio reception, coined the term "diode," and studied atmospheric disturbances of radio reception. After WW I, he made many contributions to electronic circuit development*, including the Eccles-Jordan "flip-flop" patented in 1918 and used in binary counters (working with F.W. Jordan).*TIS

1893 Joseph Fels Ritt (August 23, 1893–January 5, 1951) was an American mathematician at Columbia University in the early 20th century.
He is known for his work on characterizing the indefinite integrals that can be solved in closed form, for his work on the theory of ordinary differential equations and partial differential equations, for beginning the study of differential algebraic groups, and for the method of characteristic sets used in the solution of systems of polynomial equations.*Wik

1909 Florence Nightingale David, also known as F. N. David (August 23, 1909 - July 23, 1993) was an English statistician, born in Ivington, Herefordshire, England. She was named after Florence Nightingale, who was a friend of her parents.
David read mathematics at Bedford College for Women in London. After graduation, she worked for the eminent statistician Karl Pearson​ at University College, London as his research student. She calculated the distribution of correlation coefficients, producing in 1938 her first book, Tables of the correlation coefficient.
After Karl Pearson died in 1934, she returned to the Biometrics laboratory to work with Jerzy Neyman where she submitted her last four published papers as her PhD thesis. During World War II, David worked for the Ministry of Home Security. In late 1939 when war had started but England had not yet been attacked, she created statistical models to predict the possible consequences of bombs exploding in high density populations such as the big cities of England and especially London. From these models, she determined estimates of harm to humans and damage to non-humans This included the possible numbers living and dead, the reactions to fires and damaged buildings as well as damages to communications,utilities such as phones, water, gas, electricity and sewers. As a result when the Germans bombed London in 1940 and 1941, vital services were kept going and her models were updated and modified with the evidence from the real harms and real damage.
David became head of the Statistics Department at the University of California at Riverside in 1970.*Wik

1919 Dirk Polder (August 23, 1919, The Hague — March 18, 2001, Iran) was a Dutch physicist who, together with Hendrik Casimir, first predicted the existence of what today is known as the Casimir-Polder force, sometimes also referred to as the Casimir effect or Casimir force. He also worked on the similar topic of radiative heat transfer at nanoscale. *Wik

1933 Robert F. Curl, Jr. American chemist who with Richard E. Smalley and Sir Harold W. Kroto discovered the first fullerene, a spherical cluster of carbon atoms, in 1985. The discovery opened a new branch of chemistry, and all three men were awarded the 1996 Nobel Prize for Chemistry for their work. In Sep 1985 Curl met with Kroto of the University of Sussex, Eng., and Smalley, a colleague at Rice, and, in 11 days of research, they discovered fullerenes. They announced their findings to the public in the 14 Nov 1985, issue of the journal Nature.*TIS

DEATHS

1806 Charles-Augustin de Coulomb (14 June 1736, 23 Aug 1806) French physicist best known for the formulation of Coulomb's law, which states that the force between two electrical charges is proportional to the product of the charges and inversely proportional to the square of the distance between them. Coulombic force is one of the principal forces involved in atomic reactions.*TIS

1923 Phoebe Sarah Hertha Ayrton (28 April 1854 – 23 August 1923), was a British engineer, mathematician, physicist, and inventor. Known in adult life as Hertha Ayrton, born Phoebe Sarah Marks, she was awarded the Hughes Medal by the Royal Society for her work on electric arcs and ripples in sand and water.
In 1880, Ayrton passed the Mathematical Tripos, but Cambridge did not grant her an academic degree because, at the time, Cambridge gave only certificates and not full degrees to women. Ayrton passed an external examination at the University of London, which awarded her a Bachelor of Science degree in 1881.
In 1899, she was the first woman ever to read her own paper before the Institution of Electrical Engineers (IEE). Her paper was entitled "The Hissing of the Electric Arc". Shortly thereafter, Ayrton was elected the first female member of the IEE; the next woman to be admitted to the IEE was in 1958. She petitioned to present a paper before the Royal Society but was not allowed because of her sex and "The Mechanism of the Electric Arc" was read by John Perry in her stead in 1901. Ayrton was also the first woman to win a prize from the Society, the Hughes Medal, awarded to her in 1906 in honour of her research on the motion of ripples in sand and water and her work on the electric arc. By the late nineteenth century, Ayrton's work in the field of electrical engineering was recognised more widely, domestically and internationally. At the International Congress of Women held in London in 1899, she presided over the physical science section. Ayrton also spoke at the International Electrical Congress in Paris in 1900. Her success there led the British Association for the Advancement of Science to allow women to serve on general and sectional committees. *Wik

1973 Helmuth Kneser (April 16, 1898 – August 23, 1973) published on sums of squares in fields, on groups, on non-Euclidean geometry, on Harald Bohr's almost periodic functions, on iteration of analytic functions, on the differential geometry of manifolds, on local uniformisation and boundary values. He succeeded in pushing forward Weierstrass and Hadamard's ideas to open up the area of the value distribution of meromorphic functions. Kneser, writing of his work on this last topic said:"I hope that this theory will also prove fruitful for the special functions used in analysis, this has to be required of a new theory, in particular, if one considers that the general theory of rational functions of one indeterminate came from the treatment of special functions, namely the gamma and sigma functions by Weierstrass and of the Riemann zeta function by Hadamard. " *SAU

1988 Hans Lewy (October 20, 1904 – August 23, 1988) was an American mathematician, known for his work on partial differential equations and on the theory of functions of several complex variables. *Wik

2001 Fred Hoyle (24 Jun 1915, 23 Aug 2001) English astronomer who coined the term "Big Bang." He became Britain's best-known astronomer in 1950 with his broadcast lectures on the nature of the universe. He recalled using "big bang" for the first time in the last of those talks, though he never accepted that theory for the origin of the universe. Working with Hermann Bondi and Thomas Gold, Hoyle had proposed the steady state theory in the 1940s, arguing that the universe developed in a process of continuous growth. Over time, his belief in a "steady state" universe was shared by fewer and fewer scientists because of new discoveries. Hoyle also did theoretical work on the formation - in older, hotter stars - of other elements as helium nuclei fuse to produce carbon, oxygen, and eventually elements up to iron. *TIS

I am told he is also the author of Robin Whitty's (Theorem of the Day) favorite sci-fi novel,  The Black Cloud
.

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