## Thursday, 24 August 2017

### On This Day in Math - August 24

The shortest path between two truths in the real domain passes through the complex domain.

The 236th day of the year; 236 is the sum of twelve consecutive primes, 3 + 5 + 7 + 11 + 13 + 17 + 19 + 23 + 29 + 31 + 37 + 41

And 236 is the number of possible positions in Othello after 2 moves by both players. *Erich Friedman (Students might try to figure out how many possible positions are there in tic-tac-toe after 2 moves by each player. Entice them with this number fact from Cliff Pickover @pickover )

EVENTS

79 Thousands were killed when the cities of Pompeii and Herculaneum were buried by the eruption of Mount Vesuvius.*VFR An estimated 20,000 people died. When discovered, the sites became astonishing archaeological time capsules.

1563 Tycho Brahe watched a spectacular conjunction of Jupiter and Saturn, and found that the time of the closest approach was days away from the predictions in the Ptolemaic Tables. He emerged from the experience with a life long passion for accuracy and exactitude and a devotion to the verdict of the sky. *Timothy Ferris, Coming of Age in the Milky Way

1609 Galileo presented this telescope to the Doge in the Presence Chamber of the Doge's Palace and was confirmed in the professorship for life with his salary doubled! [Letter of 29 Aug 1609 from Galileo to his brother‑in‑law in Florence, quoted in Fahie, pp. 82‑83.] '... an object which is at a distance of nine miles will appear as if it were only one mile away, ... one can detect ships and sails of the enemy at sea ... we can see him two or more hours earlier than he can possibly see us, ....' [Galileo's letter to the Doge on 24 Aug 1609, quoted in Scandone, pp.12‑14 ; in Van Helden, pp. 7-8]. Through the connections of his friend Paolo Sarpi, Galileo presents an eight-powered telescope to the Venetian Senate. He is rewarded by a doubling of his salary and life- tenure at the University of Padua. He is disappointed by the fine print. *Galileo Project (I love the idea that the Greek name "telescope" was created by an actual Greek mathematician. It was created in 1611 by the Greek mathematician Giovanni Demisiani for one of Galileo Galilei's instruments presented at a banquet at the Accademia dei Lincei.)

1654 Pascal wrote a letter to Fermat, discussing Fermat’s solution to the “problem of points.”

I was not able to tell you my entire thoughts regarding the problem of the points
by the last post,and at the same time, I have a certain reluctance at doing it for fear lest
this admirable harmony which obtains between us and which is so dear to me should
begin to flag, for I am afraid that we may have different opinions on this subject. I
wish to lay my whole reasoning before you, and to have you do me the favor to set me
straight if I am in error or to indorse me if I am correct. I ask you this in all faith and
sincerity for I am not certain even that you will be on my side.
When there are but two players, your theory which proceeds by combinations is
very just. But when there are three, I believe I have a proof that it is unjust that you
should proceed in any other manner than the one I have. But the method which I
have disclosed to you and which I have used universally is common to all imaginable
conditions of all distributions of points, in the place of that of combinations (which I do
not use except in particular cases when it is shorter than the general method), a method
Which is good only in isolated cases and not good for others.
I am sure that I can make it understood, but it requires a few words from me and a
little patience from you. (I wish I had known this phrase early in my teaching career… it seems it would have been frequently handy)
*http://www.york.ac.uk/depts/maths/histstat/pascal.pdf

1731 Darwin receives a letter from his old teacher, J S Henslow, that will change his life: "I have been asked by Peacock who will read & forward this to you from London to recommend him a naturalist as companion to Capt Fitzroy employed by Government to survey the S. extremity of America— I have stated that I consider you to be the best qualified person I know of who is likely to undertake such a situation— I state this not on the supposition of yr. being a finished Naturalist, but as amply qualified for collecting, observing, & noting any thing worthy to be noted in Natural History." *DarwinProject

1971 The Soviet Union issued a stamp for the centenary of the birth of the British physicist, Ernest Rutherford. Beside his picture is a diagram of the movement of atomic particles which involves a hyperbola. [Scott #3888].*VFR

2006 And then there were only eight.... the International Astronomical Union decided to rescind Pluto’s status as a planet and reclassify it as another entity called a “dwarf planet”. *FFF, pg 537
I have been told that as early as 1980 at a celebration of the discovery, Brian Marsden, a long time opponent of Pluto as a planet, had said, "I will kill your Planet if it's the LAST thing I DO!". (I'm told this story is in :The Case for Pluto, by Alan Boyle)

BIRTHS
1556 Sophie Brahe, also known as Sophia Thott (24 August 1556 – 1643), was a Danish horticulturalist and student of astronomy, chemistry, and medicine, best known for assisting her brother Tycho Brahe with his astronomical observations.
She was born in Knudsturp, as the youngest of ten children, to Otte Brahe, advisor to the King of Denmark; and Beate Bille Brahe, leader of the royal household for Queen Sophie. Famous astronomer Tycho Brahe, 10 years her senior, was Sophie's oldest brother. When she was 17, she started assisting her brother with his astronomical observations in 1573, and helped him with the work that became the basis for modern planetary orbit predictions. She frequently visited his observatory Uranienborg, on the then-Danish island of Hveen. Tycho wrote that he had trained her in horticulture and chemistry, but he told her not to study astronomy. He expressed with pride that she learned astronomy on her own, studying books in German, and having Latin books translated with her own money so that she could also study them. Brother and sister were united by their work in science, and by their family's opposition to science as an appropriate activity for members of the aristocracy. Tycho referred with admiration to her 'animus invictus', her "determined mind" *Wik

1561 Bartholomeo Pitiscus born. He coined the word “Trigonometry,” and ﬁrst used it in print in 1595.*VFR Pitiscus achieved fame with his influential work written in Latin, called Trigonometria: sive de solutione triangulorum tractatus brevis et perspicuus (1595, first edition printed in Heidelberg), which introduced the word "trigonometry" to the English and French languages, translations of which had appeared in 1614 and 1619, respectively. It consists of five books on plane and spherical trigonometry. Pitiscus is sometimes credited with inventing the decimal point, the symbol separating integers from decimal fractions, which appears in his trigonometrical tables and was subsequently accepted by John Napier in his logarithmic papers (1614 and 1619).*Wik

1846 Professor Enoch Beery Seitz, the most distinguished mathematician of his day (Fairfield county, Ohio, August 24, 1846,- Kirksville, Missouri, October 8, 1883) He began his mathematical course in 1872 by contributing solutions to the problems proposed in the "Stairway" department of the Schoolday Magazine, conducted by Artemas Martin. His masterlv and original solutions to difflcult Average and Probability problems, poon attracted universal attention among mathematicians.  Dr. Martin, being desirous to know what works he had treating on that difflcult subject, was greatly surprised to learn that he had no works upon the subject, but had learned what he knew about that difficult department of mathematical science by studying the problems and solutions in the Shohlday Magazine. He then contributed to the Analyst, the Mathematical Visitor, the Mathematical Magazine, the School Visitor, and the Educational limes, of London, England.
He took a mathematical course in the Ohio Wesleyan University in 1870, but did not finish it or graduate. In 1879,he was elected one of the teachers in the Greenville High School, which position he held till 1879. On the 24th of June, 1875, he married Miss Anna E. Kerlin, one of Dark county's most refined ladies. In 1879, he was elected to the chair of mathematics in the Missouri State Normal schlool, Kirksville, Missouri. During his first year as chair, he solved a problem posed by Professor Woolhouse in 1864 concerning the probability of firing a musket ball through the air at random. In the same vein, Seitz proposed a similar problem to the editor Artemis Martin in The Mathematical Visitor. Because of its difficulty, the problem received a great deal of attention and notoriety. Perhaps inspired by the Greenville hometown legend Annie Oakly and her rifleman ship, Seitz offered the problem:

"A cube is thrown into the air and a random shot fired through it; find the chance that the shot passes through the opposite side."

After nearly a year with no solutions forthcoming, Seitz published his own solution in The Mathematical Visitor:
He remained at Kirksville until his death death from that "demon of death," typhoid fever on the 8th of October, 1883.
On March the llth, 1880,he was elected a member of the London Mathematical Society, being the fifth American so honored.
He is often called "Teacher of the Great", for his many distinguished students: "When Professor Seitz went to Kirksville, in spite of the youth of the institution, he found an enthusiastic and capable body of students. He entered upon his work with his usual energy and the results of it are still felt throughout the country. He had in his class in algebra at one time, in the autumn of 1880, John J. Pershing who was destined to be the head of the armies of the United States In the World War, and Enoch Crowder who became head of the draft boards in the same conflict. He also had as a student at Kirksville. B F. Carroll, who later became governor of the state of Iowa, and John. R. Kirk who became president of the same institution in which he was then a student of Professor Seitz." *Obit in The Herald-Advertiser of Huntington, W.Va.

Rudolf Oskar Robert Williams Geiger (24 Aug 1894, 22 Jan 1981) German meteorologist, one of the founders of microclimatology, the study of the climatic conditions within a few metres of the ground surface. His observations, made above grassy fields or areas of crops and below forest canopies, elucidated the complex and subtle interactions between vegetation and the heat, radiation, and water balances of the air and soil.*TIS

1943 Karen Uhlenbeck is a leading expert on partial differential equations. She is currently Professor, and Sid W. Richardson Regents Chairholder, Department of Mathematics, University of Texas, Austin. *Univ of Texas

DEATHS

1595 Thomas Digges (1546?, 24 Aug 1595)
English astronomer and mathematician who (with his father, Leonard) was a pioneer in the use of the telescope. He was the leader of the English Copernicans. His observations of the new star of 1572, published in his Alae seu scalae mathematicae (1573) were second only to Tycho Brahe in accuracy. He used his observations of the supernova to justify the heliocentric system. In mathematics, he wrote on platonic and archimedian solids. *TIS After his father's death he was adopted and taught by John Dee. Digges was one of the first to translate (parts of) Copernicus into English. *Renaissance Mathematicus His father, Leonard Diggs, was also a fine mathematician, and often cited as the inventor (and namer) of the theodolite.
Thomas was the first to expound the Copernican system in English but discarded the notion of a fixed shell of immoveable stars to postulate infinitely many stars at varying distances; he was also first to postulate the "dark night sky paradox". *Wik

1670 William Neile (7 December 1637 – 24 August 1670) was an English mathematician and founder member of the Royal Society. His major mathematical work, the rectification of the semicubical parabola, was carried out when he was aged nineteen, and was published by John Wallis who was his teacher. By carrying out the determination of arc lengths on a curve given algebraically, in other words by extending to algebraic curves generally with Cartesian geometry a basic concept from differential geometry, it represented a major advance in what would become infinitesimal calculus. His name also appears as Neil.

1739 Takebe Katahiro was a Japanese mathematician who wrote most of Seki's Encyclopaedia.*SAU

1796 (Nicholas Léonard) Sadi Carnot (born 1 Jun 1796, 24 Aug 1832) was a French physicist. He became a captain of engineers in the army, and spent much of his life investigating the design of steam engines. His book Reflections on the Motive Power of Heat (1824) contained a theorem which says that a maximum efficiency of heat engine can be obtained by a reversible engine, and that efficiency depends only on the temperatures of the hot and the cool sources of the engine. This theorem played an essential role for the subsequent development of thermodynamics. It was written to promote the construction of steam engines and other heat engines in France, whose industrial development was lagging behind England's. *TIS

1842 Benjamin Wright (10 Oct 1770, 24 Aug 1842)American engineer who directed the construction of the Erie Canal. A one-time judge, he helped survey the Erie Canal route. When the Erie Canal was finally funded in 1817, Wright was selected as one of the three engineers to design and build it, then named chief engineer. Wright made the Erie Canal project a school of engineering. Until mid-century, almost every civil engineer in the U.S. had trained with, or been trained by someone who had worked under, Wright on the Erie Canal. Because he trained so many engineers on that project, Wright has been called the "father of American civil engineering." He also engaged in the design and construction at the outset of the first railroads. He was the first Chief Engineer of the Erie Railroad.*TIS

1888 Rudolf (Julius Emanuel) Clausius (2 Jan 1822, 24 Aug 1888) was a German mathematical physicist who formulated the second law of thermodynamics and is credited with making thermodynamics a science. Essentially a theoretical physicist, he published his work in thermodynamics in 1865 wherein he stated the First and Second laws of thermodynamics in the following form: (1) The energy of the universe is constant. (2) The entropy of the universe tends to a maximum. In all Clausius wrote eight important papers on the topic. He restated Sadi Carnot's principle of the efficiency of heat engines. The -Clapeyron equation expresses the relation between the pressure and temperature at which two phases of a substance are in equilibrium. *TIS

1975 Anna Margaret Mullikin (March 7, 1893 - August 24, 1975) She was born in Baltimore, Maryland and attended Goucher College, which was then a women's college located in the same city. While there she managed her class basketball team, participated on the swimming team, and earned her A.B. degree in 1915. That same year her name was mentioned in the American Mathematical Monthly [Vol. 22, No. 5 (May 1915),pp. 165-166] for solving the following geometry problem:

A quadrilateral of any shape whatever is divided by a transversal into two quadrilaterals. The diagonals of the original figure and those of the two resulting (smaller) figures are then drawn. Show that their three points of intersection are collinear.

The published solution was by Vola Barton, also from Goucher College, with the remark "Also solved by Anna Mullikin."
In 1918 she entered the graduate program in mathematics at the University of Pennsylvania, earning her master's degree in 1919. She continued her graduate studies at Penn during the 1919-1920 academic year under the direction of the topologist, Robert L. Moore, while also teaching at the Stevens School in Germantown, Pennsylvania, another private preparatory school for girls. In the fall of 1920 she moved to the University of Texas along with Moore, who had convinced the Texas math department to appoint her as an instructor. Mullikin stayed in Texas for only the one academic year before returning to Philadelphia to complete the requirements for her degree from the University of Pennsylvania, with Moore still as her advisor. She received her Ph.D. in mathematics in 1922. Mullikin did not pursue mathematical research after earning her Ph.D. She spent the rest of her professional career as a high school mathematics teacher, first at William Penn High School for Girls in Philadelphia for one year, and then at Germantown High School where she remained until her retirement in 1959. She was appointed head of the mathematics department in 1952. In 1956 she was a joint author with Ethel and Ewart Grove for the textbook Algebra and Its Use. *Agnes Scott College

1982 Giorgio Abetti (5 Oct 1882,24 Aug 1982)Italian astronomer known for his studies of the sun at the University of Padua where was director at the Arcetri Observatory (1921-52), taking over from his father who also held the post (1894-1921). In 1913, Giorgio Abetti took part, as a geodetic and geophysical astronomer, in the De Filippi expedition in Karakorum, Himalaya and Turkestan. He went on expeditions to observe eclipses of the sun, including one to Siberia to observe the total eclipse on 19 Jun 1936 and in 1952 to Sudan. With the advice of George Hale, he built a solar tower at the observatory (opened 1925). He wrote a popular text on the sun, a handbook of astrophysics (1936) and a popular history of astronomy (1963).*TIS

1997 Louis Essen (6 Sep 1908, 24 Aug 1997 )English physicist who invented the quartz crystal ring clock and the first practical atomic clock. These devices were capable of measuring time more accurately than any previous clocks. He built a cesium-beam atomic clock, a device that ultimately changed the way time is measured. Each chemical element and compound absorbs and emits electromagnetic radiation at its own characteristic frequencies. These resonances are inherently stable over time and space. The cesium atom's natural frequency was formally recognized as the new international unit of time in 1967: the second was defined as exactly 9,192,631,770 oscillations or cycles of the cesium atom's resonant frequency, replacing the old second defined in terms of the Earth's motion. *TIS

Credits :
*CHM=Computer History Museum
*FFF=Kane, Famous First Facts
*NSEC= NASA Solar Eclipse Calendar
*RMAT= The Renaissance Mathematicus, Thony Christie
*SAU=St Andrews Univ. Math History
*TIA = Today in Astronomy
*TIS= Today in Science History
*VFR = V Frederick Rickey, USMA
*Wik = Wikipedia
*WM = Women of Mathematics, Grinstein & Campbell

## 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

## Tuesday, 22 August 2017

### On This Day in Math - August 22

Only professional mathematicians learn anything from professors.
Other people learn from explanations.
~Ralph Boas

The 234th day of the year, 234 is the number of ways to stack 12 pennies in a line so that each penny lies on the table or on two pennies. *What's Special About This Number? (Students might search for a pattern for n pennies)

There are 234 ways of grouping six children into rings of at least two children with one child at the center of each ring.

EVENTS

1450 Gutenberg borrowed 800 guilden in gold at 6% interest (a low rate then) to develop his invention of printing from movable metal type. The ﬁrst book produced was a 42-line Latin Bible, the famous Gutenberg Bible. [G. H. Putnam, Books and Their Makers During the Middle Ages (1896), p. 361]. *VFR

1850 Michael Faraday in a letter to William Whewell writes, "I have been driven to assume for some time, especially in relation to the gases, a sort of conducting power for magnetism. Mere space is Zero. One substance being made to occupy a given portion of space will cause more lines of force to pass through that space than before, and another substance will cause less to pass. The former I now call Paramagnetic & the latter are the diamagnetic. The former need not of necessity assume a polarity of particles such as iron has with magnetic, and the latter do not assume any such polarity either direct or reverse. I do not say more to you just now because my own thoughts are only in the act of formation, but this I may say: that the atmosphere has an extraordinary magnetic constitution, & I hope & expect to find in it the cause of the annual & diurnal variations, but keep this to yourself until I have time to see what harvest will spring from my growing ideas." * L. P. Williams (ed.), The Selected Correspondence of Michael Faraday (1971), Vol. 2, 589.

1883 Sylvester writes Cayley that, "I have been recovering my theory of multiple algebras - by slow degrees." Thus begins his first sustained assault on Matrix Theory. *The Emergence of the American Mathematical Research Community, 1876-1900, Parshal & Rowe

In 1893 "An international Congress of Mathematicians is held at the World's Columbian Exposition in Chicago, August 21-26. Felix Klein​ and E.H. Moore occupy center stage. The Committee of Ten on Secondary School Studies recommends a year of algebra, followed by two years of plane and solid geometry to be taught side by side with more algebra. The first year's course in algebra is recommended for all students."*from Milestones in (Ohio)Mathematics, by David E. Kullman

1900 It seems that Henry Ernest Dudeney may have been the first person to explore the use of primes to create a magic square. He gave the problem of constructing a magic in The Weekly Dispatch, 22nd July and 5th August 1900. At that time, 1 was sometimes (often?) considered as a prime number. His magic square gives the lowest possible sum for a 3x3 using primes (assuming one is prime)
The smallest magic square with true primes (not using one) has a magic constant of 177. Good luck.
*Christian Boyer, Multimagic Squares

1955 The first computer User Group is founded. SHARE was founded by users of IBM's Model 704 computer, ... in order for the growing community of IBM computer users (mainly aerospace companies on the U.S. West Coast) to exchange information and programs. The first meeting included scientists and engineers whose companies had ordered IBM's newest computer, the 704. Sparked by quick growth and the fact that its members were some of IBM's largest customers, the group had significant influence over IBM designs and customer support. *CHM

On August 22, 2006, four Fields Medals were awarded at the opening ceremonies of the Inter-
national Congress of Mathematicians (ICM) in Madrid, Spain. The medalists are ANDREI O KOUNKOV, GRIGORY PERELMAN, TERENCE TAO, and WENDELIN WERNER.
During the award ceremony, John Ball, president of the International Mathematical
Union, announced that Perelman declined to accept. Tao became one of the youngest persons, the first Australian, and the first UCLA faculty member ever to be awarded a Fields Medal. *AMS Notices

BIRTHS

1647 Denis Papin (22 Aug 1647; c1712) French-born British physicist who invented the pressure cooker (1679). He assisted Dutch physicist Christiaan Huygens with air-pump experiments, and went to London in 1675 to work with the English physicist Robert Boyle. A few years later, Papin invented his steam digester (pressure cooker), a closed vessel with a tightly fitting lid that confined the steam at a higher pressure, considerably raising the boiling point of the water. A safety valve of his own invention prevented explosions. Observing that the enclosed steam in his cooker tended to raise the lid, Papin conceived of the use of steam to drive a piston in a cylinder, the basic design for early steam engines. He never built an engine of his own, but his idea was improved by others and led to the development of the steam engine, a major contribution to the Industrial Revolution. *TIS If you are not familiar with Papin, check out this blog by The Renaissance Mathematicus.

1796 Baden Powell (22 August 1796–11 June 1860 Kensington, London) born in Stamford Hill, England. Savilian professor of geometry at Oxford from 1827 to 1854. He deserves credit for the modest reforms in mathematical education at Oxford in the 1850s. One son (he had 14 children by 3 wives) Robert Baden-Powell founded the scouting movement. *VFR He fought for the principle acknowledging scientific advances were compatible with Christian religion. Following Darwin's "Origin of Species" in 1859, he contributed one of seven essays in "Essays and Reviews," 1860. This was violently attacked, and the authors denounced as being inspired by "the Evil One himself." "There was some expectation of him becoming a Bishop, before Essays and Reviews were published" (letter from his widow to her nephew 20.8.1909). *Pinetreeweb.com

1834 Samuel Pierpont Langley, (22 Aug 1834; 27 Feb 1906)American astronomer, physicist, and aeronautics pioneer who built the first heavier-than-air flying machine to achieve sustained flight. He launched his Aerodrome No.5 on 6 May 1896 using a spring-actuated catapult mounted on top of a houseboat on the Potomac River, near Quantico, Virginia. He also researched the relationship of solar phenomena to meteorology. *TIS
Developed a bolometer (for measurements of the cosmic microwave background) and determent the value of the solar constant.*Wik

1915 James Hillier, OC (August 22, 1915 – January 15, 2007) was a Canadian-born scientist and inventor who designed and built, with Albert Prebus, the first successful high-resolution electron microscope in North America in 1938. *Wik

DEATHS

1664 Maria Cunitz (1604 - August 22, 1664) was an astronomer who published simpler versions of Kepler's work. *SAU The publication of the book Urania propitia gained Cunitz a European reputation. She was acclaimed as the most learned woman since Hypatia of Alexandria. Significantly for a technical publication of that period, her book was written both in Latin and German (stating that it was to increase the accessibility to her work). Urania propitia was a simplification of the Rudolphine Tables. It provided new tables, new ephemera, and a more elegant solution to Kepler's Problem, which is to determine the position of a planet in its orbit as a function of time. Today, her book is also credited for its contribution to the development of the German scientific language. *Wik

1676 Edward Cocker (1631 – 22 August 1676) was an English scholar who was the author of an influential arithmetic text which ran to more than 100 editions. Cocker died with no money in his Poke to quote his own phrase. As Wallis writes
Subsequently he might well have suffered material loss in the Fire and have had the expense of successive removals. He may also have spent extravagantly. He possessed 'some choice Manuscripts, and a great Collection of Printed Authors in several Languages' ... In any event, he died in debt, 'within the rules' of the King's Bench Prison, which was situated in Southwark; the quoted phrase meant that the prisoner had purchased the right to live within a short distance of the prison. Cocker's move to Southwark was probably an enforced one, consequent on his committal for debt.
*SAU
Benjamin Franklin's autobiography makes mention that he studied ..., Cocker's Arithmetic, after he moved from his home to Pennsylvania, " And now it was that, being on some occasion made asham'd of my ignorance in figures, which I had twice failed in learning when at school, I took Cocker's book of Arithmetick, and went through the whole by myself with great ease.

1700 Siguenza y Gongora (August 14, 1645 – August 22, 1700) was a Mexican astronomer and philosopher. *SAU He was one of the first great intellectuals born in the Spanish viceroyalty of New Spain. A polymath and writer, he held many colonial government and academic positions. In 1681 Sigüenza wrote the book "Philosophical Manifest Against the Comets" in which he tried to dismiss fears of impending superstitious predictions based from astrology; in the work he takes steps to separate the fields of astrology and astronomy. The jesuit Eusebio Kino strongly criticized the texts written by Sigüenza because they were contradicting to established Catholic beliefs in the heavens. Sigüenza often cited authors like Copernicus, Galileo, Descartes, Kepler, and Brahe. In 1690 Sigüenza took an audacious move to defend his previous work by publishing "Libra Astronómica y Filosófica". *Wik

1752 William Whiston (born 9 Dec 1667, 22 Aug 1752) English Anglican priest and mathematician who sought to harmonize religion and science, and who is remembered for reviving in England the heretical views of Arianism. He attended Newton's lectures while at Cambridge and showed great promise in mathematics. Ordained in 1693. While chaplain to the bishop of Norwich (1694-98), he wrote A New Theory of the Earth (1696), in which he claimed that the biblical stories of the creation, flood and final conflagration could be explained scientifically as descriptions of events with historical bases. The Flood, he believed, was caused by a comet passing close to the Earth on 28 Nov 2349 BC. This put stress on the Earth's crust, causing it to crack and allow the water to escape and flood the Earth. After serving as vicar of Lowestoft (1698–1701), he returned to his alma mater, Cambridge University to become assistant to the mathematician Sir Isaac Newton, whom he succeeded as professor in 1703. *TIS (His translations of the works of Josephus are still in print)

1907 Platon Sergeevich Poretsky (October 3, 1846, Elisavetgrad - August 9, 1907) He published major works on methods of solution of logical equations, and on the reverse mode of mathematical logic. He applied his logic calculus to the theory of probability. Although he retired from his teaching role at Kazan in 1889 due to ill health, this did not mean that he stopped his research. He continued to undertake research into mathematical logic for the remaining eighteen years of his life. *SAU

1940 Sir Oliver Joseph Lodge, FRS (12 June 1851 – 22 August 1940) was a British physicist and writer involved in the development of key patents in wireless telegraphy. In his 1894 Royal Institution lectures ("The Work of Hertz and Some of His Successors"), Lodge coined the term "coherer" for the device developed by French physicist Édouard Branly based on the work of Italian physicist Temistocle Calzecchi Onesti. In 1898 he was awarded the "syntonic" (or tuning) patent by the United States Patent Office. He was also credited by Lorentz (1895) with the first published description of the length contraction hypothesis, in 1893, though in fact Lodge's friend George Francis FitzGerald had first suggested the idea in print in 1889. *Wik

1974 Jacob Bronowski, (18 Jan 1908, 22 Aug 1974)Polish-born British mathematician and man of letters who eloquently presented the case for the humanistic aspects of science. He is remembered as writer and presenter of the BBC television series, The Ascent of Man. Bronowski, who had a Ph.D. in algebraic geometry, spent WW II in Operations Research, and was an official observer of the after-effects of the Nagasaki and Hiroshima bombings. After this experience, he turned to biology, to better understand the nature of violence. *TIS

1975 Andrzej Mostowski (1 November 1913 – 22 August 1975) was a Polish mathematician who worked on logic and the foundations of mathematics.*SAU His son Tadeusz is also a mathematician working on differential geometry. With Krzysztof Kurdyka and Adam Parusinski, Tadeusz Mostowski solved René Thom's gradient conjecture in 2000. *Wik

1992 Harold Maile Bacon (Jan. 13, 1907, August 22, 1992) was an elder statesmen of the Stanford faculty who taught calculus to generations of Stanford undergraduates during a career that spanned more than four decades.
Bacon was widely recognized on campus as the owner of the white colonial-style Row house with the rose-lined driveway. He had ties to the house, and the University, almost since his birth.
He was an ill 6-month-old child when he first visited the campus house he would occupy for more than 60 years. Harriet Dunn, a cousin of Harold Bacon's father, Robert, and owner of the distinctive house, suggested that the child be brought to Stanford from Southern California for examination by Dr. Ray Lyman Wilbur, who lived nearby on the site now occupied by Dinkelspiel Auditorium. (Wilbur, who prescribed medicine and a better diet for young Bacon, later became the university's third president.)
In the 1920s, Harold Bacon enrolled at Stanford, following in the footsteps of his father, who graduated in 1902. Bacon lived in the two-story, six-bedroom house during part of his undergraduate years, then moved in permanently , at the invitation of Harriet Dunn, when he returned in 1930 to teach.
In 1946, Rosamond Clarke, '30, came to the house when she married the math professor. Harriet Dunn died a month later, leaving the house and renewable land-lease to the Bacons. Jane Stanford had given permission for Mrs. Dunn a nd her husband, Orrin, to build the colonial-revival house in 1899 as recompense for Harriet Dunn's earlier work building and operating a campus boarding house.
For many years, Bacon directed the undergraduate program in mathematics, according to Halsey Royden, who took classes from Bacon during his student days and later became a faculty colleague.
To students and fellow faculty members, Bacon was "the embodiment of Stanford ways and history," Royden said. At the time he retired, Bacon, through his calculus classes, probably had taught "more engineering and science undergraduates than anyone else in the history of the university," Royden said.
*Stanford Obituary
For a wonderful story describing the nature of Harold Bacon as a man and a teacher, see this cover story, The Prisoner and the Professor, from the Stanford Alumni magazine of Mar/Apr 1997

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

## 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