Saturday, 10 June 2023

On This Day in Math - June 10

Mathematics is one of the essential emanations of the human spirit,
a thing to be valued in and for itself, like art or poetry.
~Oswald Veblen

The 161st day of the year, Every number greater than 161 is the sum of distinct primes of the form 6n - 1.  *Prime Curios (which numbers less than 161 are also the sum of distinct primes of the form 6n-1? or which are not?)

and for the gamblers out there, There are 161 ways to bet on a roulette wheel.
161 is not only a palindrome, when is rotated 180o it gives a palindromic prime, (191) (Such  reversible numbers, or words, which form a different number, or word, are called "ambigrams".)

161 is the sum of five consecutive prime numbers: 23 + 29 + 31 + 37 + 41 = 161

Benjamin West *Wik

1752 This is the most common date given, where one is supplied, for the supposed Electrical kite experiment by Benjamin Franklin. The event is poorly documented. Franklin seems never to have written about it, and the only record seems to come from the pen of Joseph Priestly some fifteen years later who was told about it by Ben. Many now think the entire event never took place.

The standard account of Franklin's experiment was disputed following an investigation and experiments based on contemporaneous records by science historian Tom Tucker, the results of which were published in 2003. According to Tucker, Franklin never performed the experiment, and the kite as described is incapable of performing its alleged role.

Further doubt about the standard account has been cast by an investigation by the television series MythBusters. The team found evidence that Franklin would have received a fatal current through his heart had the event actually occurred. Nevertheless, they confirmed that certain aspects of the experiment were feasible - specifically, the ability of a kite with sufficiently damp string to receive and send to the ground the electrical energy delivered by a lightning strike.

Despite this, mainstream historians still support the view that the experiment was performed by Franklin *Wik

1827 William Rowan Hamilton, age 21, appointed astronomer royal at Dunsink Observatory and Andrews professor of astronomy at Trinity College, Ireland. This was a unique event in that he was still an undergraduate. *VFR

1854 The first known published mention of the Four Color Problem was printed in the Athenaeum on this date, appearing in the Miscellanea portion. The letter was signed with the initials F. G., which many supposed might have been one of the two Guthrie brothers involved in discovering the story and revealing it to DeMorgan, but others suspect it may have been Francis Galton, who had requested admission to the esteemed Athenaeum Club during this period. Certainly many of the members would have heard the story of the four colors problem from DeMorgan who had first circulated it to William R. Hamilton. (see October 23, 1852) *PB Notes (unknown)

1854, G.F. Bernhard Riemann proposed that space is curved in a lecture titled Über die Hypothesen welche der Geometrie zu Grunde liegen. He described the old-fashioned Euclidean plane geometry and solid geometry, respectively, as two-, and three-dimensional examples of what we now call Riemann spaces with zero curvature. Saying that the space is curved, rather than flat or Euclidean, is another way saying that the familiar properties of Euclidean geometry - such as the Pythagorean theorem - do not hold. He went on to suggest that all physical laws become simpler when expressed in higher dimensions. Einstein in 1915 used Rieman’s work in his theory of General Relativity which incorporated time as the fourth dimension.*TIS Weber recounted how with unusual emotion Gauss praised Riemann’s profundity on their way home. John Derbyshire in his Prime Obsession calls it "one of the top ten mathematical papers ever delivered anywhere."

1919 In a letter to Irving Langmuir, Ernest Rutherford writes, "I am a great believer in the simplicity of things and as you probably know I am inclined to hang on to broad & simple ideas like grim death until evidence is too strong for my tenacity." Nelson Ernest Rutherford *Quoted in Nathan Reingold and Ida H. Reingold, Science in America: A Documentary History 1900-1939 (1981), 354.

1924 Oswald Veblen describes his ideas for the Institute for Mathematical Research in a letter to Vernon Kellogg. The senior men would devote themselves “entirely to research, and to the guidance of the research of the younger men.” (History and philosophy of modern mathematics By William Aspray)

1977 The first Apple II computer was delivered. This was the first computer I ever used in a classroom.

Image : Apple II in a common 1977 configuration, with a 9" monochrome monitor, game paddles, and a Red Book-recommended Panasonic RQ-309DS cassette deck  *Wik


In 2000, the Millennium Bridge - a footbridge across the River Thames - was opened by Queen Elizabeth. The radical new design was the work of architect Sir Norman Foster with sculptor Sir Anthony Caro and engineering support from Arup. It was the first new crossing of the River Thames in over 100. As the first few thousand people crossed the bridge, it developed an unexpected and potentially dangerous lateral "wobble". This caused people to unwittingly walk "in step", which increased the oscillation. The design had been adapted from a computer model typical for a car bridge, but which did not take into account the lateral forces associated with human walking. After structural damping was added to stop the oscillation, the bridge re-opened in 2002*TIS 


940 Abu’l-Wafa (June 10, 940 AD, Buzhgan - July 1, 998 AD, Baghdad) He worked with a rusty compass.*VFR The professors cryptic remark about a "rusty compass" refers to Abu'l wafa's preference, when possible, to do his geometric constructions with a compass with a fixed opening.
Abu'l-Wafa is best known for the first use of the tan function and compiling tables of sines and tangents at 15' intervals. This work was done as part of an investigation into the orbit of the Moon, written down in Theories of the Moon. He also introduced the sec and cosec and studied the interrelations between the six trigonometric lines associated with an arc. He is also often credited as one of the likely originators of the spherical law of sines and established several trigonometric identities such as sin(a ± b) in their modern form, where the Ancient Greek mathematicians had expressed the equivalent identities in terms of chords.

\(\sin(\alpha \pm \beta) = \sin \alpha \cos \beta \pm \cos \alpha \sin \beta \)
"A text written by Abu'l-Wafa for practical use was A book on those geometric constructions which are necessary for a craftsman. This was written much later than his arithmetic text, certainly after 990. The book is in thirteen chapters and it considered the design and testing of drafting instruments, the construction of right angles, approximate angle trisections, constructions of parabolas, regular polygons and methods of inscribing them in and circumscribing them about given circles, inscribing of various polygons in given polygons, the division of figures such as plane polygons, and the division of spherical surfaces into regular spherical polygons.
Another interesting aspect of this particular work of Abu'l-Wafa's is that he tries where possible to solve his problems with ruler and compass constructions. When this is not possible he uses approximate methods. However, there are a whole collection of problems which he solves using a ruler and fixed compass, that is one where the angle between the legs of the compass is fixed. It is suggested in Dictionary of Scientific Biography that:-
Interest in these constructions was probably aroused by the fact that in practice they give more exact results than can be obtained by changing the compass opening.

 His trigonometric tables are accurate to 8 decimal places (converted to decimal notation) while Ptolemy's were only accurate to 3 places." *SAU

In 2015, Google celebrated his 1075th birthday with a Google Doodle, and included, "contributions to science include one of the first known introductions to negative numbers, and the development of the first wall quadrant, a tool used by astronomers to examine the sky."

It is interesting that during this period there were two types of arithmetic books written, those using Indian symbols and those of finger-reckoning type. Abu'l-Wafa's text is of this second type with no numerals; all the numbers are written in words and all calculations are performed mentally. It is now believed that mathematicians wrote for two differing types of readers. Abu'l-Wafa himself was an expert in the use of Indian numerals but these :-"... did not find application in business circles and among the population of the Eastern Caliphate for a long time."

Hence he wrote his text using finger-reckoning arithmetic since this was the system used for by the business community. *SAU *Wik *PB

1710 James Short (June 10, 1710, Edinburgh, Scot. -  June 14, 1768, London, Eng) British optician and astronomer who produced the first truly parabolic and elliptic (hence nearly distortionless) mirrors for reflecting telescopes.

 During his working life of over 35 years, Short made about 1,360 instruments - not only for customers in Britain but also for export: one is still preserved in Leningrad, another at Uppsala and several in America. Short was principal British collator and computer of the Transit of Venus observations made throughout the world on 6th June 1761. His instruments traveled on Endeavour with Captain Cook to observe the next Transit of Venus on 3rd June 1769, but Short died before this event took place.

1803 Henri-Philibert-Gaspard Darcy (June 10, 1803 – January 3, 1858) French hydraulic engineer who first derived the equation (now known as Darcy's law) that governs the laminar (nonturbulent) flow of fluids in homogeneous, porous media. In 1856, modern studies of groundwater began when Darcy was commissioned to develop a water-purification system for the city of Dijon, France. He constructed the first experimental apparatus to study the flow characteristics of water through the earth. From his experiments, he derived the Darcy's Law equation, describing the flow of water in nature, which is fundamental to understanding groundwater systems.

1861 Pierre(-Maurice-Marie) Duhem (10 June 1861 – 14 September 1916)French physicist, mathematician, and philosopher of science who emphasized a history of modern science based on evolutionary metaphysical concepts. He had a wide variety of mathematical interests from mechanics and physics to philosophy and the history of mathematics. Duhem studied magnetism following the work of Gibbs and Helmholtz and also worked on thermodynamics and hydrodynamics producing over 400 papers. He maintained that the role of theory in science is to systematize relationships rather than to interpret new phenomena.  *TIS

1887 Vladimir Ivanovich Smirnov (10 June 1887 – 11 February 1974) was a Russian mathematician who made significant contributions in both pure and applied mathematics, and also in the history of mathematics.
Smirnov worked on diverse areas of mathematics, such as complex functions and conjugate functions in Euclidean spaces. In the applied field his work includes the propagation of waves in elastic media with plane boundaries (with Sergei Sobolev) and the oscillations of elastic spheres.
Smirnov is also widely known among students for his five volume book A Course in Higher Mathematics (the first volume was written jointly with Jacob Tamarkin).*Wik

1904 John Semple (10 June 1904 in Belfast, Ireland - 23 October 1985 in London, England) studied at Queen's University Belfast and Cambridge. He held a post in Edinburgh for a year before becoming Professor of Pure Mathematics at Queen's College Belfast. He moved to King's College London where he spent the rest of his career. His most important work was in Algebraic geometry. *SAU

1932 Pierre Emile Jean Cartier (10 June 1932 in Sedan , Ardennes - ) is a French mathematician . His main interest is the algebraic geometry , presentation and category theory . 1957-1959 he worked at the Institute for Advanced Study . From 1961 he was a professor at the University of Strasbourg (then Faculté de Science). In 1971 he was appointed professor at the Institut des Hautes Études Scientifiques in Paris. He was also from 1974 Director of Research CNRS. In 1982 he became a professor at the Ecole Polytechnique and 1988 at the ENS.
Pierre Cartier led the Cartier operator and is the namesake of the Cartier divisor . *Wik


1836 Andre-Marie Ampere(20 January 1775 – 10 June 1836)French mathematician and physicist who founded and named the science of electrodynamics, now known as electromagnetism. His interests included mathematics, metaphysics, physics and chemistry. In mathematics he worked on partial differential equations. Ampère made significant contributions to chemistry. In 1811 he suggested that an anhydrous acid prepared two years earlier was a compound of hydrogen with an unknown element, analogous to chlorine, for which he suggested the name fluorine. He produced a classification of elements in 1816. Ampère also worked on the wave theory of light. By the early 1820's, Ampère was working on a combined theory of electricity and magnetism, after hearing about Oersted's experiments.TIS It is said that Ampere was capable of intense concentration leading to absent-mindedness. Once walking in Paris he had an insight and pulled a piece of chalk out of his pocket and finding the back of a cab he began to cover the back of the cab with equations, and was then shocked to see his solution begin to pull away and disappear down the street.

1903 (Antonio) Luigi (Gaudenzio Giuseppe) Cremona ( Pavia , 7 December 1830 - Rome , 10 June 1903 ) was an Italian mathematician who was an originator of graphical statics (the use of graphical methods to study forces in equilibrium) and work in projective geometry. Cremona's work in statics is of great importance and he gave, in a clearer form, some theorems due to Maxwell. In a paper of 1872 Cremona took an idea of Maxwell's on forces in frame structures that had appeared in an engineering journal in 1867 and interpreted Maxwell's notion of reciprocal figures as duality in projective 3-space. These reciprocal figures, for example, have three forces in equilibrium in one figure represented by a triangle while in the reciprocal figure they are represented by three concurrent lines.*TIS

1948 Philippa Garrett Fawcett (4 April 1868 - 10 June 1948)
Fawcett's performance in the Trinity Intercollege Examination which she sat after two years at Cambridge was outstanding and it was clear that she would excel in the Tripos Examinations of 1890. At this time only the men were ranked in the Tripos Examination but women who took the examination were made aware of their place by being told they were placed between the nth and (n+1)st man or equal to the nth man. Expectations were high that Fawcett would perform well and her mother wrote in a letter to a friend):-

I am going to Cambridge tomorrow week and shall have my last sight of [Philippa] till after the exam. I have made up my mind not to be too anxious about it. There are a great many better things in the world than beating other people in examinations.

However, beat other people is exactly what Fawcett did in the twelve three hour examination papers. The Senior Moderator of the Mathematical Tripos Examinations of 1890 was Walter Rouse Ball and it was his duty to read the women's list after the men's ranked list had been read. When Rouse Ball came to read the women's list he read out first:-
Miss Philippa Garrett Fawcett - above the Senior Wrangler.
Fawcett had become the first woman at Cambridge to come top in the Mathematical Tripos Examinations. A description of the event is recorded in the North Hall Diary of Newnham College:-
The great event of the year was Philippa Garrett Fawcet's achievement in the Mathematical Tripos. For the first time a woman has been placed above the Senior Wrangler. The excitement in the Senate House when the lists were read was unparalleled. The deafening cheers of the throng of undergraduates redoubled as Miss Fawcett left the Senate House by the side of the Principal. On her arrival at the College she was enthusiastically greeted by a crowd of fellow-students, and carried in triumph into Clough Hall. Flowers, letters, and telegrams poured in upon her throughout the day. The College was profusely decorated with flags. In the evening the whole College dined in Clough Hall. After dinner toasts were proposed: the healths drunk were those of the Principal, Miss Fawcett, her Coach (Mr Hobson) and Senior and Junior Optimes. At 9.30 p.m. the College gardens were illuminated, and a bonfire was lighted on the hockey-ground, round which Miss Fawcett was three times carried amid shouts of triumph and strains of "For she's a jolly good fellow." *SAU

Following Fawcett's great achievement in the Mathematical Tripos, she won a scholarship at Cambridge through which she conducted research in Fluid Dynamics. Her published papers include "Note on the Motion of Solids in a Liquid".

She went on to be a College Lecturer in Mathematics at Newnham College, Cambridge a position she held for 10 years. In this capacity, her teaching abilities received considerable praise. One student wrote:
“ What I remember most vividly of Miss Fawcett's coaching was her concentration, speed, and infectious delight in what she was teaching. She was ruthless towards mistakes and carelessness... My deepest debt to her is a sense of the unity of all truth, from the smallest detail to the highest that we know. ”
Fawcett left Cambridge in 1902, when she was appointed as a lecturer to train mathematics teachers at the Normal School, Johannesburg, South Africa. Here, she remained until 1905, setting up schools in South Africa. She then returned to England to take a position in the administration of education for London County Council. Here, she attained the highest LCC rank ever for a woman, in her work developing secondary schools.
Philippa Fawcett maintained strong links with Newnham College throughout her life. The Fawcett building (1938) was named in recognition of her contribution to Newnham, and that of her family. She died on 10 June 1948, two months after her 80th birthday, just one month after the Grace that allowed women to be awarded the Cambridge BA degree received royal assent, and fifty eight years after coming above the `Senior Wrangler'. *Wik

1974 Jaroslav Hájek (4 Feb 1926 in Podebrady, Bohemia (now Czech Republic) - 10 June 1974 in Prague, Czechoslovakia) He was among the pioneers of unequal probability sampling. The name "Hájek predictor" now labels his contributions to the use of auxiliary data in estimating population means. In 1967 Hájek published (jointly with Z Sidak) Theory of rank tests but it was a work which had in fact been written four years before in 1963. Their methods use three lemmas of Le Cam in order to treat rank statistics under local alternatives and they established the efficiency of rank tests. *SAU

1992 Morris Kline (May 1, 1908 – June 10, 1992) was a Professor of Mathematics, a writer on the history, philosophy, and teaching of mathematics, and also a popularizer of mathematical subjects.
Kline grew up in Brooklyn and in Jamaica, Queens. After graduating from Boys High School in Brooklyn, he studied mathematics at New York University, earning a bachelor's degree in 1930, a master's degree in 1932, and a doctorate in 1936. He continued at NYU as an instructor until 1942.
During World War II, Kline was posted to the Signal Corps (United States Army) stationed at Belmar, New Jersey. Designated a physicist, he worked in the engineering lab where radar was developed. After the war he continued investigating electromagnetism, and from 1946 to 1966 was director of the division for electromagnetic research at the Courant Institute of Mathematical Sciences.
Kline resumed his mathematical teaching at NYU, becoming a full professor in 1952. He taught at New York University until 1975, and wrote many papers and more than a dozen books on various aspects of mathematics and particularly mathematics teaching. He repeatedly stressed the need to teach the applications and usefulness of mathematics rather than expecting students to enjoy it for its own sake. Similarly, he urged that mathematical research concentrate on solving problems posed in other fields rather than building structures of interest only to other mathematicians. *Wik

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

Friday, 9 June 2023

Regular Polygons Inscribed in a Similar Regular Polygon

A long time back, I wrote about some geometric options for a problem I had found on Greg Ross' Futility Closet. Shortly afterward I got a note from a blogger at "Five Triangles" who mentioned he had posted a very similar problem (above) about a year earlier.

What I especially enjoyed about his presentation of the problem was the obvious invitation to generalize the idea to regular polygons of more sides.
Each of the figures is simplified by the visual approach of rotating the inner polygon until it has its vertices at the midpoints of the sides of the larger. From there it is almost trivial that for the triangles, the smaller is 1/4 the larger (the logo of the five-triangles web site shows this clearly), and the smaller square is 1/2 the larger.

When you go to five sides the quick visual solutions disappear, but a generalization should offer itself to a clever trig student. If we assume the sides of the larger n-gon are each of unit length, then the area of the two polygons should be in the same ratio as the square of the side of the smaller polygon..... ( some were confused by this, the area of two similar polygons are in the ratio of the square of their corresponding side, but since we et the larger at one unit, its square is 1 square unit, and so the ratio of the two area is the square of the inner edge length over one.)....and a clever trig student looking at all those triangles (such as the blue FGB) formed between the two polygons should know a quick rule for finding the square of the side lengths of the inner polygon.... the beautiful extension of the Pythagorean theorem they know as the law of cosines.

Since each leg on the outside of the triangle is \(\frac{1}{2}\) unit, and the angle is \(\frac{\pi(n-2)}{n}\) it should be easy to determine that the square of the sides of the inner polygon is \(\frac {1}{2})^2 + (\frac {1}{2})^2 - 2 *(\frac {1}{2}*\frac {1}{2} * \cos(\frac{\pi(n-2)}{n})\) Or more simply, \(\frac {1}{2}(1-\cos(\frac{\pi(n-2)}{n}))\)
For values from n= 3 to 12 I came up with the following with the support of Wolframalpha:

Only the triangle, square, and hexagons produced rational roots, in convenient consecutive quarters for easy remembering.  The decimal approximations clearly support the intuitive idea that the limit should approach one as n grows larger without bound. By the time you get to the hectogon, the ratio is ,9990.  Fans of the "golden ratio will appreciate its appearance in the pentagon even if slightly camouflaged.

N      Ratio
3 ..... 0.25
4 ..... 0.5
5 ..... 0.654508
6 ..... 0.75
7 ..... 0.811745
8 ..... 0.853553
9 ..... 0.883022 
10 .... 0.904508
11 .... 0.920627
12 .... 0.933013
An interesting exploration, I think, for good trig students to explore.  Enjoy

On This Day in Math - June 9

The Boat House, Paducah, Ky

I've been giving this lecture to first-year classes
for over twenty-five years. 
You'd think they would begin to understand it by now.
~ J E Littlewood

The 160th day of the year; 160 is the smallest number which is sum of cubes of 3 distinct primes, the first three. (23+33+53) *Prime Curios (It is also the sum of the first power of the first 11 primes )

160! - 159! + 158! - ... -3! + 2! - 1! is prime.

160 is also the sum of two non-zero squares (122 + 42) and like all such numbers, you can show that 1602n+1 will also be the sum of two non-zero squares.

160 is the longest edge of the integer Heronian tetrahedron with smallest possible surface area and volume.  Its edges are 25, 39, 56, 120, 153, and 160; for a total surface area of 6384, and volume 8064.

160 is the largest year day (and second largest known) for which the alternating factorial sequence is prime: 160!- 159! + 158! - 157! .... + 2! - 1!. The alternating factorial 5! - 4! + 3! - 2! + 1! = 121. The alternating factorial sequence is prime for n= 3 through 8 (5, 19, 101, 619, 4421, 35899). In spite of this run of consecutive primes, John D Cook checked and found only 15 n values for which the alternating factorial starting with n is prime (There are now at least 17 known primes). 14 are year days, the largest being 160. 

More info on these here 
Find more math facts for each year day here


1750 Euler finally was able to prove the pentagonal theorem on June 9, 1750, in a letter to Goldbach. His proof is algebraic. The proof was first published in 1760, and Euler gives more details about points which were vague in his letter to Goldbach.
Euler had mentioned the theorem many times in the years following his first correspondence with Daniel Bernoulli (January 28,1741), in letters to Niklaus Bernoulli, Christian Goldbach, d’Alembert, and others, and in the first publication of 1751. (This paper was written on April 6, 1741 and had no proof. Euler wrote so many papers that the publishers fell dramatically behind; they were publishing new papers many years after his death.) A typical entry, from a letter to Goldbach, reads “If these factors \((1 − n)(1 − n^2)(1 − n^3) etc. are multiplied out onto infinity, the following series \(1 − n − n^2 + n^5 + n^7− etc is produced. I have however not yet found a method by which I could prove the identity of these two expressions. The Hr. Prof. Niklaus Bernoulli has also been able to prove nothing beyond induction.” Here the word “induction” means “by experiment” rather than “a proof by induction”. *Dick Koch, The Pentagonal Theorem and All That

1795 a provisional meter bar was constructed in brass by Lenoir. On 1 Aug 1793, the metre had been defined to be 1/10 000 000 of the northern quadrant of the Paris meridian (5 132 430 toises of Paris, from the north pole to the equator). On 7 Apr 1795, the first legal definition of the metre was made by the French National Assembly. A second measure was made along the Dunkirk-Barcelona axis (5 130 740 toises of Paris).
Closeup of National Prototype Metre Bar No. 27, made in 1889 by the International Bureau of Weights and Measures (BIPM) and given to the United States, which served as the standard for defining all units of length in the US from 1893 to 1960.  (the distance between two lines on a standard bar of an alloy of platinum with 10% iridium, measured at the melting point of ice) *Wik

1798 Napoleon’s fleet of 500 ships arrived in Malta, and three days later they captured the place. Monge started fifteen elementary schools and one high school there.*VFR

1905  Albert Einstein published his analysis of Planck's quantum theory and its application to light. His article appeared in Annalen der Physik. Though no experimental work was involved, it was for these insights that Einstein earned his Nobel Prize. *TIS
 Einstein quickly realized that Planck’s hypothesis about the quantization of radiant energy could also explain the photoelectric effect.

1934 First Donald Duck Cartoon. Amazingly, the "Donald in Mathland" videos that were popular in the eighties in middle schools are still for sell.


1669 Leonty Filippovich Magnitsky (9 June 1669 in Ostashkov, Russia - 30 October 1739 in Moscow, Russia) Peter the Great, Tsar of Russia, founded the School of Mathematics and Navigation in Moscow in 1701. Russia was a major power at this time but had no access to the sea. Peter decided that he would push north to try to dislodge the Swedes who controlled the Baltic coast and war had begun on this front in 1700. The many reforms, including the start of secular education, which Peter introduced to modernize Russia aimed to ensure victory in his wars for access to the seas. The declaration setting up the Moscow School was dated 14 January 1701, but formal classes did not begin immediately. There was a delay since facilities were not properly in place to allow teaching to begin. Peter the Great then appointed Magnitskii to the School on 2 February
In February, Magnitskii was appointed to the school and simultaneously ordered to compile a book "in the Slavonic dialect, selected from arithmetic, geometry and navigation." The 'Arithmetic' was therefore specifically commissioned to be the textbook of the Moscow School. Little is known about the classes in the school while the book was being prepared. It was sent to the publisher on 2 November 1702, and appeared bearing the date 11 January 1703. With its appearance the success of the school was assured.
The 'Arithmetic' was the first mathematics textbook published in Russia by a Russian which was not a translation or adaptation of a foreign textbook. It was a textbook for the courses which Magnitskii himself taught at the school, essentially a published version of his lecture notes. It was in effect an encyclopaedia of the mathematical sciences of its day, based strongly on applications in navigational astronomy, geodesy and navigation. It used the methods of algebra, geometry, and trigonometry. The 'Arithmetic',remained the basic Russian mathematics textbook for 50 years. *SAU

1812 Johann Gottfried Galle (9 June 1812 – 10 July 1910) German astronomer who on 23 Sep 1846, was the first to observe the planet Neptune, whose existence had been predicted in the calculations of Leverrier. Leverrier had written to Galle asking him to search for the 'new planet' at a predicted location. Galle was then a member of the staff of the Berlin Observatory and had discovered three comets. In 1838, while assistant to Johann Franz Encke, Galle discovered the dark, inner C ring of Saturn at the time of the maxium ring opening. In 1851, he became professor of astronomy at Breslau and director of the observatory there. In 1872, he proposed the use of asteroids rather than regular planets for determinations of the solar parallax, a suggestion which was successful in an international campaign (1888-89).

1885 John Edensor Littlewood born. (9 June 1885 – 6 September 1977) Littlewood’s Miscellany (1986) is a delightful little book, for it shows a mathematician having fun.*VFR
He collaborated for many years with G. H. Hardy. Together they devised the first Hardy–Littlewood conjecture, a strong form of the twin prime conjecture, and the second Hardy–Littlewood conjecture.
In a 1947 lecture, the Danish mathematician Harald Bohr said, "To illustrate to what extent Hardy and Littlewood in the course of the years came to be considered as the leaders of recent English mathematical research, I may report what an excellent colleague once jokingly said: 'Nowadays, there are only three really great English mathematicians: Hardy, Littlewood, and Hardy–Littlewood.'"
There is a story (related in the Miscellany) that at a conference Littlewood met a German mathematician who said he was most interested to discover that Littlewood really existed, as he had always assumed that Littlewood was a name used by Hardy for lesser work which he did not want to put out under his own name; Littlewood apparently roared with laughter. There are versions of this story involving both Norbert Wiener and Edmund Landau, who, it is claimed, "so doubted the existence of Littlewood that he made a special trip to Great Britain to see the man with his own eyes"*Wik

1906 Albert Cyril Offord FRS (June 9, 1906 – June 4, 2000) was a British mathematician. He received two Ph.D.s in mathematics: from the University of London in 1932, and from Oxford in 1936. He was the first professor of mathematics at the London School of Economics.
His Erdős number is 1. *Wik

1960  Carlo W. J. Beenakker (born June 9, 1960) is a professor at Leiden University and leader of the university's mesoscopic physics group, established in 1992. In 1997, he was awarded the Spinoza Prize, the "Dutch Nobel prize". *Wik

1751 John Machin (bapt. 1686?—June 9, 1751) was an English mathematician and astronomer best known for the formulas he invented for calculating π.*VFR
He was a professor of astronomy at Gresham College, London, and is best known for developing a quickly converging series for Pi in 1706 and using it to compute Pi to 100 decimal places.
Machin's formula is:
\frac{\pi}{4} = 4 \cot^{-1}5 - \cot^{-1}239
The benefit of the new formula, a variation on the Gregory/Leibniz series (Pi/4 = arctan 1), was that it had a significantly increased rate of convergence, which made it a much more practical method of calculation.
To compute Pi to 100 decimal places, he combined his formula with the Taylor series expansion for the inverse tangent. (Brook Taylor was Machin's contemporary in Cambridge University.) Machin's formula remained the primary tool of Pi-hunters for centuries (well into the computer era).*Wik "This formula of John Machin (1680–1751) was publicized by William Jones in his 1706 Synopsis palmariorum matheseos. Variations of it remained the standard method for calculating τ/2 (pi) until the 1970s, when better methods due to Ramanujan came to light." *Theorem of the Day

1818 Joel E. Hendricks, (March 10, 1818 - June 9, 1893) a noted mathematician, was born in Bucks County, Pennsylvania, March 10, 1818. He early developed a love of mathematics and began to teach school at nineteen years of age. He chanced to procure Moore's Navigation and Ostrander's Astronomy and, without instruction, soon became able to work in trigonometry and calculate solar and lunar eclipses. He took up algebra while teaching and soon became master of that science without instruction. He taught mathematics two years in Neville Academy, Ohio, and then occupied a position on a Government survey in Colorado in 1861. In 1864 he located in Des Moines, Iowa and pursued his mathematical studies. In 1874 he began the publication of the Analyst, a journal of pure and applied mathematics and soon won a reputation in Europe among eminent scholars as one of the most advanced mathematicians of the day. His Analyst was taken by the colleges and universities of Europe and found a place in the best foreign libraries. His name became famous among all mathematical experts of the world. Among his correspondents were Benjamin Silliman, John W. Draper and James D. Dana; while his journal was authority at Yale and Johns Hopkins Universities. For ten years, up to 1884, this world-famous Analyst was published at Des Moines by Dr. Joel E. Hendricks. Up to the time it was discontinued, no journal of mathematics had been published so long in America. It is one of the remarkable events of the Nineteenth Century that a self-educated man should, by his own genius and industry, without instruction, reach such an exalted place among the world's great scholars. Dr. Hendricks died in Des Moines on the 9th of June, 1893. *History of Iowa From the Earliest Times to the Beginning of the Twentieth Century/Volume 4 by Benjamin F. Gue
A more complete mathematical biography of Mr. Hendricks can be found in The American Mathematical Monthly, Vol 1, #3, 1894.

1847 John Hailstone (13 Dec, 1759– 9 June, 1847), English geologist, born near London, was placed at an early age under the care of a maternal uncle at York, and was sent to Beverley school in the East Riding. Samuel Hailstone was a younger brother. John went to Cambridge, entering first at Catharine Hall, and afterwards at Trinity College, and was second wrangler and second in the Smith Prize of his year (1782). He was second in both competitions to James Wood who became master of Saint Johns, and Dean of Ely. Hailstone was elected fellow of Trinity in 1784, and four years later became Woodwardian Professor of Geology, an office which he held for thirty years.
He went to Germany, and studied geology under Werner at Freiburg for about twelve months. On his return to Cambridge he devoted himself to the study and collection of geological specimens, but did not deliver any lectures. He published, however, in 1792, ‘A Plan of a course of lectures.’
He married, and retired to the vicarage of Trumpington, near Cambridge, in 1818, and worked zealously for the education of the poor of his parish. He devoted much attention to chemistry and mineralogy, as well as to his favourite science, and kept for many years a meteorological diary. He made additions to the Woodwardian Museum, and left manuscript journals of his travels at home and abroad, and much correspondence on geological subjects. He was elected to the Linnean Society in 1800, and to the Royal Society in 1801, and was one of the original members of the Geological Society. Hailstone contributed papers to the ‘Transactions of the Geological Society’ (1816, iii. 243–50), the ‘Transactions of the Cambridge Philosophical Society’ (1822, i. 453–8), and the British Association (Report, 1834, p. 569). He died at Trumpington in his eighty-eighth year. *Wik

1897 Alvan Graham Clark (July 10, 1832 – June 9, 1897) U.S. astronomer, one of an American family of telescope makers and astronomers who supplied unexcelled lenses to many observatories in the U.S. and Europe during the heyday of the refracting telescope. He began a deep interest in astronomy while still at school, then joined the family firm of Alvan Clark & Sons, makers of astronomical lenses. In 1861, testing a new lens, he looked through it at Sirius and observed faintly beside it, Sirius B, the twin star predicted by Friedrich Bessel in 1844. Carrying on the family business, after the deaths of his father and brother, Clark made the 40" lenses of the Yerkes telescope (still the largest refractor in operation in the world). Their safe delivery was a source of anxiety. He died shortly after their first use.

1969 Harold Davenport (30 October 1907 – 9 June 1969) worked on number theory, in particular the geometry of numbers, Diophantine approximation and the analytic theory of numbers. He wrote a number of important textbooks and monographs including The higher arithmetic (1952)*SAU

1977 Dr. Gustav Doetsch (November 29, 1892 – June 9, 1977) was a German mathematician, aviation researcher, decorated war veteran, and Nazi supporter. The modern formation and permanent structure of the Laplace transform is found in Doetsch's 1937 work Theorie und Anwendung der Laplace-Transformation,[5] which was well-received internationally. He dedicated most of his research and scientific activity to the Laplace transform, and his books on the subject became standard texts throughout the world, translated into several languages. His texts were the first to apply the Laplace transform to engineering. *Wik

1995  Vivienne Lucille Malone-Mayes (February 10, 1932 – June 9, 1995) was an American mathematician and professor. Malone-Mayes studied properties of functions, as well as methods of teaching mathematics. She was the fifth African-American woman to gain a PhD in mathematics in the United States, and the first African-American member of the faculty of Baylor University (which had rejected her application to study there five years earlier).
She decided to attend the University of Texas full-time as a graduate student when rejected entry at Baylor. In graduate school she was very much alone. In her first class, she was the only Black, the only woman. Her classmates ignored her completely, even terminating conversations if she came within earshot. She was denied a teaching assistantship, although she was an experienced and excellent teacher.
She wrote, "... it took a faith in scholarship almost beyond measure to endure the stress of earning a Ph.D. degree as a Black, female graduate student. I could not join my advisor and other classmates to discuss mathematics over coffee at Hilsberg's cafe .... Hilsberg's would not serve Blacks.
Some classes were closed to her despite the fact that the University of Texas was required to take Black students. For example R L Moore refused to have any Black students in his classes.
She was a member of the board of directors of the National Association of Mathematicians. She was elected Director-at-large for the Texas section of Mathematical Association of America and served as director of the High School Lecture Program for the Texas section.
She had a successful, lengthy career and served on several boards and committees of note, retiring in 1994 due to ill health.  She was the fifth African-American woman to be allowed in the White House.She was also active in her local community as a lifetime member of New Hope Baptist Church. She served on boards of directors for Cerebral Palsy, Goodwill Industries, and Family Counseling and Children. She was on the Texas State Advisory Council for Construction of Community Mental Health Centers and served on the board of the Heart of Texas Region Mental Health and Mental Retardation Center.
After Lillian K. Bradley in 1960, Malone-Mayes became one of the first African-American women to receive a PhD in Mathematics from University of Texas (and fifth African-American woman in the United States). She was the first African-American member of the faculty at Baylor University, and the first African-American person elected to Executive Committee of the Association of Women in Mathematics.
The student congress of Baylor voted her the "Outstanding Faculty Member of the Year" in 1971.  *Wik & *SAU


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

Thursday, 8 June 2023

On This Day in Math - June 8

If you open a mathematics paper at random, 
on the pair of pages before you, you will find a mistake.
~Joseph Doob

The 159th day of the year; 159 = 3 x 53, and upon concatenating these factors in order we have a peak palindrome, 353, which is itself a prime.*Prime Curios

159 is the sum of 3 consecutive prime numbers: 47 + 53 + 59 and can be written as the difference of two squares in two different ways.

Deshouillers (1973) showed that all integers are the sum of at most 159 prime numbers. I'm waiting for someone to tell me the number that takes 159 prime numbers to form??? 

 48 x 159 = 5346, uses all nine non-zero digits

159 is the fifth Woodall number, a number of the form n*2n -1.  The numbers were first studied by Allan J. C. Cunningham and H. J. Woodall in 1917, inspired by James Cullen's earlier study of the similarly-defined Cullen numbers (n*2n +1. )


1612 Paolo Gualdo wrote from Padua to say that Sagredo had sent him Galileo's letter on sunspots, which he had shown to many of his friends. *Stillman Drake, Galileo at Work

1637 The printing of Descartes’ Discours de la Methode, with its important appendix “La G´eom´etrie,” was completed. *VFR In 1637, the book Discourse on Method of Rightly Conducting the Reason, and Seeking Truth in the Sciences, was published by René Descartes, regarded as a major work in science and mathematics. He expresses his disappointment with traditional philosophy and with the limitations of theology; only logic, geometry and algebra hold his respect, because of the utter certainty which they can offer. Ushering in the "scientific revolution" of Galileo and Newton, Descartes' ideas swept aside ancient and medieval traditions of philosophical methods and investigation. *TIS

1724 Euler received his master’s degree in philosophy at age 17, giving a lecture comparing the philosophical ideas of Descartes and Newton. His bachelor’s speech, in the summer of 1722, was “On temperance.” *VFR  Graduation with the same degree on that day was Johann II (Jean) Bernouli, only 14. *Ronald S. Calinger; Leonhard Euler: Mathematical Genius in the Enlightenment

1887 Herman Hollerith receives a patent for his punch card calculator. * The Geek Manual (I wonder what age is the lower  threshold for recognition of the term "punch card" as a computer term.)

1911  The Aero Club of America issued its first pilot licenses to five established aviators. Presented alphabetically, Glenn Curtiss received license #1. Orville and Wilbur Wright held licenses #4 and #5 behind U.S. Army pilot Frank Lahm (#2) and French aviator Louis Paulhan (#3). Subsequent pilots had to pass a flight test to earn a license.
Thirty-six-year-old Harriet Quimby became the first female licensed pilot in the U.S. on August 1, 1911, when she earned license #37 from the Aero Club of America. She became a prize-winning pilot at air meets and was the first woman to fly across the English Channel in April 1912. Like many aviators of her generation, Quimby’s life was cut short when she died in a plane crash near Boston on July 1, 1912.

*Linda Hall Org


In 1918, Nova Aquila, the brightest nova since Kepler's nova of 1604, was discovered in the constellation of Aquila the eagle, a 1st magnitude star 6 degrees north of the Scutum star cloud. For the months that it shone, it was the brightest star in the sky, briefly half a million times brighter than the sun, but seen from 1200 light years (70,000 trillion miles) away. Between 1899 and 1936 there were 20 fairly bright novae, and five of those were in this same small area of the sky, the constellation Aquila. Seven years later Nova Aquila had faded to a bluish star apparently much smaller and denser than our sun. (Aquila belonged to Zeus, and was the eagle that carried the mortal Ganymede to the heavens to serve as Zeus' cup bearer.)TIS

1918 The total solar eclipse of June 8, 1918 crossed the United States from Washington State to Florida. This path is roughly similar to the August 21, 2017 total solar eclipse and was the last time totality crossed the nation from the Pacific to the Atlantic. *

1921 Edith Clarke submits patent for the Clark Calculator. The calculator was a simple graphical device that solved equations involving electric current, voltage and impedance in power transmission lines. The device could solve line equations involving hyperbolic functions ten times faster than previous methods. She filed a patent for the calculator in 1921 and it was granted in 1925. Ms. Clarke is generally thought of as the first female electrical engineer in the U. S.

1923 Art historian Joan Evans speaks on “Jewels of the Renaissance”, and becomes the first woman to give a Discourse at the Ri. *Royal Institution web page,    
She was a British historian of French and English mediaeval art, especially Early Modern and medieval jewellery. Her notable collection was bequeathed to the Victoria and Albert Museum in London *Wik

1948 Carl Savit, a graduate student at Caltech, appeared in court to demand $1000 from Mottant Company of Chicago for solving the three classical construction problems. This offer was made in an advertisement that neglected to require that compass and straightedge be used. It is not known if he collected. [Mathematics Magazine 61 (1988), p 158].*VFR There are are many beautiful approaches to trisecting a general angle using other tools as I wrote in "Trisecting the General Angle, A Plethora of Pretty Approaches"

1979 The Source, the first computer public information service, goes on line.

2004 The second most recent (most recent was in 2012) transit of Venus when observed from Earth took place on June 8, 2004. The event received significant attention, since it was the first Venus transit to take place after the invention of broadcast media. No human alive at the time had witnessed a previous Venus transit, since the previous Venus transit took place on December 6, 1882. The next transit of Venus occurred on June 5–June 6 in 2012,. If you missed these two, the next transits of Venus will be in December 2117 and December 2125.*Wik


1625 Jean Dominique Cassini (June 8, 1625, Perinaldo - September 14, 1712, Paris)
Italian-born French astronomer who in 1675 discovered Cassini's division, the dark gap subdividing Saturn's rings into two parts. He stated that Saturn's ring, believed by Huygens to be a single body, was actually composed of small particles. Cassini also discovered four of Saturn's moons: Iapetus (Sep 1671), Rhea (1672) and on 21 Mar 1684,* Tethys and Dione. He compiled new tables (1662) on the annual motion of the Sun. He observed shadows of four Galilean satellites on Jupiter (1664), and measured its rotation period by studying the bands and spots on its surface. He determined the period of rotation of Mars (1666), and attempted the same for Venus. His son Jacques was also an astronomer.*TIS

1724 John Smeaton (8 June 1724 – 28 October 1792)  English civil engineer, who coined the term "civil engineering" (to distinguish from military engineers). He built the third Eddystone Lighthouse, Plymouth, Devon, using dovetailed blocks of portland stone (1756-59). He discovered the best mortar for underwater construction to be limestone with a high proportion of clay. Smeaton also constructed the Forth and Clyde Canal in Scotland between the Atlantic and the North Sea; built bridges in towns including Perth, Banff, and Coldstream, Scotland; and completed Ramsgate harbour, Kent. He introduced cast-iron shafts and gearing into wind and water mills, designed large atmospheric pumping engines for mines, and improved the safety of the diving bell.)*TIS

1725 Caspar Wessel(June 8, 1745, Vestby – March 25, 1818, Copenhagen)  was a Norwegian mathematician who invented a geometric way of representing complex numbers which pre-dated Argand. *SAU
His fundamental paper, Om directionens analytiske betegning, was published in 1799 by the Royal Danish Academy of Sciences and Letters. Since it was in Danish, it passed almost unnoticed, and the same results were later independently found by Argand and Gauss.
One of the more prominent ideas presented in "On the Analytical Representation of Direction" was that of vectors. Even though this wasn't Wessel's main intention with the publication, he felt that a geometrical concept of numbers, with length and direction, was needed. Wessel's approach on addition was: "Two straight lines are added if we unite them in such a way that the second line begins where the first one ends and then pass a straight line from the first to the last point of the united lines. This line is the sum of the united lines". This is the same idea as used today when summing vectors. Wessel's priority to the idea of a complex number as a point in the complex plane is today universally recognized. His paper was re-issued in French translation in 1899, and in English in 1999 as On the analytic representation of direction (ed. J. Lützen et al.).*Wik

1858 Charlotte Agnas Scott (8 June 1858 – 10 November 1931, Cambridge) born in Lincoln, England. She attended Girton, the first (1869) college in England for women. In 1880 she took the tripos exam at Cambridge, but because she was a woman, her name could not be announced at the award ceremony. “The man read out the names and when he came to ‘eighth,’ before he could say the name, all the undergraduates called out ‘Scott of Girton,’ and cheered tremendously, shouting her name over and over again with tremendous cheers and waving of hats.” [Women of Mathematics. A Biobibliographic Sourcebook (1987), edited by Louise S. Grinstein and Paul J. Campbell] *VFR

1860 Alicia Boole Stott  (June 8, 1860, Cork, Ireland – December 17, 1940, England) was the third daughter of George Boole. (Read more about Boole's descendents in my blog, "Those Amazing Boole Girls." ) George Boole died when Alicia was only four years old and she was was brought up partly in England by her grandmother,(Mary Everest Boole was a mathematician educator who was an early advocate of teaching children math through playful activities. It is almost certain she would have exposed her daughters to such activities {pb}) partly in Cork by her great-uncle. When she was twelve years old she went to London where she joined her mother and sisters.
With no formal education she surprised everyone when, at the age of eighteen, she was introduced to a set of little wooden cubes by her brother-in-law Charles Howard Hinton. Alicia Boole experimented with the cubes and soon developed an amazing feel for four dimensional geometry. She introduced the word 'polytope' to describe a four dimensional convex solid.

MacHale, writes:-
She found that there were exactly six regular polytopes on four dimensions and that they are bounded by 5, 16 or 600 tetrahedra, 8 cubes, 24 octahedra or 120 dodecahedra. She then produced three-dimensional central cross-sections of all the six regular polytopes by purely Euclidean constructions and synthetic methods for the simple reason that she had never learned any analytic geometry. She made beautiful cardboard models of all these sections....
After taking up secretarial work near Liverpool in 1889 she met and married Walter Stott in 1890. Stott learned of Schoute's work on central sections of the regular polytopes in 1895 and Alicia Stott sent him photographs of her cardboard models. Schoute came to England and worked with Alicia Stott, persuading her to publish her results which she did in two papers published in Amsterdam in 1900 and 1910.
The University of Groningen honoured her by inviting her to attend the tercentenary celebrations of the university and awarding her an honorary doctorate in 1914.
In 1930 she was introduced to Coxeter and they worked together on various problems. Alicia Stott made two further important discoveries relating to constructions for polyhedra related to the golden section. *Wik

1867 Frank Lloyd Wright (June 8, 1867 – April 9, 1959) was born in Richland Center, Wisconsin. Widely regarded as America's most significant architect, Wright transformed twentieth-century
residential design; his influential Prairie School houses and plans for public buildings proved simultaneously innovative, aesthetically striking, and practical. A social visionary, Wright's commitment to a context-driven "organic architecture," which harmonized with both its occupants' needs and the surrounding landscape, underscored his creative genius across a long and productive career.*Library of Congress

1870 Peter Pinkerton (8 June 1870 in Kilmarnock, Scotland -22 November 1930 in Glasgow, Scotland) studied at Glasgow and Dublin. After teaching at various schools he became Rector of Glasgow High School. He became President of the EMS in 1908. *SAU

1896 Eleanor Pairman (June 8, 1896-September 14, 1973) graduated from Edinburgh. She went to London where she worked with Karl Pearson and then went to the USA where she gained a doctorate from Radcliffe College.*SAU

1905 Edward Hubert Linfoot (8 June 1905, Sheffield, England - 14 October 1982, Cambridge, England)
After attending King Edward VII School he won a scholarship to Balliol College at the University of Oxford.
During his time at Oxford he met the number theorist G. H. Hardy, and after graduating in 1926, Linfoot completed a D.Phil under the supervision of Hardy with a thesis entitled Applications of the Theory of Functions of a Complex Variable.
After brief stints at the University of Göttingen, Princeton University, and Balliol College, Linfoot took a job in 1932 as assistant lecturer, and later lecturer, at the University of Bristol. During the 1930s Linfoot's interests slowly made the transition from pure mathematics to the application of mathematics to the study of optics, but not before proving an important result in number theory with Hans Heilbronn, that there are at most ten imaginary quadratic number fields with class number 1 *WIK

1923 Gloria Olive (8 June 1923, New York City, USA - 17 April 2006, Dunedin, New Zealand)
Gloria Olive completed her school educations at Abraham Lincoln High School in Brooklyn, New York, graduating in 1940. She then entered Brooklyn College in New York where she studied mathematics, graduating with an B.A. in 1944. Perhaps the most famous of her lecturers was Jesse Douglas who had been awarded the Fields Medal at the International Congress of Mathematicians at Oslo in 1936. After graduating, Olive was appointed as a Graduate Assistant at the University of Wisconsin where she spent the two academic years 1944-46. In addition to teaching she studied for her Master's Degree during these two years and was awarded the degree in 1946.
From Wisconsin, Olive moved to the University of Arizona in 1946 where she was appointed as an instructor. After two years she was appointed to Idaho State University where again she spent two years teaching as an instructor. Her next appointment in Oregon State University in 1950 was as a Graduate Assistant and after this one-year post she left the academic world for a short time, taking a job as a cryptographer in the U.S. Department of Defense in Washington, D.C. After a year in Washington, Olive returned to an academic position being appointed to Anderson College in 1952.

Anderson Bible Training School had been founded in 1917 as an educational establishment to train leaders and workers for a life in the church. It rapidly developed a broader, more general, education program, and changed its name first to Anderson College and Theological Seminary, and then to Anderson College. At Anderson College, Olive built up the mathematics department and began to become interested in mathematical research, in particular studying generalised powers. C C MacDuffee, who had taught Olive at the University of Wisconsin, agreed to accept a visiting professorship at Oregon State University so that he could supervise her doctoral thesis. Sadly he died in 1961 and Olive was left without a thesis advisor. However she was awarded a Ph.D. for her thesis Generalized Powers in 1963.

Olive continued to at Anderson College until 1968 when she accepted a professorship at the University of Wisconsin-Superior. She stayed at the University of Wisconsin-Superior until 1972, the year after it joined the University of Wisconsin, and went to New Zealand where she was appointed as a senior lecturer at the University of Otago. She continued in this post until she retired in 1989. Mac Lane and Rayner wrote on her retirement
For all of her time with the Mathematics and Statistics Department of Otago University, Gloria has been the only female on the staff with tenure, and as such has been a shining example to both staff and students. She has fought hard for the issues she championed, and contributed to several worthwhile changes (such as the current internal assessment policy applauded by both staff and students). Her colleagues will miss her lively contributions to the debates in departmental meetings.
Much of Olive's research was on applications of generalised powers. She published papers such as Binomial functions and combinatorial mathematics (1979), A combinatorial approach to generalized powers (1980), Binomial functions with the Stirling property (1981), Some functions that count (1983), Taylor series revisited (1984), Catalan numbers revisited (1985), A special class of infinite matrices (1987), and The ballot problem revisited (1988). *SAU

1924 Samuel Karlin (June 8, 1924 - December 18, 2007) made fundamental contributions to game theory, analysis, mathematical statistics, total positivity, probability and stochastic processes, mathematical economics, inventory theory, population genetics, bioinformatics, and biomolecular sequence analysis, was born in Yonova, Poland, and immigrated to Chicago as a child. Karlin earned a doctorate in mathematics at age 22 from Princeton in 1947. He taught at Caltech from 1948 to 1956 before moving to Stanford as a Professor of Math and Stat. Overall, Karlin had over 70 PhD students, to whom he was an extraordinary teacher and advisor.(*David Bee)

1955 Tim Berners-Lee (8 June 1955- ), English computer scientist who invented the World Wide Web and director of the World Wide Web Consortium, which oversees its continued development. In 1984, he took up a fellowship at CERN, to work on distributed real-time systems for scientific data acquisition and system control. While there , in 1989, he proposed a global hypertext project, to be known as the World Wide Web, which permitted people to collaborate by sharing knowledge in a web of hypertext documents. On 6 Aug 1991, the first World Wide Web site was made available to the Internet at large, giving information on a browser and how to set up a Web server. He then expanded its reach, always nonprofit, to become an international mass medium. *TIS


1882 John Scott Russell (9 May 1808, Parkhead, Glasgow – 8 June 1882, Ventnor, Isle of Wight)  British civil engineer best known for researches in ship design. He designed the first seagoing battleship built entirely of iron. He was the first to record an observation of a soliton, while conducting experiments to determine the most efficient design for canal boats. In Aug 1834, he observed what he called the "Wave of Translation," a solitary wave formed in the narrow channel of a canal which continues ahead after a canal boat stops. [This is now recognised as a fundamental ingredient in the theory of 'solitons', applicable to a wide class of nonlinear partial differential equations.] He also made the first experimental observation of the "Doppler shift" of sound frequency as a train passes (1848). He designed (with Brunel) the Great Eastern and built it; he designed the Vienna Rotunda and helped to design Britain's first armored warship, the Warrior. *TIS

1920 Augusto Righi (27 August 1850 – 8 June 1920) was an Italian physicist and a pioneer in the study of electromagnetism. He was born and died in Bologna.
Righi was the first person to generate microwaves,[citation needed] and opened a whole new area of the electromagnetic spectrum to research and subsequent applications. His work L'ottica delle oscillazioni elettriche (1897), which summarised his results, is considered a classic of experimental electromagnetism. Marconi was his student. *Wik

1935 Alexander Wilhelm von Brill (20 September 1842 – 18 June 1935) was a German mathematician.
Cardboard 'Sliceforms' by John Sharp.
Born in Darmstadt, Hesse, Brill was educated at the University of Giessen, where he earned his doctorate under supervision of Alfred Clebsch. He held a chair at the University of Tübingen, where Max Planck was among his students. In 1933, he joined the National Socialist Teachers League as one
of the first members from Tübingen.
The London Science Museum contains sliceform objects prepared by Brill and Felix Klein. *Wik

1998 Maria Reiche (May 15, 1903, Dresden -  June 8, 1998, Peru) German-born Peruvian mathematician and archaeologist who was the self-appointed keeper of the Nazca Lines, a series of desert ground drawings over
1,000 years old, near Nazcain in southern Peru. For 50 years the "Lady of the Lines" studied and protected these etchings of animals and geometric patterns in 60 km (35 mi) of desert. Protected by a lack of wind and rain, the figures are hundreds of feet long best seen from the air. She investigated the Nazca lines from a mathematical point of view. Death at age 95 interrupted her new mathematical calculations: the possibility that the lines predicted cyclical natural phenomena like El Nino, a weather system that for centuries has periodically caused disastrous flooding along the Peruvian coast.

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