Rheticus, and The Names of Trigonometric Ratios

   Spending lots of time lately reading old English journal articles (1825-45) sent me by Dave Renfro who tries to help me stay up on the history of math. It is kind of great reading and watching the actual history of ideas unfold as they did in the old journals.... I came across an interesting letter from Agustus De Morgan about the protege of Copernicus, George Joachim of Rhaetia, also called Rheticus. It was Rheticus who managed to convince Copernicus to publish his long withheld manuscript. In fact, the first account of the Copernican system was not published by Copernicus, but  in Rheticus’s Narratio prima in 1540.

I didn't realize for some years of teaching that in the very early days before the trigonometric functions, the early astronomers used the length of the chord of an angle.  The lost tables of Hipparchus (c. 190 BC – c. 120 BC) and Menelaus (c. 70–140 CE) and those of Ptolemy (c. AD 90 – c. 168) were all tables of chord

 lengths of central angles of a circle of specified radius.  The first step towards the common sine of an angle was by the fifth century Indian mathematician and astronomer Āryabhata, who chose to print tables of half-chords, or more specifically, a table of the first differences of the values of trigonometric sines expressed in arcminutes. were first thought conceived to be lengths of segments in a circle of a given diameter (or radius) rather than the more modern view of ratios. I did not know until I read this article, that apparently it was Rheticus who first developed the use of trig functions based on the ratios of sides of a triangle. In fact, the tables he created to include in his publication of the trigonometric sections of De Revolutionibus were the first tables to include all six functions and  (although he did not use the current names). 

" Rheticus published his first trigonometric canon, the Canon doctrinæ triangulorum, in 1551 in Leipzig . This table gave the six trigonometric functions at intervals of 10' of degree, semi-quadrantically arranged. Each function was given to 7 places, or more exactly as integers for a radius of 10^7.

Rheticus did not consider angles in circles, but considered triangles of which one of the side (the hypotenuse) was constant, and he gave the lengths of the other sides as a function of the angle at the center" *Denis Roegel

 This is a very rare table, and it was practically unknown when De Morgan happened to find a copy of it in the 1840s .

Here is the way De Morgan wrote it:
" Modern teachers (he writes in 1845) of trigonometry have pretty generally abandoned the system of independent lines, which used to be called sines, tangents, &c.; and have substituted, for the meaning of these words, the ratio of the sides of right-angled triangles. It appears that they have antiquity in their favor; indeed so completely has the idea of representing the ratios of the sides of triangles taken possession of the mind of Rheticus, that he abandons the use of the word sine. He dwells on the importance of the right-angled triangles, without any reference to the circle: his maxim expressed in the dialogue, is Triquetrum in planicie cum angulo recto, est magister Mathesos . It would also seem as if his choice of the semi-quadrantal arrangement with double descriptions was dictated merely by the convenience of heading one division with majus latus, and the other with minus latus. [Rheticus had labeled the top of his table with perpendiculum and basis, then the bottoms of these columns were reversed, much as Sine and Cosine were reversed at the top and bottom of tables used in my youth before calculators]........ The names cosine, cotangent, and cosecant are the consequence, not the cause, of this duplicate system of arrangements.......The introduction of the terms sine of the complement, complemental sine, and cosine, &c., followed after an interval of more than half a century."
De Morgan points out that one of the reasons it is so hard to find copies of much of Rheticus' work is that ", In the Index Expurgatorius, it is not Copernicus who is forbidden to be read generally; the prohibition only extends to the work De Revolutionibus, and is accompanied with a nisi corrigatur. But Rheticus is wholly forbidden to be read in any of his works. "
I think the difference in the two mens treatment in the Index may be because of the fact that Rheticus was Protestant, and in fact, was at Wittenburg, the very University where Luther had taught, and burned the Papal Bull.

(Another perhaps, was that Rheticus was more zealous about the Copernican system than Copernicus, insisting on the physical truth of the motion of the earth.

An interesting anecdote told about Rheticus while he was, "puzzling himself about the motion of Mars, he invoked his genius or guardian angel to help him out of the difficulty: the angel accordingly lifted him up by the hair of his head to the roof and threw him down upon the pavement saying with a bitter laugh, 'That's the way Mars moves.' "

addendum James asked about the phrase "semi-quadrantal"... this just means he only went from 0 degrees to 45 degrees (1/2 of a quadrant) and then put Sin-Cos (he didn't use these words) at the top of the columns and Cos-Sin in the reverse order at the bottom... so that from 45 to 90 degrees was simply read up from the bottom....My old CRC tables were arranged the same way, and many textbooks did as well in the Fifties-sixties. (See image below)
 Giving Sin and Cosine as ratios was still pretty new when this was written by De Morgan. It appears that Peacock had initiated the practice in his lectures at Cambridge around 1830, and by 1837, according to De Morgan, it had become the accepted way to define the terms.

Another newish feature of Rheticus' tables were the use of decimal fractions, introduce  by Regiomontanus (1436–76), German astronomer and mathematician, who composed the first tables with decimal fractions.

Some Notes About the Names from MacTutor at Saint Andrews University :

The Hindu word jya for the sine was adopted by the Arabs who called the sine jiba, a meaningless word with the same sound as jya. Now jiba became jaib in later Arab writings and this word does have a meaning, namely a 'fold'. When European authors translated the Arabic mathematical works into Latin they translated jaib into the word sinus meaning fold in Latin. In particular Fibonacci's use of the term sinus rectus arcus soon encouraged the universal use of sine.

Edmund Gunter was the first to use the abbreviation sin in 1624 in a drawing. The first use of sin in a book was in 1634 by the French mathematician Hérigone while Cavalieri used Si and Oughtred S.

It is perhaps surprising that the second most important trigonometrical function during the period we have discussed was the versed sine, a function now hardly used at all. The versine is related to the sine by the formula

versin $$�=1−cos⁡�.

It is just the sine turned (versed) through 90°.

The cosine follows a similar course of development in notation as the sine. Viète used the term sinus residuae for the cosine, Gunter (1620) suggested co-sinus. The notation Si.2 was used by Cavalieri, s co arc by Oughtred 

The tangent and cotangent came via a different route from the chord approach of the sine. These developed together and were not at first associated with angles. They became important for calculating heights from the length of the shadow that the object cast. The length of shadows was also of importance in the sundial. Thales used the lengths of shadows to calculate the heights of pyramids.

The first known tables of shadows were produced by the Arabs around 860 and used two measures translated into Latin as umbra recta (shadow erect) and umbra versa (shadow turned). Viète used the terms amsinus and prosinus. The name tangent was first used by Thomas Fincke in 1583 in his book Geometria rotundi, which is about plane and spherical trigonometry. The word comes from the Latin word tangens, which means "touching". . The term cotangens was first used by Edmund Gunter in 1620.

The common abbreviation used today is tan whereas the first occurrence of this abbreviation was used by Albert Girard in 1626, but tan was written over the angle.  \( Tan \choose {35^o}\). [By the way, the first known use of the degree symble as a raised o in the modern notation appears in print in the 1570s, with a borderline example by Jacques Pelletier du Mans in 1569, and was popularized by, among others, Tycho Brahe and Johannes Kepler, but didn't become universal.]

 

The secant and cosecant were not used by the early astronomers or surveyors. These came into their own when navigators around the 15th Century started to prepare tables. Copernicus knew of the secant which he called the hypotenusa.

The abbreviations used by various authors were similar to the trigonometric functions already discussed. Cavalieri used Se and Se.2, Oughtred used se arc and sec co arc while Wallis used s and σ. Albert Girard used sec, written above the angle as he did for the tan.

And just for the record, the term 'trigonometry' first appears as the title of a book Trigonometria by B Pitiscus, published in 1595.

On This Day in Math - August 13

 

It is clear that Economics, if it is to be a science at all,

must be a mathematical science.

~William Jevons

The 225th day of the year; 225 is the ONLY three digit square with all prime digits. Can you find a four digit square with all prime digits?

225 = 01+23+45+67+89  sequence differs by 22

225 = (3!)³+(2!)³+ (1!)³

\(225 = 1^3 + 2^3 + 3^3 + 4^3 + 5^3 \) (which means, of course, that \( 225 = (1+2+3+4+5)^2 \)

 225 is the last year day that is a sum of first n cubes. Called Nicomachus's theorem, after Nicomachus of Gerasa (c. 60 – c. 120 CE)

Nicomachus's theorem states that a square whose side length is a triangular number can be partitioned into squares and half-squares whose areas add to cubes.

225 is also the largest year day which is a square number that is the sum of three distinct positive cubes.  \(15^2= 1^3 + 2^3 + 6^3\)

See Math Facts for every Year Day here.

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EVENTS

3114 BC The first day of the previous Mayan “long count” calendar (adjusted for the Gregorian Calendar). The long count calendar lasts 22,507,528 days and the previous calendar ended on December 21 of 2012. Many predicted the end of the world at that time (my current theory is that it did NOT end on that day). If the world did NOT end, we went back to year zero of the Mayan calendar.

For the Classic Maya, the beginning of the present creation was marked by this date, with each great cycle lasting 5,128 years and repeating indefinitely. *(The Maya Calendar Explained) This wasn't considered a historical date but rather a mythological starting point for the current world age - similar to how we mark years from the birth of Christ, though the Maya creation date predates recorded history by millennia.

Mayan time is marked in days (one day is called a kin), periods of 20 days (a uinal, or 20 kin), 360 days (a tun, or 18 uinal), 7,200 days (a katun, or 20 tun) and 144,000 days (a baktun, or 20 katun). December 21, 2012 marks the ending of the 13th baktun, which ends the Long Count cycle of 5,126 solar years.*aaas org 

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1661 , Sir Robert Moray, senior courtier to Charles II, advises Wren that since he did not have time to construct microscope-based drawings that the king had requested, the task was passed to Hooke.  This assignment from the king would lead to Hooke's publication of Micrographia in 1665.  *Lisa Jardine, Ingenious Pursuits, pg 62

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1672, Christiaan Huygens discovered the Martian south polar cap.*TIS He created the drawing at right, *Dept of History, Un Cal Irvine

Huygens was indeed a pioneering astronomer who made several important observations of Mars during the 17th century. His 1672 discovery of what appeared to be a bright polar region was one of the earliest telescopic observations of Martian surface features. This was quite remarkable given the limitations of telescopes available at that time.

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1727 Charles-Etienne-Louis Camas elected to the French Academy of Sciences because he had earlier won half the prize money in their competition for the best manner of masting vessels. Did Euler get the other half? *VFR

The world first became aware of Euler's abilities when he published a paper about the "masting of ships". Euler submitted this paper as an entry in the French Academy of Science's annual contest. In competition not only with other graduate students but with many accomplished mathematicians and scientists, he was still able to win second prize. (Muir, p. 139) Presumably this paper discussed the physics and mathematics involved in the support of the mast, "a tall vertical spar that rises from the keel of a sailing vessel to support the sail and rigging."

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1849 Gauss writes to his former student, Mobius, to thank him for sending a copy of Mobius' paper on third order curves and advises him to investigate the form of analytic curves from Gauss' 1799 dissertation. *Carl Friedrich Gauss: Titan of Science
By Guy Waldo Dunnington, Jeremy Gray, Fritz-Egbert Dohse

Although the geometry of the Mobius strip was found independently by German mathematicians Johann Benedict Listing and August Ferdinand Möbius in 1858, the curve existed in art back to antiquity.

These were probably not seen in the mathematical sense but more as coiled ribbons for decoration.

Mosaic from ancient Sentinum depicting Aion holding a Möbius strip

The Mobius strip was used as a way to reduce wear and "walking" of drive belts for powering machines as early as the 12th Century.

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1849 George Boole writes to De Morgan to tell him he has received the math professorship at Queen's College Cork. In spite of stating clearly in his application, "I am not a member of any university and have never studied at a college." He had written numerous papers in the mathematical journals including one that won a Gold Medal from the Royal Society, and he included recommendations from some heavyweights of the period, Cayley, De Morgan, Kelland (professor at Edinburgh) and Charles Graves(professor of math at Trinity College Dublin).

Sir Edward Thomas ffrench Bromhead encouraged the young George Boole from Lincoln. Bromhead was President of the Lincoln Mechanics Institute in the Lincoln Greyfriars, where George Boole's father was the curator. Boole first came to public notice when he gave a lecture on the work of Sir Isaac Newton on 5 February 1835. The young Boole's development was fed by books that Bromhead supplied.  Bromhead had earlier been the patron of mathematician and physicist George Green, also of Lincoln. *Wik

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1894 Sir William Ramsay and Lord Rayleigh announced the discovery of the first noble gas argon, named after the Greek word ‘argos’ (meaning ‘lazy’) because it was completely unreactive. For this work, Sir William Ramsey was awarded the Nobel Prize in Chemistry and Lord Rayleigh the Nobel Prize in Physics in 1904. *RSC.org

Ramsay and Rayleigh used two different methods to remove all known gases from air and discovered that argon made up almost 1% of the atmosphere. 

Ramsay's interest in argon began after he learned from American scientists that heating uranium minerals in sulfuric acid produced unidentified gases. He continued to experiment with similar methods, eventually discovering another new element, helium, while trying to isolate argon from cleveite. Helium had previously only been known in the solar spectrum. Based on the positions of argon and helium in the periodic table, Ramsay predicted the existence of other noble gases, including neon, krypton, and xenon. 

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1898 The first Near Earth Asteroid, 433 Eros was discovered by Carl Gustav Witt *David Dickinson @Astroguyz It was discovered on the same night by Witt in Berlin and Auguste Charlois at Nice. Eros was one of the first asteroids to be visited by a spacecraft, and the first to be orbited and soft-landed on. NASA spacecraft NEAR Shoemaker entered orbit around Eros in 2000, and came to rest on its surface in 2001. On January 31, 2012, Eros passed the Earth at 0.17867 AU (26,729,000 km; 16,608,000 mi), or about 70 times the distance to the Moon. *Wik

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1903 The journal Nature reported that helium gas is produced by the radioactive decay of the radium. This key discovery by William Ramsay and Frederick Soddy helped to reveal the structure of atoms. In 1908, Rutherford confirmed that alpha rays and these radium emanations were one and the same: the nuclei of helium atoms, bearing a positive electrical charge. Each were future Nobel laureates in Chemistry. Ramsey won the Nobel Prize in 1904 for his discovery of the noble gases. Rutherford was recognized in 1908 for his investigations into the disintegration of the elements. Soddy was honored in 1921 for his pioneering contributions to understanding the chemical properties of radioactive elements such as radium and uranium.*TIS

*Soddy

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On this day in 1952, Willie Mae “Big Mama” Thornton—the “biggest, baddest, saltiest chick” in blues music—recorded “Hound Dog.” (Yep, that Hound Dog True to her reputation, she gave the song everything she had—and changed rock and roll history.

“Hound Dog” had Willie Mae Thornton’s name on it from the get-go. And a ferocious performance with Johnny Otis’s band at Harlem’s Apollo Theater would soon earn her the nickname “Big Mama.”

Otis had an impeccable eye for talent (one of his other discoveries was R&B great Jackie Wilson). He asked Jerry Leiber and Mike Stoller, two teenage songwriters, to meet with Thornton. Leiber said, “We saw Big Mama and she knocked me cold.”

That first impression inspired them to write “Hound Dog,” a song about a woman who won’t put up with any more of her man’s cheating and mooching. Thornton didn’t just sing the lyrics, she screamed and growled them. “You ain’t nothin’ but a hound dog / quit snoopin’ ’round my door.” As if she knew exactly what kind of man those words were about.

In 2024 Big Mama Thornton was inducted into the Rock and Roll Hall of Fame.

“Hound Dog” was released in 1953 and spent seven weeks at the top of the Billboard R&B chart. Thornton became a star.(Here is a link to let you see how the song was meant to be sung>)

Another singer also found success with the song a few years later. You may have heard of him: Elvis Presley. His version, released in 1956, topped the pop, country, and R&B charts and launched the young rocker’s career straight into the stratosphere. (Thornton reportedly wasn’t thrilled about Presley’s success with the song, probably because she wasn’t given much credit for the original.)*Brittanica

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1973  The Institute for Certification of Computing Professionals was founded. The bearer of the standards for the computer industry, ICCP promoted high professional standards for the computer industry and offered a certification program in which engineers earned the designations of Certified Computing Professional or Associate Computing Professional.

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2014 At the opening ceremony of the International Congress of Mathematicians 2014 on August 13, 2014, the Fields Medals (started in 1936) were presented. Among the winners was Maryam Mirzakhani, the first female (and mother) ever to receive the award. (Sadly, she would die within three years of cancer.)
The three other winners were Artur Avila, Martin Hairer, and Manjul Bhargava.
You can read about them here . *Springer

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BIRTHS

1625 Erasmus Bartholin (13 August 1625, Roskilde – 4 November 1698, Kopenhagen)..Bartholin was the editor of van Schooten's "Introduction to the geometry of Descartes", He also discovered double refraction of light using Icelandic Spar crystals. He worked with Ole Roamer in publishing some of Tycho Brahe's observations. His maternal grandfather was Thomas Fincke, the geometer who invented the terms tangent and secant. (*pb)

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1704 Alexis Fontaine des Bertins, (13 August 1704 – 21 August 1771) in 1734 he gave a solution of the tautochrone problem which was more general than that given by Huygens, Newton, Euler or Jacob Bernoulli, and in 1737 he gave a solution to an orthogonal trajectories problem. The methods which he developed to solve these problems led to the calculus of variations. He used what he called the "fluxio-differential" method, so called because it used two independent first-order Leibniz type differential operators. This technique was praised by Johann Bernoulli, Euler and d'Alembert. Fontaine then used differential coefficients instead of differentials and Greenberg shows how Fontaine progressed from a calculus of variations to a calculus of several variables. *SAU

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1814 Anders Jonas Ångström (13 August 1814, Lögdö, – 21 June 1874) was a Swedish physicist whose pioneering use of spectroscopy is recognized in the name of the angstrom, a unit of length equal to 10^-10 meters. In 1853, he studied the spectrum of hydrogen for which Balmer derived a formula. He announced in 1862 that analysis of the solar spectrum showed that hydrogen is present in the Sun's atmosphere. In 1867 he was the first to examine the spectrum of aurora borealis (northern lights). He published his extensive research on the solar spectrum in Recherches sur le spectre solaire (1868), with detailed measurements of more than 1000 spectral lines. He also published works on thermal theory and carried out geomagnetical measurements in different places around Sweden.*TIS

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1819 George Gabriel Stokes born. (13 August 1819 – 1 February 1903) (1st Baronet) British mathematical physicist who studied viscous fluids and formulated his law of viscosity for the speed of a solid sphere falling in a fluid. Other laws and mathematical work for which he is known includes Stokes's theorem, in the field of vector analysis. Stokes also worked in optics, the wave theory of light, diffraction (1849), the ultraviolet spectrum and other spectrum analysis. He investigated the nature of fluorescence and was a founder of the field of geodesy with his study of variations in gravity (1849). From 1849 until his death in 1903, he held the Lucasian Chair of Mathematics at Cambridge (held earlier by Isaac Newton, and more recently by Stephen Hawking). He came from a family with generations of scientists, mathematicians and engineers.*TIS

The formula now called Stokes Law

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1861 Cesare Burali-Forti, born(13 August 1861 – 21 January 1931). He discovered the antinomy(paradox) of the class of all ordinals in 1897. He never held a permanent university position for he failed his libera docenze, or license to teach, because of the antagonism to the new methods of vector analysis on the part of some members of the examining committee. *VFR He was an assistant of Giuseppe Peano in Turin from 1894 to 1896, during which time he discovered what came to be called the Burali-Forti paradox of Cantorian set theory. He died in Turin.

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1861 Herbert Hall Turner (13 August 1861, Leeds – 20 August 1930, Stockholm) was a British astronomer and seismologist.
He was educated at Clifton College and Trinity College, Cambridge. In 1884 he accepted the post of Chief Assistant at Greenwich Observatory and stayed there for nine years. In 1893 he became Savilian Professor of Astronomy and Director of the Observatory at Oxford University, a post he held for 37 years until his sudden death in 1930.
He was one of the observers in the Eclipse Expeditions of 1886 and 1887. In seismology, he is credited with the discovery of deep focus earthquakes. He is also credited with coining the word parsec.*Wik

He pioneered many of the procedures now universally employed in determining stellar positions from astronomical photographs. After serving as chief assistant at the Royal Greenwich Observatory for nine years, he spent most of his career as Savilian professor of astronomy at Oxford University. One of the leaders in the worldwide effort to produce an astrographic chart of the sky, he developed improved methods for obtaining both positions and magnitudes from photographic plates. *SAU

A few months before Turner's death in 1930, the Lowell Observatory announced the discovery of a new minor planet, and an eleven-year-old Oxford schoolgirl, Venetia Burney, proposed the name Pluto for it to her grandfather Falconer Madan, who was retired from the Bodleian Library Madan passed the name to Turner, who cabled it to colleagues at the Lowell Observatory in the United States. The new minor planet was officially named "Pluto" on 24 March 1930*Wik

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1866 Frances Hardcastle (13 August 1866 – 26 December 1941) was an English mathematician, in 1894 one of the founding members of the American Mathematical Society. Her work included contributions to the theory of point groups.

Born in Writtle, just outside Chelmsford, Essex, Hardcastle was a daughter of Henry Hardcastle, a barrister, by his marriage in 1865 to Maria Sophia Herschel, daughter of the astronomer, mathematician, and chemist Sir John Herschel.

She was educated at Girton College (Tripos Part I 1891 & Part II 1892), and obtained a Certificate in Mathematics.

In 1892, she went to the University of Chicago for a year as an honorary fellow, then spent another year at Bryn Mawr College studying under Charlotte Scott. While at Bryn Mawr she was president of the Graduate Club and translated Felix Klein's book On Riemann's Theory of Algebraic functions and Integrals. In 1895, she recommenced postgraduate studies at Cambridge, and within a few years had published several papers on point-groups. She earned a BA degree from the University of London in 1903. Trinity College Dublin awarded her an MA (ad eundem) in 1905.

Hardcastle was one of 156 British women who publicly supported the aims of the International Congress of Women, held in The Hague in April 1915. These aims were, "1. To demand that international disputes shall in future be settled by some other means than war," and "2. To claim that women shall have a voice in the affairs of nations." Until 1909, she was an Honorary Secretary of the National Union of Women's Suffrage Societies (NUWSS). *Wik

*SAU

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1866 Dr Clara Latimer Bacon (13 August 1866 – 14 April 1948) was a mathematician and Professor of Mathematics at Goucher College. She was the first woman to earn a PhD in mathematics from Johns Hopkins University.

In October 1907 she began graduate work at Johns Hopkins University in mathematics, education and philosophy. A fellowship from the Baltimore Association for Promotion of University Education of Women allowed her to spend the 1910-1911 academic year at the university. In 1911 she became the first woman to receive a Ph.D. in mathematics from Johns Hopkins University. Her dissertation was on "The Cartesian oval and the elliptic functions p and σ," later published in the American Journal of Mathematics, Vol. 35, No. 3. (July, 1913), pp. 261-280.

Bacon was promoted to associate professor at Goucher in 1905 and to full professor in 1914. She continued to teach at Goucher College until her retirement in 1934 as Professor Emeritus of Mathematics. She was by all accounts an outstanding teacher. One student wrote of her :

She believed in us so simply and so deeply that we could not disappoint her. When she felt that circumstances prevented us from doing all she hoped, she tried to change the circumstances. It was her support that made graduate study possible for me. Her patience and understanding as a teacher opened up the beauty of mathematics. For many years her faith in all of us made life seem good.

At least eight of her students went on to earn the Ph.D. degree in mathematics, 

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1909  Fabio Conforto (13 August 1909 – 24 February 1954) was an Italian mathematician. His contributed to the fields of algebraic geometry, projective geometry and analytic geometry.*Wik 

The range of Conforto's mathematical publications is great with contributions to algebraic geometry, projective geometry, and analytic geometry. In addition, as we have seen above, he wrote articles on the history of mathematics, for example (with Guido Zappa) La geometria algebrica in Italia (dal 1939 a tutto il 1945) Ⓣ (1946) and La geometria proiettiva: suo sviluppo storico e suo significato Ⓣ (1949). 

Jean Dieudonné, reviewing a 1979 reprint of this article, writes that Conforto:-

... recalls briefly the well-known history of projective geometry, from Poncelet to von Staudt. He stresses the role of perspective as developed in art (especially by the Italians) in the birth of Desargues' ideas in the 17th century, and the analogous influence of the drawing techniques promoted by Monge ("descriptive geometry") on his students and especially on Poncelet. A special section is devoted to the Italian treatises on projective geometry, particularly those of Enriques and Severi. In a closing section the author rightly insists on the influence of projective geometry on the concepts of modern mathematics, in introducing such general notions as transformation, correspondence, invariant, and duality, and in giving one of the first examples of a "hypothetico-deductive system", where fundamental notions are created, as it were, by the axioms of the theory. *SAU

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1927 Frances Sarnat Hugle (August 13, 1927 – May 24, 1968) was an American scientist, engineer, and inventor who contributed to the understanding of semiconductors, integrated circuitry, and the unique electrical principles of microscopic materials. She also invented techniques, processes, and equipment for practical (high volume) fabrication of microscopic circuitry, integrated circuits, and microprocessors which are still in use today.

In 1962, Hugle co-founded Siliconix, one of Silicon Valley's first semiconductor houses. She is the only woman included in the "Semiconductor Family Tree *Wik

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1959 Steven Henry Strogatz (August 13, 1959, Torrington, Connecticut - ) is an American mathematician and the Jacob Gould Schurman Professor of Applied Mathematics at Cornell University. He is known for his contributions to the study of synchronization in dynamical systems, and for his work in a variety of areas of applied mathematics, including mathematical biology and complex network theory.

Strogatz recalled that as a young student, "when data he was plotting in a Physics lab created a curve he had met in algebra class.   While recording how the length of a pendulum string affects the time for the pendulum to complete a complete a swing;... it was as if the pendulum knew algebra."  *Loving + Hating Mathematics, Hersch and John-Steiner

In particular, his 1998 Nature paper with Duncan Watts, entitled "Collective dynamics of small-world networks", is widely regarded as a seminal contribution to the interdisciplinary field of complex networks, whose applications reach from graph theory and statistical physics to sociology, business, epidemiology, and neuroscience. As one measure of its importance, it was the most highly cited article about networks between 1998 and 2008, and the sixth most highly cited paper in all of physics.
Strogatz's writing includes the 1994 textbook Nonlinear Dynamics and Chaos, two popular books, and frequent newspaper articles. His most recent book, published in 2009, was The Calculus of Friendship, called "a genuine tearjerker" and "part biography, part autobiography and part off-the-beaten-path guide to calculus". His trade book Sync was chosen as a Best Book of 2003 by Discover Magazine. Strogatz also filmed a series of lectures on chaos theory for the Teaching Company, released in 2008, and, in late January 2010, Strogatz began writing a weekly column on mathematics in The New York Times. These columns, along with many others penned by Strogatz, will appear in a book slated for release in 2012. The New York Times columns have been described as "must reads for entrepreneurs and executives who grasp that mathematics is now the lingua franca of serious business analysis. *Wik 

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1965 Kate Adebola Okikiolu (born 1965) is a British mathematician.She is known for her work with elliptic differential operators as well as her work with inner-city children.

Okikiolu was born in 1965 in England. Her father was George Olatokunbo Okikiolu, a renowned Nigerian mathematician and the most published black mathematician on record. Her British mother was a high school mathematics teacher. Okikiolu received a B.A. in mathematics from Cambridge University in 1987. In 1991 she earned her Ph.D. in mathematics from the University of California at Los Angeles, for her thesis The Analogue of the Strong Szego Limit Theorem on the Torus and the 3-Sphere.

Okikiolu was an instructor and later assistant professor at Princeton University from 1993 to 1995. She then worked as a visiting assistant professor at the Massachusetts Institute of Technology and joined the faculty at the University of California at San Diego in 1995. In 2011 she joined the Mathematics Department at Johns Hopkins University.

She was an invited speaker at the 1996 meeting of the Association of Women in Mathematics. She also delivered the Claytor-Woodard lecture at the 2002 meeting of the National Association of Mathematicians, an organization for African-American mathematicians.

In 1997, Okikiolu won a Sloan Research Fellowship, becoming the first black recipient of this fellowship. In 1997 she also was awarded a Presidential Early Career Award for Scientists and Engineers for both her mathematical research and her development of mathematics curricula for inner-city school children. This award is given to only 60 scientists and engineers each year and has a prize of $500,000.*Wik

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DEATHS

1822 Jean Robert Argand, (July 18, 1768 – August 13, 1822) Argand Diagrams, the method of drawing complex numbers as vectors on a coordinate plane, are named for him, as an amateur mathematician he described them in a paper in 1806. A similar method, although less complete, had been suggested as early as 120 years before by John Wallis, and developed extensively by Casper Wessel(1745-1818), a Norwegian surveyor. (Actually, at the time Wessel lived, the area where he was born was a part of Denmark. Norway became an independent government in 1905 after years of domination by Denmark and Sweden.) It may be that even after these multiple discoveries, the method was unknown to Gauss and he had to rediscover it for himself in 1831 although it has been suggested that Gauss may have discovered the idea as early as Wessel. Some parts of his Demonstratio Nova would seem almost miraculously derived without a knowledge of the ideas of the geometry of complex numbers.
Wessel's paper was published in Danish, and was not circulated in the languages more common to mathematics at that time. It was not until 1895 that his paper came to the attention of the mathematical community, long after the name Argand Diagram had stuck. Incredibly, there were at least three more individuals who may have independently discovered and written on the same idea; Abbe Bruee, C. V. Mourney, and John Warren.
Argand's Book, Essai sur une maniere de representer les quantities imaginaires dans les constructions geometriques, might have suffered the same fate as Wessel except for an unusual chain of events. I give here the version as presented by Michael Crowe in his A History of Vector Analysis

In 1813 J. F. Francais published a short memoir in volume IV of Gergonne's Annales de mathematiques in which Francais presented the geometrical representation of complex numbers. At the conclusion of his paper Francais stated that the fundamental ideas in his paper were not his own, he had found them in a letter written by Legendre to his (Francis') brother who had died. In this letter Legendre discussed the ideas of an unnamed mathematician. Francis added that he hoped this mathematician would make himself known and publish his results.
The unnamed mathematician had in fact already published his ideas, for Legendre's friend was Jean Robert Argand. Hearing of Francais' paper, Argand immediately sent a communication to Gergonne in which he identified himself as the mathematician in Legendre's letter, called attention to his book, summarized its contents, and finally presented an (unsuccessful) attempt to extend his system to three dimensions.

Even with so much interest and attention to the geometry of complex numbers, it was not until Gauss published a short work on the ideas that they became popular.
Translations of both Wallis' and Wessel's papers on the imaginaries can be found in A Sourcebook of Mathematics by David Eugene Smith. (*pb)

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1882 Logician William Stanley Jevons died (1 September 1835 – 13 August 1882) . He was a British economist and logician.
Irving Fisher described his book The Theory of Political Economy (1871) as beginning the mathematical method in economics. It made the case that economics as a science concerned with quantities is necessarily mathematical. In so doing, it expounded upon the "final" (marginal) utility theory of value. Jevons' work, along with similar discoveries made by Carl Menger in Vienna (1871) and by Léon Walras in Switzerland (1874), marked the opening of a new period in the history of economic thought. Jevons' contribution to the marginal revolution in economics in the late 19th century established his reputation as a leading political economist and logician of the time. *Wik

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1884 Rufus Porter (May 1, 1792 – August 13, 1884) was an American painter, inventor, and founder of Scientific American magazine.  He put out the first issue of Scientific American on 28 Aug 1845, but sold that business 10 months later to Orson Munn and Alfred Ely Beach. He editted it for one more year. 

As an inventor, he had little business sense, but held over 100 patents, including a fire alarm, signal telegraph, fog whistle, and a washing machine. He sold his patent for a revolving rifle to Samuel Colt for $100 in 1844. He had an interest in painting portraits, and in 1820 built a camera obscura. From 1820, he became interested in the hot-air balloon. He constructed his first model in 1833. Porter built and exhibited other models. By 1853, he demonstrated a 22-foot model airship which circled in the rotunda of the New York Merchant's Exchange. Ultimately, despite trying, he had no major success in aerial navigation.*TIS

Rufus Porter advertisement for his 1849 New York to California transport

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1907 Hermann Karl Vogel (April 3, 1841 – August 13, 1907) German astronomer who discovered spectroscopic binaries (double-star systems that are too close for the individual stars to be discerned by any telescope but, through the analysis of their light, have been found to be two individual stars rapidly revolving around one another). He pioneered the study of light from distant stars, and introduced the use of photography in this field.*TIS

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1910 Florence Nightingale​ died; (May 12, 1820 – August 13, 1910) She is best remembered for her work as a nurse during the Crimean War​ and her contribution towards the reform of the sanitary conditions in military field hospitals. However, what is less well known about this amazing woman is her love of mathematics, especially statistics, and how this love played an important part in her life's work. *SAU Florence Nightingale had exhibited a gift for mathematics from an early age and excelled in the subject under the tutorship of her father. Later, Nightingale became a pioneer in the visual presentation of information and statistical graphics. Among other things she used the pie chart, which had first been developed by William Playfair in 1801. While taken for granted now, it was at the time a relatively novel method of presenting data.
Indeed, Nightingale is described as "a true pioneer in the graphical representation of statistics", and is credited with developing a form of the pie chart now known as the polar area diagram (This diagram, commonly known as the Nightingale rose, was created in collaboration with medical statistician William Farr, one of the most significant influences on medical statistics in the 19th century.), or occasionally the Nightingale rose diagram, equivalent to a modern circular histogram, in order to illustrate seasonal sources of patient mortality in the military field hospital she managed. Nightingale called a compilation of such diagrams a "coxcomb", but later that term has frequently been used for the individual diagrams. She made extensive use of coxcombs to present reports on the nature and magnitude of the conditions of medical care in the Crimean War to Members of Parliament and civil servants who would have been unlikely to read or understand traditional statistical reports.*Wik

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1957  Fredrik (Carl Mülertz) Størmer ( 3 Sep 1874,13 Aug 1957  ) was a Norwegian geophysicist and mathematician who developed a mathematical theory of auroral phenomena. An aurora is the light emitted by energetic protons and electrons at the top of Earth's atmosphere when they come in contact with solar wind particles. He also contributed both important photographic observations and mathematical data to the understanding of the polar aurora, of stratospheric and mesospheric clouds, and of the structure of the ionosphere. The discovery of the Van Allen Radiation Belts by James Van Allen confirmed with surprising accuracy Størmer's theoretical analysis of solar charged particle trajectories in Earth's magnetic field. TiS

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1968 Subbaramiah Minakshisundaram (12 October 1913 - 13 August 1968), also known as Minakshi or SMS, was an Indian mathematician who worked on partial differential equations and heat kernels. In 1946, he worked at the Institute for Advanced Study in Princeton, America, where he met Åke Pleijel. In 1949, the two wrote a paper together called, Some properties of the eigenfunctions of the Laplace-operator on Riemannian manifolds, in which they introduced the Minakshisundaram-Pleijel zeta function.

On the 13th of August 1968, Subbaramiah suffered a heart attack and died at the age of 55.

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1968 Oystein Ore, (7 October 1899 in Oslo, Norway – 13 August 1968 in Oslo) Ore is known for his work in ring theory, Galois connections, and most of all, graph theory. His early work was on algebraic number fields, how to decompose the ideal generated by a prime number into prime ideals. He then worked on noncommutative rings, proving his celebrated theorem on embedding a domain into a division ring. He then examined polynomial rings over skew fields, and attempted to extend his work on factorisation to non-commutative rings.
In 1930 the Collected Works of Richard Dedekind were published in three volumes, jointly edited by Ore and Emmy Noether. He then turned his attention to lattice theory becoming, together with Garrett Birkhoff, one of the two founders of American expertise in the subject. Ore's early work on lattice theory led him to the study of equivalence and closure relations, Galois connections, and finally to graph theory, which occupied him to the end of his life. Ore had a lively interest in the history of mathematics, and was an unusually able author of books for laypeople, such as his biographies of Cardano and Niels Henrik Abel.*Wik

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2008 Henri Cartan (July 8, 1904 – August 13, 2008)is known for work in algebraic topology, in particular on cohomology operations, the method of "killing homotopy groups", and group cohomology. His seminar in Paris in the years after 1945 covered ground on several complex variables, sheaf theory, spectral sequences and homological algebra, in a way that deeply influenced Jean-Pierre Serre, Armand Borel, Alexander Grothendieck and Frank Adams, amongst others of the leading lights of the younger generation. The number of his official students was small, but includes Adrien Douady, Roger Godement, Max Karoubi, Jean-Louis Koszul, Jean-Pierre Serre and René Thom.
Cartan also was a founding member of the Bourbaki group and one of its most active participants. His book with Samuel Eilenberg Homological Algebra (1956) was an important text, treating the subject with a moderate level of abstraction and category theory.*Wik

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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

On This Day in Math - August 12

 

I belong to those theoreticians who know by direct observation what it means to make a measurement. Methinks it were better if there were more of them.
~Erwin Schrodinger

The 224th day of the year; 224 is the sum of the cubes of 4 consecutive integers:
224 = 2³ + 3³ + 4³ + 5³ and also 2³ + 6³

Cool thing about 224: 224 = 23+45+67+89 *Derek Orr ‏@Derektionary

Every number smaller than 224 can be expressed as the sum of distinct divisors of 224.

224 = 2^5 x 7. With so many factors of two, it has lots of representations as the difference of two squares. 224 = 57^2 - 55^2 = 30^2 - 26^2 = 15^2 - 1^2

See More Math Facts for every Year Day here.

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EVENTS
1269 A letter written on this day (the date is questioned as Aug 6, 8, or 12th) by Master Peter de Maricourt (Perigrinus, Spanish for pilgrim or traveller)  (to a fellow named Sygerius of Foucaucourt,) indicates that he had a knowledge of magnetic polarity, knew that opposites attract, understood that splitting a bar magnet preserved two poles in each part, and was aware that a weaker magnet could have its polarity reversed by a stronger one.  *A history of physics in its elementary branches  By Florian Cajori

This letter was later included in his treatise "Epistola de Magnete" ("Letter on the Magnet"). Peregrinus’s Epistola represents one of the earliest examples of the experimental method in physics, more than 300 years before Gilbert's De Magnete (1600). His work shows how medieval natural philosophers were capable of real scientific insight, grounded in observation and experimentation.  Gilbert acknowledged his debt to Peregrinus and incorporated this thirteenth-century scientist's experiments on magnetism into his own treatise, called De magnete.  *PB notes

Pivoting compass needle in a 14th-century handcopy of Peter's Epistola de magnete (1269)

*Wik

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1654 Earliest known Solar Eclipse map, by Erhard Weigel. According to German historian of science Klaus-Dieter Herbst, this map of the total solar eclipse of August 12, 1654 was published by Erhard Weigel on the day before the eclipse! On the right is a reconstruction of the map using modern eclipse calculations and geographic information system software. The map applies an orthographic projection from the moon’s perspective at the time of greatest eclipse. *eclipse-maps.com

Pierre Gassendi produced an anonymous pamphlet attempting to reassure the people of Paris that a predicted eclipse of the sun on this day in 1654 would not lead to a disaster. He was not entirely successful as many of the inhabitants of Paris hid in their cellars on this day.  (Why anonymous? Was he worried about the possible effect if he was wrong?)

 There is an interesting painting at the Rijksmuseum,  a Dutch national museum dedicated to arts and history in Amsterdam,  showing the various ways people viewed this eclipse. On the left a man points to a basin with water. Two men view the eclipse with a mirror. Others look at the sun through a piece of glass. And the first view I've ever seen of the "man in the Sun".  (*John McCafferty)

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1755 19 year old Joseph Louis Lagrange sends a letter to Euler where he described his "method of variations" and work on isoperimetric problems. *Optimal Control and Forecasting Euler responded promptly,and with great fervor and the two began a long series of correspondence. "You seem to have brought the theory of maxima and minima almost to its highest degree of perfection." Euler also promoted the admission of Lagrange to the Berlin Academy.

Lagrange’s letter to Euler described a general method—what he called the “method of variations”—that allowed these kinds of problems to be solved more systematically. His work led to the formal foundations of the calculus of variations, providing a technique for finding functions that optimize functionals (expressions involving integrals of functions and their derivatives). Lagrange’s method was not just about solving specific problems—it changed the approach to mathematical optimization and laid groundwork for what we now call optimal control theory, which plays a key role in physics, economics, and engineering.

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1851 Today in 1851  Isaac Singer is granted a patent for his sewing machine. 

*the painter flynn@thepainterflynn

But Wait!!! There's More

 Elias Howe and Isaac Singer patented sewing machines in the 1840s and ’50s. Howe invented and patented the first practical sewing machine that used lock-stitching. This machine could produce 300 stitches per minute compared to a professional seamstress’s 40–50 stitches per minute but only in a straight line, a severe limitation. As sewing technology improved, garment factories were able to quickly and cheaply mass-produce fashionable clothing for the general population. The practical sewing machine was later available for home use, becoming a staple of self-reliance of the American family. In 1851 Singer designed an improved model that utilized Howe’s patented lock-stitch method and a new up-and-down motion mechanism. Howe was able to reestablish his rights in 1854 after a five-year legal battle against Singer and others, whereupon he received royalties on all U.S.-made sewing machines.

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1877 Asaph Hall discovered Deimos, outer satellite of Mars. It is named after Deimos, a figure representing dread or terror in Greek Mythology. The two moons of Mars, Phobos and Deimos, were found when American astronomer Hall identified them after a long search, although their existence had been a source of speculation before. The possibility of Martian moons had been speculated long before Hall's discovery. The astronomer Johannes Kepler (1571–1630) even predicted their number correctly, although with faulty logic: he wrote that since Jupiter had four known moons and Earth had one, it was only natural that Mars should have two.

Perhaps inspired by Kepler (and quoting Kepler's third law), Jonathan Swift's satire Gulliver's Travels (1726) refers to two moons in Part 3, Chapter 3 (the "Voyage to Laputa"), in which the astronomers of Laputa are described as having discovered two satellites of Mars orbiting at distances of 3 and 5 Martian diameters, and periods of 10 and 21.5 hours, respectively. The actual orbital distances and periods of Phobos and Deimos of 1.4 and 3.5 Martian diameters, and 7.6 and 30.3 hours, respectively.
Hall discovered Deimos on August 12, 1877 at about 07:48 UTC and Phobos on August 18, 1877, at the US Naval Observatory in Washington, D.C., at about 09:14 GMT (contemporary sources, using the pre-1925 astronomical convention that began the day at noon, give the time of discovery as August 11, 14:40 and August 17 16:06 Washington mean time respectively)*Wik
In the words of Asaph Hall, "Of the various names that have been proposed for these satellites, I have chosen those suggested by Mr Madan of Eton, England, viz: Deimos for the outer satellite; Phobos for the inner satellite. These are generally the names of the horses that draw the chariot of Mars. " *assorted

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1883 Fragmented Comet Nearly Hits The Earth: On 12th and 13th August 1883, an astronomer at a small observatory in Zacatecas in Mexico made an extraordinary observation. José Bonilla counted some 450 objects, each surrounded by a kind of mist, passing across the face of the Sun.  Today, Hector Manterola at the National Autonomous University of Mexico in Mexico City,  gave a different interpretation. He thinks Bonilla must have been seeing fragments of a comet that had recently broken up. This explains the 'misty' appearance of the pieces and why they were so close together. Manterola and co end their paper by spelling out just how close Earth may have come to catastrophe that day. They point out that Bonilla observed these objects for about three and a half hours over two days. This implies an average of 131 objects per hour and a total of 3275 objects in the time between observations.
Each fragment was at least as big as the one thought to have hit Tunguska. Manterola and co end with this: "So if they had collided with Earth we would have had 3275 Tunguska events in two days, probably an extinction event." *MIT Technology Review,  (Many question the interpretation)

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1949 On Aug. 12, 1949, time slowed briefly in London. Fifty starlings settled on Big Ben’s minute hand and delayed the striking of the hour by four and a half minutes. *Greg Ross, Futility Closet (A “murmuration” of starlings, as this phenomenon is known, must be one of the most magical, yet underrated, wildlife spectacles on display in winter. Impenetrable as the flock’s movements might seem to the human eye, the underlying maths is comparatively straightforward. Each bird strives to fly as close to its neighbors as possible, instantly copying any changes in speed or direction. As a result, tiny deviations by one bird are magnified and distorted by those surrounding it, creating rippling, swirling patterns. In other words, this is a classic case of mathematical chaos (larger shapes composed of infinitely varied smaller patterns). Whatever the science, however, it is difficult for the observer to think of it as anything other than some vast living entity. Until recently such sights were common over London. *Daniel Butler, Telegraph, 23 Feb 2009)

Big Ben is the nickname for the Great Bell of the Great Clock of Westminster, at the north end of the Palace of Westminster in London, England, but the name is frequently extended to refer also to the clock and the clock tower.

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 In 1960, the U.S. launched the first telecommunications satellite, Echo 1, from Cape Canaveral, packed in a Thor-Delta rocket. At the altitude for low Earth orbit, above almost all of the Earth's atmosphere, the satellite was deployed and inflated with gas at low pressure to form a 100-ft (30.5-m) diameter spherical balloon made of metallized Mylar, 0.5 mils (12.7-μm) thick. Thus it is known as a balloon satellite, as originally conceived by William J. O'Sullivan (26 Jan 1956). Its orbit was at about 1,000 miles (1600-km). It was merely passive, to reflect microwave signals between points on Earth, similar to the way the Moon reflects light while the Sun is below the horizon. A commemorative stamp was issued 15 Dec 1960. Echo 1 remained in orbit until 24 May 1968. Telstar 1 followed 10 Jul 1962 *TiS

*Linda Hall Org

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1961  Construction of the Berlin Wall began.  In the early morning hours of 13 August 1961 [Film 5.80 MB], temporary barriers were put up at the border separating the Soviet sector from West Berlin, and the asphalt and cobblestones on the connecting roads were ripped up. Police and transport police units, along with members of “workers’ militias,” stood guard and turned away all traffic at the sector boundaries. The SED leadership’s choice of a Sunday during the summer holiday season for its operation was probably no coincidence.

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1981  IBM introduces its Personal Computer (PC) also known as the IBM Model 5150, lending legitimacy to microprocessor-based computers. IBM's first PC ran with a 4.77 MHz Intel 8088 microprocessor and used Microsoft's MS-DOS operating system. In 1983, Compaq Computer Corp. released the first clone of the IBM PC, a machine embodying an identical copy of the PC architecture -- which IBM had made publicly available -- and begining the gradual decline of IBM's share of the personal computer market.

The PC architecture, based on Intel's x86 microprocessor family, continues to dominate desktop computing with over 85% of PCs using an x86-based CPU. *CHM

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1985 Celebration of the centenary of the International Statistical Institute in Amsterdam begins. It lasted until August 22. *VFR

The origins of the International Statistical Institute (ISI) can be traced back to a series of International Statistical Congresses, the first of which was convened by Adolphe Quetelet in 1853 in Brussels. 

The ISI was formally founded in 1885, during a meeting held to celebrate the Jubilee of the London Statistical Society. 

The initial 81 members were the elite of that era’s statisticians in government and academia. 

They established our first statutes, and our first half-century was a period of general stability. Major changes, such as a proposed affiliation in 1920 with the League of Nations, were resisted.

Adolphe Quetelet, ISI

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2014 BBC announces the first Female Fields Medal winner. An Iranian mathematician working in the US has become the first ever female winner of the celebrated Fields Medal. In a landmark hailed as "long overdue", Prof Maryam Mirzakhani was recognized for her work on complex geometry. Four of the medals were presented in Seoul at the International Congress of Mathematicians, *BBC

Four Fields medallists left to right Artur Avila, Martin Hairer (at back), Maryam Mirzakhani + epsilon (with her daughter) and Manjul Bhargava at the ICM 2014 in Seoul

Four Field's Medalist + epsilon

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2026 Next total solar eclipses in Europe, total in North of Spain shortly before sunset also in parts of Portugal.*NSEC Hoping to get my picture and post here It will be Europe's first total solar ewclipse in over 25 years.

The next total solar eclipse in the United States will occur on March 30, 2033 (in Alaska only), whereas the next total solar eclipse in the contiguous United States will occur on August 22, 2044.  OK, if you have to wait that long, here's a picture of an earlier Solar eclipse.  *PB notes 

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BIRTHS
1769 Johann Christian Martin Bartels (12 August 1769 – 7/20 December 1836) was a German mathematician. He was the tutor of Carl Friedrich Gauss in Brunswick and the educator of Lobachevsky at the University of Kazan. *Wik

In 1808 Nikolai Ivanovich Lobachevsky had the good fortune to study with Bartels at Kazan University not long after he took up his post there. Not only did Bartels assist Lobachevsky with his studies, but he also looked after his young student, supporting him when he got into trouble with the authorities (which happened quite often!) When Lobachevsky was due to graduate it was Bartels who spent three days lobbying the other professors to award him a Master's degree. The university authorities did not want to give Lobachevsky a degree at all because of his poor behaviour. Bartels won the argument and Lobachevsky was awarded a Master's Degree. After graduating in 1811, Lobachevsky remained in Kazan to study with Bartels who guided his reading of Gauss's Disquisitiones Arithmeticae Ⓣ and Laplace's Mécanique Céleste Ⓣ. In 1814 it was mainly due to Bartels that Lobachevsky was appointed as an assistant professor. We should note that Lobachevsky took Bartels' course on the History of Mathematics which, following Montucla, considered in detail Euclid's Elements and his theory of parallel lines. It was this course which made Lobachevsky think about non-euclidean geometry.*SAU

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1862 Jules Antoine Richard (12 August 1862 in Blet, Département Cher,- 14 October 1956) Richard worked mainly on the foundations of mathematics and geometry, relating to works by Hilbert, von Staudt and Méray.
Further according to Richard, it is the aim of science to explain the material universe. And although non-Euclidean geometry had not found any applications (Albert Einstein finished his general theory of relativity only in 1915), Richard already stated clairvoyantly:"One sees that having admitted the notion of angle, one is free to choose the notion of straight line in such a way that one or another of the three geometries is true." *Wik

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1887 Erwin Schrodinger, born (12 August 1887 – 4 January 1961). Austrian theoretical physicist who shared the 1933 Nobel Prize for Physics with the British physicist P.A.M. Dirac. Schrödinger took de Broglie's concept of atomic particles as having wave-like properties, and modified the earlier Bohr model of the atom to accommodate the wave nature of the electrons. This made a major contribution to the development of quantum mechanics. Schrödinger realized the possible orbits of an electron would be confined to those in which its matter waves close in an exact number of wavelengths. This condition, similar to a standing wave, would account for only certain orbits being possible, and none possible in between them. This provided an explanation for discrete lines in the spectrum of excited atoms. *

This cat doesn't like the odds.

TIS

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1897 Otto Struve (August 12, 1897 – April 6, 1963) Ukrainian-Russian-American astronomer who spent most of his life and his entire scientific career in the United States.
He was one of the few eminent astronomers in the pre-Space Age era to publicly express a belief that extraterrestrial intelligence was abundant, and so was an early advocate of the search for extraterrestrial life.
"An intrinsically improbable event may become highly probable if the number of events is very great. ... [I]t is probable that a good many of the billions of planets in the Milky Way support intelligent forms of life. To me this conclusion is of great philosophical interest. I believe that science has reached the point where it is necessary to take into account the action of intelligent beings, in addition to the classical laws of physics."
Struve received the Gold Medal of the Royal Astronomical Society (1944), the Bruce Medal (1948), the Henry Draper Medal (1949), and the Henry Norris Russell Lectureship of the American Astronomical Society (1957)
The crater Struve on the Moon (commemorating three of the Struve astronomers), Asteroid 2227 Otto Struve and the Otto Struve Telescope of McDonald Observatory are named in his honor. *TIA

He was a fourth generation astronomer, the great-grandson of Friedrich Struve. *TiS

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1908 Caryl Parker Haskins (August 12, 1908 to October 8, 2001) was a scientist, author, inventor, philanthropist, governmental adviser and pioneering entomologist in the study of ant biology. In the 1930s he was inspired by Alfred Lee Loomis to establish his own research facility. Along with Franklin S. Cooper, he founded the Haskins Laboratories, a private, non-profit research laboratory, in 1935. Affiliated with Harvard University, MIT, and Union College in Schenectady, NY, Haskins conducted research in microbiology, radiation physics, and other fields in Cambridge, MA and Schenectady. In 1939 Haskins Laboratories moved its center to New York City. Seymour Hutner joined the staff to set up a research program in microbiology, genetics, and nutrition. The descendant of this program is now part of Pace University in New York. In the 1940s Luigi Provasoli joined the Laboratories to set up a research program in marine biology which disbanded with his retirement in 1978. Since the 1950s, the main focus of the research of Haskins Laboratories has been on speech and its biological basis. The main facility of Haskins Laboratories moved to New Haven, Connecticut in 1970 where it entered into affiliation agreements with Yale University and the University of Connecticut. Haskins Laboratories continues to be a leading, multidisciplinary laboratory with an international scope that does pioneering work on the science of the spoken and written word.
Haskins served as President, Research Director, and Chairman of the Board of Haskins Laboratories, 1935-'87; Director, E.I. du Pont de Nemours, 1971-'81 and Research Professor, Union College, 1937-'55. In 1956, he was appointed to the Presidency of the Carnegie Institution of Washington, a position he held until 1971. He was also President of the Sigma Xi society in 1967-'68. He remained a Trustee of Carnegie Institution and of Haskins Laboratories, as well as Trustee Emeritus of the National Geographic Society until his death. He also continued his research on entomology, working with his wife, Edna Haskins, and other colleagues. *Wik

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1919 Eleanor Margaret Burbidge, née Peachey, FRS (August 12, 1919 Davenport, England - ) is a British-born American astrophysicist, noted for original research and holding many administrative posts, including director of the Royal Greenwich Observatory.
During her career, she served at the University of London Observatory, Yerkes Observatory of the University of Chicago, Cavendish Laboratory in Cambridge, England, the California Institute of Technology, and from 1979 to 1988 was first director of the Center for Astronomy and Space Sciences at the University of California at San Diego (UCSD), where she has worked since 1962.
After receiving her Ph.D. in 1943, she started to research galaxies by linking a spectrograph to telescopes. At the Yerkes Observatory in the USA her work involved studying B stars and galaxy structure.
In 1957, the B²FH group showed the famous result that all of the elements except the very lightest, are produced by nuclear processes inside stars. For this they received the Warner Prize in 1959. In her later research she was one of the first to measure the masses and rotation curves of galaxies and was one of the pioneers in the study of quasars.
At UCSD she also helped develop the faint object spectrograph in 1990 for the Hubble Space Telescope. Currently, she is a professor emeritus of physics at UCSD and continues to be active in research, such as engaging in non-standard cosmologies such as, intrinsic redshift.*Wik

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1926 Horace Chandler Davis (August 12, 1926 – September 24, 2022) was an American-Canadian mathematician, writer, educator, and political activist. an American-Canadian mathematician, writer, and educator.
He was born in Ithaca, New York, to parents Horace B. Davis and Marian R. Davis. In 1948 he married Natalie Zemon Davis; they have three children.
In 1950 he received a doctorate in mathematics from Harvard University.
His principal research investigations involve linear algebra and operator theory in Hilbert space. Furthermore he has made contributions to numerical analysis, geometry, and algebraic logic. He is one of the eponyms of the Davis–Kahan theorem and Bhatia–Davis inequality (along with Rajendra Bhatia). The Davis-Kahan-Weinberger dilation theorem is one of the landmark results in the dilation theory of Hilbert space operators and has found applications in many different areas. A PhD thesis titled "Backward Perturbation and Sensitivity Analysis of Structured Polynomial Eigenvalue Problem" is dedicated to this theorem. In total Chandler Davis has written around eighty research papers in mathematics.
He is currently one of the co-Editors-in-Chief of the Mathematical Intelligencer. In 2012 he became a fellow of the American Mathematical Society.

He began his writing career in Astounding Science Fiction in 1946. From 1946 through 1962 he produced a spate of science fiction stories, mostly published there. One of the earliest, published May 1946, was The Nightmare, later the lead story in A Treasury of Science Fiction, edited by Groff Conklin; it argued for a national policy of decentralizing industry to evade nuclear attacks by terrorists. He also issued the fanzine "Blitherings" in the 1940s.

Davis came from a radical family and has identified himself as a socialist and former member of the Communist Party of America.
Davis—along with two other professors, Mark Nickerson and Clement Markert—refused to cooperate with the House Unamerican Activities Committee and was subsequently dismissed from the University of Michigan. Davis was then sentenced to a six-month prison term where he was able to do some research. A paper from this era has the following acknowledgement:

"Research supported in part by the Federal Prison System. Opinions expressed in this paper are the author's and are not necessarily those of the Bureau of Prisons."

The Federal government released Davis from prison in 1960. After his release, Davis moved to Canada, where he currently resides. He began teaching at the University of Toronto. He has lived in Canada longer than he lived in the US.

In 1991, the University of Michigan Senate initiated the annual Davis, Markert, Nickerson Lecture on Academic and Intellectual Freedom. Recent speakers have included: Cass Sunstein (2008), Nadine Strossen (2007), Bill Keller (2006), Floyd Abrams (2005), and Noam Chomsky (2004). *Wik

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1930 Jacques Tits (12 August 1930 – 5 December 2021)  was a Belgian and French mathematician who works on group theory and geometry and who introduced Tits buildings, the Tits alternative, and the Tits group. Tits was an "honorary" member of the Nicolas Bourbaki group; as such, he helped popularize Harold Scott MacDonald Coxeter's work, introducing terms such as Coxeter number, Coxeter group, and Coxeter graph.
He received the Wolf Prize in Mathematics in 1993, the Cantor Medal from the Deutsche Mathematiker-Vereinigung (German Mathematical Society) in 1996, and the German distinction "Pour le Mérite". In 2008 he was awarded the Abel Prize, along with John Griggs Thompson, “for their profound achievements in algebra and in particular for shaping modern group theory." *Wik

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1933 James Ray Vanstone ( August 12, 1933 near Owen Sound, Ontario , Canada ; April 9, 2001 in Florida ) was a Canadian mathematician who worked on differential geometry and multilinear algebra, particularly in connection with relativity theory.

Vanstone studied at the University of Toronto with a bachelor's and master's degree and received his doctorate in 1959 from the University of Natal in South Africa under Hanno Rund ( Generalized Metric Differential Geometry ).  In 1959 he became lecturer , in 1961 assistant professor, in 1965 associate professor and in 1973 professor at the University of Toronto. He retired in 1995. He died of a heart attack in his winter residence in Florida.

With his colleagues in Toronto Stephen Halperin and Werner H. Greub, he wrote a three-volume textbook on differential geometry.

He was visiting professor and visiting scientist at Flinders University in Australia, the University of Western Australia in Perth , the ETH Zurich , the University of Arizona and the University of Mannheim and he was on the executive board of the Canadian Mathematical Society (CMS) from 1969 to 1972 and from 1981 to 1983. From 1965 to 1967 he was editor of the Bulletin of the CMS and from 1983 to 1988 of the Journal of the CMS.

 

He was married and had two daughters and two sons.*Wik

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DEATHS
1900 James Edward Keeler (September 10, 1857 – August 12, 1900) was an American astronomer who confirmed Maxwell's theory that the rings of Saturn were not solid (requiring uniform rotation), but composed of meteoric particles (with rotational velocity given by Kepler's 3rd law). His spectrogram of 9 Apr 1895 of the rings of Saturn showed the Doppler shift indicating variation of radial velocity along the slit. At the age of 21, he observed the solar eclipse of July, 1878, with the Naval Observatory expedition to Colorado. He directed the Allegheny Observatory (1891-8) and the Lick Observatory from 1898, where, working with the Crossley reflector, he observed large numbers of nebulae whose existence had never before been suspected. He died unexpectedly of a stroke, age 42.*TIS

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1901 Ernest de Jonquières (3 July 1820 Carpentras, France – 12 Aug 1901 Mousans-Sartoux, France) was a French naval officer who discovered many results in geometry. After his introduction to advanced mathematics by Chasles it is not surprising that his main interests were geometry throughout his life. He made many contributions many of them extending the work of Poncelet and Chasles. An early work, the treatise Mélanges de géométrie pure (1856) contains: an amplifications of Chasles' ideas on the geometric properties of an infinitely small movement of a free body in space; a commentary on Chasles' work on conic sections; the principle of homographic correspondence; and constructions relating to curves of the third order. In a final section de Jonquières presented a French translation of Maclaurin's work on curves. *SAU

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1928 Charles Chree, FRS (5 May 1860 – 12 August 1928) was a British physicist, an authority on terrestrial magnetism and atmospheric electricity, and for 32 years Superintendent of Kew Observatory.

Chree was born in Lintrathen, Forfarshire, Scotland on 5 May 1860, second son to Rev Charles Chree. He was educated at the Grammar School, Old Aberdeen, the University of Aberdeen where he graduated MA in 1879 and the University of Cambridge where he graduated as Sixth Wrangler (MA, 1883).

Chree was elected a Fellow of the Royal Society in 1897. 

He was awarded the James Watt medal by the Institution of Civil Engineers in 1905.

He was President of the Physical Society of London between 1908 and 1910.

Chree won the Royal Society Hughes Medal in 1919 "for his researches in terrestrial magnetism" and served as president of the Royal Meteorological Society from 1922 to 1923.

He was appointed Superintendent of Kew Observatory in 1893, a post he retained until 1925, a remarkably long period of 32 years. During his tenure of office he was responsible for testing thousands of chronometers, watches, thermometers and other scientific instruments, success in which tests gained the award of a "Kew Certificate".

Chree received degrees of D.Sc. from Cambridge in 1895 and LL.D. from Aberdeen in 1898.

The Chree Medal and Prize of the Institute of Physics was named for him. The awards were renamed in 2008.

He died on Sunday 12 August 1928 in Worthing, Sussex. He was unmarried.

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1989 William B. Shockley (February 13, 1910 – August 12, 1989) English-American engineer and teacher, co-winner (with John Bardeen and Walter H. Brattain) of the Nobel Prize for Physics in 1956 for their development of the transistor, a device that largely replaced the bulkier and less-efficient vacuum tube and ushered in the age of microminiature electronics. *TIS

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2004 Sir Godfrey Newbold Hounsfield (28 August 1919 – 12 August 2004) English electrical engineer who shared the 1979 Nobel Prize for Physiology or Medicine (with Allan Cormack) for creation of computerised axial tomography (CAT) scanners. He originated the idea during a country walk in 1967 when he realized that the contents of a box could be reconstructed by taking readings at all angles through it. He applied the concept for scanning the brain using hundreds of X-ray beams imaging cross-sections that were reconstructed as high-resolution graphics by a computer program handling complex algebraic calculations. By 1973 his CAT scanner could produce cross-section images of a brain in 4-1/2-min, invaluable for the diagnosis of brain diseases. He later built a larger machines able to make a full body scan. *TIS

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2007 Ralph Asher Alpher (February 3, 1921 – August 12, 2007) was an American cosmologist. Alpher's dissertation in 1948 dealt with a subject that came to be known as Big Bang nucleosynthesis. In a strange mathematical pun, his pre-publication of his thesis may have caused his independent role to have been minimized.
Although his name appears on the paper, Hans Bethe had no direct part in the development of the theory, although he later worked on related topics; Gamow added his name to make the author list Alpher, Bethe, Gamov, a pun on alpha, beta, gamma (α, β, γ), the first three letters of the Greek alphabet. Thus, Alpher's independent dissertation was first published on April 1, 1948 in the Physical Review with three authors. The humor engendered by the prodigious Gamow may at times have obscured the critical role Alpher played in developing the theory. This seminal paper was based on his dissertation (defended shortly thereafter).
With the award of the 2005 National Medal of Science, Alpher's original contributions (nucleosynthesis and the cosmic microwave background radiation predicition) to the modern big bang theory are beginning to receive due recognition. Neil deGrasse Tyson was instrumental in a NSF committee recommendation.
In 2005 Alpher was awarded the National Medal of Science. The citation for the award reads "For his unprecedented work in the areas of nucleosynthesis, for the prediction that universe expansion leaves behind background radiation, and for providing the model for the Big Bang theory." The medal was presented to his son Dr. Victor S. Alpher on July 27, 2007 by President George W. Bush, as his father could not travel to receive the award. Ralph Alpher died following an extended illness on August 12, 2007. He had been in failing health since falling and breaking his hip in February 2007. *Wik

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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