## Wednesday, 16 March 2016

### On This Day in Math - March 17

 *WolframAlpha

St. Patrick’s Day. The equation of the day is the four-leaved rose r = sin(2θ). Work on this curve was ﬁrst published by the Italian priest Guido Grandi in 1723. *VFR

The 77th day of the year; 77 is the only number less than 100 with a multiplicative persistence of 4. Can you find the next? (Multiply all the digits of a number n by each other, repeating with the product until a single digit is obtained. The number of steps required is known as the multiplicative persistence, and the final digit obtained is called the multiplicative digital root of n.)

772 is the smallest square number that can be the sum of consecutive squares greater than 1, $sum_{k=18}^{28}k^2 = 77^2$

The concatenation of all palindromes from one up to 77 is prime.

77 is equal to the sum of three consecutive squares, $4^2 + 5^2 + 6^2= 77$ and also the sum of the first 8 primes. *Prime Curios

EVENTS
1694 L’Hospital hires his former tutor Johann Bernoulli to “work on what I shall ask you ... and also to communicate to me your discoveries, with the request not to mention them to others.” The ﬁrst calculus text resulted in 1696. It contained the famous “L’Hospital’s rule,” which, we now know, is the work of Bernoulli. [Eves, Circles, 208◦] VFR
(Because L'Hospital is so often discredited by Intro Calculus teachers for his role, I wanted to add more detail in the hopes they will share a more enlightened presentation of his work.)
In a letter from March 17, 1694, l'Hôpital made the following proposal to Johann Bernoulli: in exchange for an annual payment of 300 Francs, Bernoulli would inform L'Hôpital of his latest mathematical discoveries, withholding them from correspondence with others, including Varignon. Bernoulli's immediate response has not been preserved, but he must have agreed soon, as the subsequent letters show. L'Hôpital may have felt fully justified in describing these results in his book, after acknowledging his debt to Leibniz and the Bernoulli brothers, "especially thle younger one" (Johann). Johann Bernoulli grew increasingly unhappy with the accolades bestowed on l'Hôpital's work and complained in private correspondence about being sidelined. After l'Hôpital's death, he publicly revealed their agreement and claimed credit for the statements and portions of the text of Analyse, which were supplied to l'Hôpital in letters. Over a period of many years, Bernoulli made progressively stronger allegations about his role in the writing of Analyse, culminating in the publication of his old work on integral calculus in 1742: he remarked that this is a continuation of his old lectures on differential calculus, which he discarded since l'Hôpital had already included them in his famous book. For a long time, these claims were not regarded as credible by many historians of mathematics, because l'Hôpital's mathematical talent was not in doubt, while Bernoulli was involved in several other priority disputes. For example, both H. G. Zeuthen and Moritz Cantor, writing at the cusp of the 20th century, dismissed Bernoulli's claims on these grounds. However, in 1921 Paul Schafheitlin discovered a manuscript of Bernoulli's lectures on differential calculus from 1691–1692 in the Basel University library. The text showed remarkable similarities to l'Hôpital's writing, substantiating Bernoulli's account of the book's origin.
L'Hôpital's pedagogical brilliance in arranging and presenting the material remains universally recognized. Regardless of the exact authorship (one should also note that the book was first published anonymously), Analyse was remarkably successful in popularizing the ideas of differential calculus stemming from Leibniz. *Wik

1856 Joseph Lacomme, a French well-sinker, and illiterate laborer who asked a mathematics professor to tell him the amount of stone needed to cover the bottom of a circular cistern, and unsatisfied with the reply that it would be impossible to tell him exactly, set about experimenting and determined the "True" ratio of the circumference to diameter of a circle. Teaching himself arithmetic and writing to confirm the results he obtained by experimentation he shared his computation with the commissioner of police in Paris. The commissioner introduced Lacomme to his father, who presented him to the Academie and after consideration by a committee, Lacomme received a silver medal from the French Academie for his discovery of the true ratio of diameter to circumfrence of a circle. He would later receive three more medals from other societies for his value of 3 1/8. *Augustus DeMorgan, A Budget of Paradoxes, pgs 46-47
The Kindle edition of A Budget of Paradoxes, Volume I is currently free.

1889 A political cartoon in the New York World lampooned President Benjamin Harrison's advisers and cabinet members showing the group sitting around playing the game, Pigs in Clover which had recently been invented by Charles Martin Crandall. The caption read "Will Mr. Harrison be able to get all these hungry pigs in the official pen?"
The events which prompted the story were related in a New York Tribune's March 13, 1889 issue:
Senator William M. Evarts purchased one from a street fakir in order to get rid of him. He took the puzzle home and worked it for hours. The following morning he brought it with him into senate chambers where Senator George Graham Vest stopped by Evarts' desk, borrowed the puzzle and took it to a cloak room. Soon thereafter he was joined by Senators James L. Pugh, James B. Eustis, Edward C. Walthall and John E. Kenna. A page was sent out to buy five of the puzzles and upon his return, the group engaged in a "pig driving contest". About 30 minutes later, Senator Vest announced his accomplishment of driving the last pig in the pen.
*Antique Toy Collectors of America *Wik (Will negotiate trade of off-spring or other not-to-valuable property for a imageof this cartoon. )

1905 Albert Einstein submits his paper "On a Heuristic Point of View Concerning the Production and Transformation of Light" to the Annalen der Physik. In this revolutionary paper he proposes that light can be conceived both as waves and as discrete quanta (later to be called photons) which are localized at points in space. This paper was the primary reason for his Nobel Prize.

1914 Ramanujan boarded the S.S. Nevasa on 17 March 1914, and at 10 o'clock in the morning, the ship departed from Madras. He arrived in London on 14 April, with E. H. Neville waiting for him with a car. A tweet from @amanicdroid pointed out that, "this was significant for him culturally as a high-caste Hindu as crossing the ocean was taboo. "

1941 The National Gallery of Art opened its doors on the mall in Washington D.C. The gallery was a gift of Pittsburgh ﬁnancier Andrew W. Mellon. His personal collection of 152 masterpieces has grown to 80,000 priceless works today. Today it is a good place to see some mathematics, from the lack of perspective in its medieval works, to The Lady in the Red Hat with its camera obscura technique, to the geometric starkness of the East Wing. *VFR

1988 Apple Computer sues Microsoft Corporation for copyright infringement in its Windows design. After Apple developed a highly successful graphical user interface for its Macintosh computer released in 1984, Microsoft fought back with an operating system of its own, called "Windows." In 1995, Apple lost the lawsuit, in which it claimed that the similarities of the Windows and Macintosh environments extended too far.*CHM

2013 Flash of Meteor hitting moon visible to naked eye. Scientists monitoring the moon for meteorite impacts spotted the biggest impact event to date: a space rock the size of a basketball slammed into the lunar surface at a speed of 56,000 miles per hour (90,000 km/hr), creating a new crater around 20 meters wide.
The flash was impressive — it unleashed the equivalent energy of 5 tons of TNT exploding and would have been visible to anyone casually looking at the moon, no telescope required. *NASA The impact hit almost exactly on a crater already present. This animated gif shows before and after shots of the site.

BIRTHS
1733 Carsten Niebuhr(March 17, 1733 Lüdingworth – April 26, 1815 Meldorf, Dithmarschen), German mathematician, cartographer, and explorer in the service of Denmark. Niebuhr's first book, Beschreibung von Arabien, was published in Copenhagen in 1772, the Danish government providing subsidies for the engraving and printing of its numerous illustrations. This was followed in 1774 and 1778 by the two volumes of Niebuhr's Reisebeschreibung von Arabien und anderen umliegenden Ländern. These works (particularly the one published in 1778), and most specifically the accurate copies of the cuneiform inscriptions found at Persepolis, were to prove to be extremely important to the decipherment of cuneiform writing. Before Niebuhr's publication, cuneiform inscriptions were often thought to be merely decorations and embellishments, and no accurate decipherments or translations had been made up to that point. Niebuhr demonstrated that the three trilingual inscriptions found at Persepolis were in fact three distinct forms of cuneiform writing (which he termed Class I, Class II, and Class III) to be read from left to right. His accurate copies of the trilingual inscriptions gave Orientalists the key finally crack the cuneiform code, leading to the discovery of Old Persian, Akkadian, and Sumerian. *Wik

1876 Ernest Benjamin Esclangon (March 17, 1876 – January 28, 1954) was a French astronomer and mathematician. During World War I, he worked on ballistics and developed a novel method for precisely locating enemy artillery. When a gun is fired, it initiates a spherical shock wave but the projectile also generates a conical wave. By using the sound of distant guns to compare the two waves, Escaglon was able to make accurate predictions of gun locations.
After the armistice, Esclangon became director of the Strasbourg Observatory and professor of astronomy at the university the following year. In 1929, he was appointed director of the Paris Observatory and of the International Time Bureau, and elected to the Bureau des Longitudes in 1932. In 1933, he initiated the talking clock telephone service in France. He was elected to the Académie des Sciences in 1939.
Serving as director of the Paris Observatory throughout World War II and the German occupation of Paris, he retired in 1944. He died in Eyrenville, France.
The binary asteroid 1509 Esclangona and the lunar crater Esclangon are named after him.*Wik

1915 Wolfgang Döblin, known in France as Vincent Doblin, (17 March 1915 – 21 June 1940) was a German-French mathematician. Wolfgang was the son of the Jewish-German novelist, Alfred Döblin. His family escaped from Nazi Germany to France where he became a citizen. Studying probability theory at the Institute Henri Poincaré under Fréchet, he quickly made a name for himself as a gifted theorist. He became a doctor at age 23. Drafted in November 1938, after refusing to be exempted of military service, he had to stay in the active Army when World War II broke out in 1939, and was quartered at Givet, in the Ardennes, as a telephone operator. There, he wrote down his latest work on the Chapman-Kolmogorov equation, and sent this as a "pli cacheté" (sealed envelope) to the French Academy of Sciences. His company, sent to the sector of the Saare on the ligne Maginot in April 1940, was caught in the German attack in the Ardennes in May, withdrew to the Vosges, and capitulated on June 22, 1940. On June 21, Doblin had committed suicide in Housseras (a small village near to Epinal), at the moment where German troops came in sight of the place. In his last moments, he burned his mathematical notes.
The sealed envelope was opened in 2000, revealing that Döblin was ahead of his time in the development of the theory of Markov processes. In recognition of his results, Itō's lemma is now referred to as the Itō–Doblin Theorem.
His life was recently the subject of a movie by Agnes Handwerk and Harrie Willems, A Mathematician Rediscovered. *Wik

1972 Kalpana Chawla (March 17, 1962 – February 1, 2003) was an American astronaut and the first indian woman in space. She first flew on Space Shuttle Columbia in 1997 as a mission specialist and primary robotic arm operator. In 2003, Chawla was one of the seven crew members killed in the Space Shuttle Columbia disaster. *Wik

DEATHS
1652 Benjamin Bramer (15 Feb 1588 in Felsberg, Germany - 17 March 1652 in Ziegenhain, Germany) was an architect who published work on the calculation of sines. He was tutored by Jost Bürgi in a wide range of subjects but it was mathematics that he loved and he passed this love on to Bramer. (Bramer married Bürgi's daughter) Bramer followed Alberti (1435), Dürer (1525) and Bürgi (1604) when in 1630 he constructed a device that enabled one to draw accurate geometric perspective. The instrument had been described in a 1617 publication Trigonometrica planorum mechanica oder Unterricht und Beschreibung eines neuen und sehr bequemen geometrischen Instrumentes zu allerhand Abmessung. Bramer designed several other mathematical instruments, for example a description of the pantograph appears in the same 1617 publication. The instrument is designed to copy a geometric shape and reproduce it at a reduced or enlarged scale. It consists of an assemblage of rigid bars adjustably joined by pin joints; as the point of one bar is moved over the outline to be duplicated, the motion is translated to a point on another bar, which makes the desired copy according to the predetermined scale. Bramer has not been recognised as the inventor of the pantograph, this distinction going to the Jesuit Christoph Scheiner who describes a similar instrument in his 1631 publication Pantographice seu acre delineandi res quaslibet by parallelogrammum linear seu cavum mechanicum, mobile. Although Scheiner's publication did much to spread knowledge of the pantograph, the instrument he describes is technically inferior to the earlier instrument as described by Bramer. *SAU

1767 George Parker (born 1697, 17 Mar 1764) [2nd Earl of Macclesfield] English astronomer who was instrumental in changing the computation of current chronology, subsequently enacted as the British Calendar Act of 1751 which co-authored and co-promoted. (Shortly thereafter, he was elected President of the Royal Society, 1752-1764). Since 1582, the new calendar of Pope Gregory XIII had been used in most of Europe. In England the new calendar was rejected as popish. By 1750, the old calendar became 11 days out of sequence with the position of the Earth in its orbit due to its lack of leap years. Parker was assisted in these calculations by his friend James Bradley, the astronomer royal, and received influential support from Philip Dormer Stanhope, 4th Earl of Chesterfield. *TIS

1771 Chester Moor Hall, (Dec. 9, 1703, Leigh, Essex, Eng.— March 17, 1771, Sutton, Surrey), English jurist and mathematician who invented the achromatic lens, which he utilized in building the first refracting telescope free from chromatic aberration (colour distortion).
Convinced from study of the human eye that achromatic lenses were feasible, Hall experimented with different kinds of glass until he found (1729) a combination of crown glass and flint glass that met his requirements. In 1733 he built several telescopes with apertures of 2.5 inches (6.5 cm) and focal lengths of 20 inches (50 cm).*britannica.com

1782 Daniel Bernoulli (29 January 1700 (8 Feb new style), 8 March 1782) was a Dutch-Swiss mathematician and was one of the many prominent mathematicians in the Bernoulli family. He is particularly remembered for his applications of mathematics to mechanics, especially fluid mechanics, and for his pioneering work in probability and statistics. Bernoulli's work is still studied at length by many schools of science throughout the world. The son of Johann Bernoulli (one of the "early developers" of calculus), nephew of Jakob Bernoulli (who "was the first to discover the theory of probability"), and older brother of Johann II, He is said to have had a bad relationship with his father. Upon both of them entering and tying for first place in a scientific contest at the University of Paris, Johann, unable to bear the "shame" of being compared as Daniel's equal, banned Daniel from his house. Johann Bernoulli also plagiarized some key ideas from Daniel's book Hydrodynamica in his own book Hydraulica which he backdated to before Hydrodynamica. Despite Daniel's attempts at reconciliation, his father carried the grudge until his death.
He was a contemporary and close friend of Leonhard Euler. He went to St. Petersburg in 1724 as professor of mathematics, but was unhappy there, and a temporary illness in 1733 gave him an excuse for leaving. He returned to the University of Basel, where he successively held the chairs of medicine, metaphysics and natural philosophy until his death.
In May, 1750 he was elected a Fellow of the Royal Society. He was also the author in 1738 of Specimen theoriae novae de mensura sortis (Exposition of a New Theory on the Measurement of Risk), in which the St. Petersburg paradox was the base of the economic theory of risk aversion, risk premium and utility.
One of the earliest attempts to analyze a statistical problem involving censored data was Bernoulli's 1766 analysis of smallpox morbidity and mortality data to demonstrate the efficacy of vaccination. He is the earliest writer who attempted to formulate a kinetic theory of gases, and he applied the idea to explain Boyle's law. He worked with Euler on elasticity and the development of the Euler-Bernoulli beam equation. *Wik

1846 Friedrich Wilhelm Bessel (22 Jul 1784, 17 Mar 1846 at age 61). He is noted for the special class of functions that have become an indispensable tool in applied mathematics. This, like all of his mathematical work, was motivated by his work in astronomy. *VFR In 1809, at the age of 26, Bessel was appointed director of Frederick William III of Prussia's new Königsberg Observatory and professor of astronomy, where he spent the rest of his career. His monumental task was determining the positions and proper motions for about 50,000 stars, which allowed the first accurate determination of interstellar distances. Bessel's work in determining the constants of precession, nutation and aberration won him further honors. Other than the sun, he was the first to measure the distance of a star, by parallax, of 61 Cygni (1838). In mathematical analysis, he is known for his Bessel function. *TIS

 Doppler Monument at Salzburg's airport

1853 Christian Doppler (29 Nov 1803; 17 Mar 1853) Austrian physicist who first described how the observed frequency of light and sound waves is affected by the relative motion of the source and the detector, known as the Doppler effect. In 1845, to test his hypothesis, Doppler used two sets of trumpeters: one set stationary at a train station and one set moving on an open train car, all holding the same note. As the train passed the station, it was obvious that the frequency of the notes from the two groups didn't match. Sound waves would have a higher frequency if the source was moving toward the observer and a lower frequency if the source was moving away from the observer. Edwin Hubble used the Doppler effect of light from distant stars to determine that the universe is expanding.*TIS

1922 Heinrich Suter (4 January 1848, Hedingen near Zurich, Switzerland – 17 March 1922) was a historian of science specializing in Islamic mathematics and astronomy.*Wik

1956 Irène Joliot-Curie (12 Sep 1897; 17 Mar 1956) French physicist and physical chemist, wife of Frédéric Joliot-Curie, who shared the 1935 Nobel Prize for Chemistry "in recognition of their synthesis of new radioactive elements." For example, in their joint research they discovered that aluminium atoms exposed to alpha rays transmuted to radioactive phosphorus atoms. She was the daughter of Nobel Prize winners Pierre and Marie Curie. From 1946, she was director of the Radium Institute, Paris, founded by her mother. She died of leukemia, like her mother, resulting from radiation exposure during research.*TIS

1956 Henry Frederick Baker FRS (3 July 1866 – 17 March 1956) was a British mathematician, working mainly in algebraic geometry, but also remembered for contributions to partial differential equations (related to what would become known as solitons), and Lie groups.
Baker was born in Cambridge, England and educated at The Perse School before winning a scholarship to St John's College, Cambridge in October 1884. Baker graduated as Senior Wrangler in 1887, bracketed with 3 others.
Baker was elected Fellow of St John's in 1888 where he remained for 68 years.
In June, 1898 he was elected a Fellow of the Royal Society. In 1911, he gave the presidential address to the London Mathematical Society.
In January 1914 he was appointed Lowndean Professor of Astronomy. *Wik
In the 1920's and 30's before the war Baker's graduate students would meet at what they called Professor Baker’s "Tea Party". They met each Saturday to discuss the areas of research in which they were working. It was to one of these meetings that a young Donald Coxeter brought his "Aunt Alice", the 69 year old Alicia Boole to co-present on the subject of Polytopes in higher dimensions.

1962 Wilhelm Blaschke (13 Sep 1885; 17 Mar 1962) German mathematician whose major contributions to geometry concerned kinematics and differential geometry. Kinetic mapping (important later in the axiomatic foundations of various geometries) he both discovered and established it as a tool in kinematics. He also initiated topological differential geometry (the study of invariant differentiable mappings)*TIS

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