Tuesday 12 March 2024

On This Day in Math - March 12


Sidereus Nuncius *Wik

If my impressions are correct, our educational planing mill cuts down all the knots of genius, and reduces the best of the men who go through it to much the same standard.
~Simon Newcomb,

The 71st day of the year;71= 5041 = 7! +1! *Prime Curios
 4! +1, and 5!+1 are also squares but not the factorial of the digits. Whether there is a larger value of n for which n! + 1 is a perfect square is still an open question, called the Brocard problem after Henri Brocard who asked it in 1876. It has been proven that no other numbers exist less than 109*Professor Stewart's Incredible Numbers  

And  from Pickover, 71 is the largest known prime, p, such that p2 is the sum of distinct factorials.

and too good to leave out, 71 is the only two-digit number n such that (nn-n!)/n is prime. *Tanya Khovanova, Number Gossip (Be the first on your block to find a three digit example.)

713=357,911 where the digits are the odd numbers 3 to 11 in order * ‏@Mario_Livio

713 is also the only cube of a 2-digit number that ends in 11.  There is only one 1digit cubed that ends in 1, and only one three digit cubed that ends in 111(Don't just sit there children, go find them!). Could there be a four digit cube that ends in 1111

71 is the largest prime p that humans will ever discover such that 2p doesn't contain the digit 9. *Cliff Pickover (I do wonder how they go about proving such facts.)


1610 Galileo dedicates his Sidereus nuncius to Grandduke Cosmos II. According to Albert Van Helden in his introduction to his translation, "The Dedicatory letter of Sidereus nuncius is dated 12 March 1610, and on the next day Galileo sent an advance, unbound copy, accompanied by a letter, to the Tuscan court."
Thony Christie sent this translation from page 33 of the same book, "Written in Padua on the fourth day before the Ides of March 1610. Your Highnesses's most loyal servant, Galileo Galilei."  Laura Snyder points out that this was, " the first book featuring drawings based on observations with a telescope."

1615 Castelli reported to Galileo that the Archbishop of Pisa had demanded he relinquish the letter Galileo had sent him which were the foundation of a heresy charge to the church office by Nicolo Lorini. Galileo had tried to influence Cardinal Ballarmine with a modification of the original he had sent via Peiro Dini in February. *Brody & Brody, The Science Class You Wish You Had

1763 Jerome Lelande records a visit with Jean-Charles Borda in Dunkirk while on his way to visit England. "Mr Borda, came to dine with me at Mr Tully’s, the Irish doctor in Dunkirk, who told me he had very carefully observed the relationship of the moon with diseases.
From the top of the tower in Dunkirk you can see the Thames. There is a telescope at the top.
Mr Borda experiments on the resistance of air and water. He found it as the square of the speed, but not as the square of the sine of the angle of incidence; this varies a lot according to the shape of the bodies. (in 1762 he showed that a spherical projectile experiences only half the air resistance of a cylindrical object of the same diameter.) *Richard Watkins  
Borda formulated a ranked preferential voting system that is referred to as the Borda count. 

1832 Faraday wrote a secret letter predicting the existence of electromagnetic waves. Faraday submitted his letter to the Secretary of the Royal Society of London where it lay for over a century in a strong box. The letter only came to light when it was opened by Sir William Bragg on June 24, 1937.
Royal Institution March 12, 1832
Certain of the results of the investigations which are embodied in the two papers entitled ‘Experimental Researches in Electricity’ lately read to the Royal Society, and the views arising therefrom, in connexion with other views and experiments lead me to believe that magnetic action is progressive, and requires time, i.e. that when a magnet acts upon a distant magnet or piece of iron, the influencing cause (which I may for the moment call magnetism) proceeds gradually from the magnetic bodies, and requires time for its transmission, which will probably be found to be very sensible.
I think also, that I see reason for supposing that electric induction (of tension) is also performed in a similar progressive way. I am inclined to compare the diffusion of magnetic forces from a magnetic pole to the vibrations upon the surface of disturbed water, or those of air in the phenomenon of sound; i.e. I am inclined to think the vibratory theory will apply to these phenomena as it does to sound, and most probably to light. By analogy, I think it may possibly apply to the phenomenon of induction of electricity of tension also. These views I wish to work out experimentally; but as much of my time is engaged in the duties of my office, and as the experiments will therefore be prolonged, and may in their course be subject to the observation of others, I wish, by depositing this paper in the care of the Royal Society, to take possession as it were of a certain date; and so have right, if they are confirmed by experiment, to claim credit for the views at that date; at which time as far as I know, no one is conscious of or can claim them but myself.
M. Faraday
As many know, although the letter was not opened, in a lecture on 10 April, 1846, Faraday would comment on these ideas while covering for the very shy Charles Wheatstone who was scheduled to give a talk on his chronoscope. At the end of the short notes of Wheatstone, Faraday filled the time with his recollections of the ideas of the electromagnetic field. 

1883 Professor George Chrystal gave an address on "Present Fields of Mathematical Research" to the first regular meeting of hte Edinburgh Mathematical Society. *Proceedings of the Edinburgh Mathematical Society, Volumes 1-4

Pockels circa 1892 *Wik

 The journal, Nature, published what must have been one of it's most unusual articles. It was an unsolicited letter from a German hausfrau Miss Agnes Pockels to John William Strutt, aka Lord Rayleigh.
Miss Pockels wrote:
My lord,
Will you kindly excuse my venturing to trouble you with a German letter on a scientific subject? Having heard of the fruitful researches carried on by you last year on the hitherto little understood properties of water surfaces, I thought it might interest you to know of my own observations on the subject For various reasons I am not in a position to publish them in scientific periodicals, and I therefore adopt this means of communicating to you the most important of them. First, I will describe a simple method, which I have employed for several years, for increasing or diminishing the surface of a liquid in any proportion, by which its purity may be altered at pleasure. … …
The letter went on to describe many of the results of Strutt's own experiments, and described results and conjectures even beyond his, all done in her own kitchen.

Lord Rayleigh demonstrated the integrity he was known for, by translating the letter into English, and sending it to the journal Nature, requesting it be printed without correction.

The story, with some additional detail about curiosity with his urine stream and its relation to the discovery of ink-jet printing can be found in Len Fisher's blog here. *Len Fisher

Despite her lack of formal training, Pockels was able to measure the surface tension of water by devising an apparatus known as the Pockels trough, a key instrument in the new discipline of surface science. Using an improved version of this slide trough, American chemist Irving Langmuir made additional discoveries on the properties of surface molecules, which earned him a Nobel Prize in chemistry in 1932. She published a number of papers and eventually received recognition as a pioneer in the new field of surface science. In 1931, together with Henri Devaux, Pockels received the Laura Leonard award from the Colloid Society. In the following year, the Braunschweig University of Technology granted her an honorary PhD. Pockels died in 1935 in Brunswick, Germany. She never married.*Wik
Her original letter had a made a splash, however. In 1917, the polymath head of research at General Electric (GE), Irving Langmuir, began using Pockels’ approach for his exquisitely simple studies of oil films. He proved the existence of a monolayer of elongated molecules sitting on the surface. Later, he and Katherine Blodgett, GE’s first female scientist, adapted Wilhelmy’s technique for measuring the surface tension to withdraw monolayers from the surface one at a time onto a substrate. Today, their improved Langmuir–Blodgett trough is the starting point for the deliberate construction of self-assembled structures. *Chemistry World

The Langmuir-Blodgett trough owes its existence to Pockels' early work

1926 John von Neumann, 22, received his doctorate summa cum laude in mathematics with minors in experimental physics and chemistry from the University of Budapest. *Goldstein, The Computer form Pascal to von Neumann, p. 170

1997 Fairchild Semiconductor Sold: National Semiconductor Corp. completes the sale of its Fairchild Semiconductor business. Many consider Fairchild the "original" Silicon Valley company for its profound and diverse institutional legacy: a survey of over 100 large silicon valley companies in the 1980s found that almost all of them had links to Fairchild, mostly through ex-Fairchild employees who had spun off and started these companies on their own. Fairchild had been founded by Robert Noyce, Gordon Moore and six others who left en masse from Shockley Semiconductor, after that firm's founder and co-inventor of the transistor, William Shockley, struggled with a confrontational management style. Noyce and Moore later co-founded Intel Corporation. *CHM

2009 The U.S. House of Representatives passed a non-binding resolution (HRES 224), recognizing March 14, 2009, as National Pi Day .
In 1988 The earliest known official or large-scale celebration of Pi Day was organized by Larry Shaw in 1988 at the San Francisco Exploratorium, where Shaw worked as a physicist, with staff and public marching around one of its circular spaces, then consuming fruit pies. The Exploratorium continues to hold Pi Day celebrations.*Wik

1683 John Theophile Desaguliers (12 Mar 1683, 29 Feb 1744 at age 60)French-English chaplain and physicist who studied at Oxford, became experimental assistant to Sir Isaac Newton. As curator at the Royal Society, his experimental lectures in mechanical philosophy and electricity (advocating, substantiating and popularizing the work of Isaac Newton) attracted a wide audience (In his lectures Newton, it is said, often spoke only to the walls.). In electricity, he coined the terms conductor and insulator. He repeated and extended the work of Stephen Gray in electricity. He proposed a scheme for heating vessels such as salt-boilers by steam instead of fire. He made inventions of his own, such as a planetarium, and improvements to machines, such as Thomas Savery's steam engine (by adding a safety valve, and using an internal water jet to condense the steam in the displacement chambers) and a ventilator at the House of Commons. He was a prolific author and translator. *TIS

1685 Bishop George Berkeley (12 March 1685 in Kilkenny, County Kilkenny, Ireland
- 14 Jan 1753 in Oxford, England). In 1734 he published The Analyst, Or a Discourse Addressed to an Infidel Mathematician (namely, Edmund Halley). This work was a strong and reasonably justified attack on the foundation of the differential calculus. He called differentials “the ghosts of departed quantities.” *VFR

1824 Gustav Robert Kirchhoff (12 Mar 1824, 17 Oct 1887) German physicist who, with Robert Bunsen, established the theory of spectrum analysis (a technique for chemical analysis by analyzing the light emitted by a heated material), which Kirchhoff applied to determine the composition of the Sun. He found that when light passes through a gas, the gas absorbs those wavelengths that it would emit if heated, which explained the numerous dark lines (Fraunhofer lines) in the Sun's spectrum. In his Kirchhoff's laws (1845) he generalized the equations describing current flow to the case of electrical conductors in three dimensions, extending Ohm's law to calculation of the currents, voltages, and resistances of electrical networks. He demonstrated that current flows in a zero-resistance conductor at the speed of light. *TIS

1835 Simon Newcomb (12 Mar 1835; died 11 Jul 1909 at age 74) Canadian-American astronomer and and mathematician who prepared ephemerides (tables of computed places of celestial bodies over a period of time) and tables of astronomical constants. He was an astronomer (1861-77) before becoming Superintendent of the U.S. Nautical Almanac Office (1877-97). During this time he undertook numerous studies in celestial mechanics. His central goal was to place planetary and satellite motions on a completely uniform system, thereby raising solar system studies and the theory of gravitation to a new level. He largely accomplished this goal with the adoption of his new system of astronomical constants at the end of the century. *TIS This astonomer and mathematician
was the most honored scientist of his time. *VFR
Newcomb is buried in Arlington National Cemetery 
Newcomb is often quoted as saying that heavier than air flight was impossible from a statement he made only two months before the Wright Brothers flight at Kitty Hawk, N.C.
"The mathematician of today admits that he can neither square the circle, duplicate the cube or trisect the angle. May not our mechanicians, in like manner, be ultimately forced to admit that aerial flight is one of that great class of problems with which men can never cope… I do not claim that this is a necessary conclusion from any past experience. But I do think that success must await progress of a different kind from that of invention."   He also is famously quoted for saying, "We are probably nearing the limit of all we can know about astronomy." 

Sir William Henry Perkin FRS (12 March 1838 – 14 July 1907)  was an English chemist and inventor who, in his youth, was enthused about chemistry by attending public lectures by Michael Faraday. While experimenting to synthesize quinine from a coal tar chemical, Perkins mixed aniline and sodium dichromate and unexpectedly found a dense colour - he named as aniline purple - which he extracted with alcohol. He had discovered the first artificial dye. Textiles of his era were coloured from natural sources; his was a valuable alternative. At the age of 18, he patented the dye. His father invested in his efforts to manufacture the dye. It went on sale in 1857, and it became popular in France. By age 23 he was fathering a new synthetic organic chemical industry. He continued synthesis research. He was knighted in 1906. *TIS   The dye he eventually called mauveine produced a color we now call Mauve.  The word muave is from the French (and earlier Latin) plant called mallow of a similar color.
The craze for aniline dyes, satirised in this George du Maurier cartoon

1859 Ernesto Cesaro (12 March 1859 , 12 Sept 1906) died of injuries sustained while aiding a drowning youth. In addition to differential geometry Cesàro worked on many topics such as number theory where, in addition to the topics we mentioned above, he studied the distribution of primes trying to improve on results obtained in this area by Chebyshev. He also contributed to the study of divergent series, a topic which interested him early in his career, and we should note that in his work on mathematical physics he was a staunch follower of Maxwell. This helped to spread Maxwell's ideas to the Continent which was important since, although it it hard to realise this now, it took a long time for scientists to realize the importance of his theories.
Cesàro's interest in mathematical physics is also evident in two very successful calculus texts which he wrote. He then went on to write further texts on mathematical physics, completing one on elasticity. Two further works, one on the mathematical theory of heat and the other on hydrodynamics, were in preparation at the time of his death.
Cesàro died in tragic circumstances. His seventeen year old son went swimming in the sea near Torre Annunziata and got into difficulties in rough water. Cesàro went to rescue his son but sustained injuries which led to his death. *SAU
I was reminded by Offer Pade' (Thanks that In mathematical analysis, Cesàro summation assigns values to some infinite sums that are not necessarily convergent in the usual sense. The Cesàro sum is defined as the limit, as n tends to infinity, of the sequence of arithmetic means of the first n partial sums of the series. 

1925 Leo Esaki (12 Mar 1925, )Japanese physicist who shared (with Ivar Giaever and Brian Josephson) the Nobel Prize in Physics (1973) in recognition of his pioneering work on electron tunneling in solids. From some deceptively simple experiments published in 1958, he was able to lay bare the tunneling processes in solids, a phenomena which had been clouded by questions for decades. Tunneling is a quantum mechanical effect in which an electron passes through a potential barrier even though classical theory predicted that it could not. Dr. Esaki's discovery led to the creation of the Esaki diode, an important component of solid state physics with practical applications in high-speed circuits found in computers and communications networks.*TIS

1945 Vijay Kumar Patodi (March 12, 1945 – December 21, 1976) was an Indian mathematician who made fundamental contributions to differential geometry and topology. He was the first mathematician to apply heat equation methods to the proof of the Index Theorem for elliptic operators. He was a professor at Tata Institute of Fundamental Research, Mumbai (Bombay). *Wik

1834 Karl Wilhelm Feuerbach (30 May 1800 in Jena, Germany - 12 March 1834 in Erlangen, Germany) His mathematical fame rests entirely on three papers. Most important was this contribution to Euclidean geometry: The circle which passes through the feet of the
altitudes of a triangle touches all four of the circles which are tangent to the three sides; it is internally tangent to the inscribed circle and externally tangent to each of the circles which touches the sides of the triangle externally. *VFR
The circle is also commonly called the Nine-point circle. It passes through the feet of the altitudes, the midpoints of the three sides, and the point half way between the orthocenter and the vertices.
Feuerbach did undertake further mathematical research. He sent a note from Ansbach to the journal Isis (dated 22 October 1826) entitled Einleitung zu dem Werke Analysis der dreyeckigen Pyramide durch die Methode der Coordinaten und Projectionen. Ein Beytrag zu der analytischen Geometrie von Dr. Karl Wilhelm Feuerbach, Prof. d. Math. (Introduction to the analysis of the triangular pyramid, by means of the methods of coordinates and projections. A study in analytic geometry by Dr Karl Wilhelm Feuerbach, Professor of Mathematics). This note announced results which were to appear in full in a later publication and indeed they did in a 48-page booklet Grundriss zu analytischen Untersuchungen der dreyeckigen Pyramide (Foundations of the analytic theory of the triangular pyramid) published in 1827. This is a second major work by Feuerbach and it has been studied carefully by Moritz Cantor who discovered that in it Feuerbach introduces homogeneous coordinates. He must therefore be considered as the joint inventor of homogeneous coordinates since Möbius, in his work Der barycentrische Calcul also published in 1827, introduced homogeneous coordinates into analytic geometry.*SAU
Although he is credited for its discovery, Karl Wilhelm Feuerbach did not entirely discover the nine-point circle, but rather the six point circle, recognizing the significance of the midpoints of the three sides of the triangle and the feet of the altitudes of that triangle. (See Fig. 1, points D, E, F, G, H, and I.) (At a slightly earlier date, Charles Brianchon and Jean-Victor Poncelet had stated and proven the same theorem.) But soon after Feuerbach, mathematician Olry Terquem himself proved the existence of the circle. He was the first to recognize the added significance of the three midpoints between the triangle's vertices and the orthocenter.*Wik

1898 Johann Jakob Balmer (1 May 1825, 12 Mar 1898 at age 72) Swiss mathematician and physicist who discovered a formula basic to the development of atomic theory. Although a mathematics lecturer all his life, Balmer's most important work was on spectral series by giving a formula relating the wavelengths of the spectral lines of the hydrogen atom (1885) at age 60. Balmer's famous formula is λ= hm2/(m2-n2). Wavelengths are accurately given using h = 3.6456 x10-7m, n = 2, and m = 3, 4, 5, 6, 7. He suggested that giving n other small integer values would give other series of wavelengths for hydrogen. Why this prediction agreed with observation was not understood until after his death when the theoretical work of Niels Bohr was published in 1913. *TIS

In 1895, a mathematical relationship between the frequencies of the hydrogen light spectrum was reported by a Swiss school teacher, Johann Balmer, in Annalen der Physik. Its significance was overlooked until Niels Bohr realized this showed a structure of energy levels of the electron in the hydrogen atom. *TIS

1905 William Allen Whitworth (1 February 1840 – 12 March 1905) was an English mathematician and a priest in the Church of England.
As an undergraduate, Whitworth became the founding editor in chief of the Messenger of Mathematics, and he continued as its editor until 1880. He published works about the logarithmic spiral and about trilinear coordinates, but his most famous mathematical publication is the book Choice and Chance: An Elementary Treatise on Permutations, Combinations, and Probability (first published in 1867 and extended over several later editions). The first edition of the book treated the subject primarily from the point of view of arithmetic calculations, but had an appendix on algebra, and was based on lectures he had given at Queen's College. Later editions added material on enumerative combinatorics (the numbers of ways of arranging items into groups with various constraints), derangements, frequentist probability, life expectancy, and the fairness of bets, among other topics.
Among the other contributions in this book, Whitworth was the first to use ordered Bell numbers to count the number of weak orderings of a set, in the 1886 edition. These numbers had been studied earlier by Arthur Cayley, but for a different problem. He was the first to publish Bertrand's ballot theorem, in 1878; the theorem is misnamed after Joseph Louis François Bertrand, who rediscovered the same result in 1887. He is the inventor of the E[X] notation for the expected value of a random variable X, still commonly in use, and he coined the name "subfactorial" for the number of derangements of n items.
Another of Whitworth's contributions, in geometry, concerns equable shapes, shapes whose area has the same numerical value (with a different set of units) as their perimeter. As Whitworth showed with D. Biddle in 1904, there are exactly five equable triangles with integer sides: the two right triangles with side lengths (5,12,13) and (6,8,10), and the three triangles with side lengths (6,25,29), (7,15,20), and (9,10,17). *Wik

1915 Arthur Edwin Haynes,(May 23, 1849;Baldwinsville, Onondaga County, New York, USA - Mar. 12, 1915; Minneapolis, Minnesota) Professor of Mathematics and Physics at Hillsdale College from 1875 until 1890. He came to Michigan in June 1858. They located near the village of Reading in southwestern Hillsdale Co. where the father had a farm.
Arthur received a common school education and remained on the family farm until he reached twenty years of age.
In the fall of 1870, Arthur entered Hillsdale College where he remained, a diligent student, until he was graduated from that institution in June 1875. He taught several terms of district school before graduation and was also employed during his college course as a tutor in mathematics in the college. During the summer between his junior and senior years, he assisted in the erection of the Central College building, in order to earn money to continue his studies. He carried a hod from the first story until the completion of the fourth, shouldering 80 pounds of brick and walking from the bottom to the top of the ladder (20 feet) without touching the hod handle, a feat that he was justly proud of. His classroom at Hillsdale was in that same building.
Immediately following graduation,he married and was appointed instructor in mathematics in Hillsdale College in the fall of 1875, and two years later was elected to the full Professorship. In 1885 he was elected a member of the London Mathematical Society. In 1890 he switched to the University of Minnesota. He wrote a paper on "The Mounting and Use of a Spherical Blackboard." He died in Minneapolis in 1915 and his body was removed back to Hillsdale where he was buried in Oak Grove Cemetary *PB notes

1942 Sir William Henry Bragg (2 July 1862 – 10 March 1942) was a pioneer British scientist in solid-state physics who was a joint winner (with his son Sir Lawrence Bragg) of the Nobel Prize for Physics in 1915 for research on the determination of crystal structures. During the WW I, Bragg was put in charge of research on the detection and measurement of underwater sounds in connection with the location of submarines. He also constructed an X-ray spectrometer for measuring the wavelengths of X-rays. In the 1920s, while director of the Royal Institution in London, he initiated X-ray diffraction studies of organic molecules. Bragg was knighted in 1920. *TIS 

1946 Leonida Tonelli (19 April 1885 – 12 March 1946) was an Italian mathematician, most noted for creating Tonelli's theorem, usually considered a forerunner to Fubini's theorem. (A result which gives conditions under which it is possible to compute a double integral using iterated integrals. As a consequence it allows the order of integration to be changed in iterated integrals.)*Wik He published 137 papers, all single authored except one in 1915 written in collaboration with Guido Fubini, and a number of important books including Fondamenti di calcolo delle variazioni (2 volumes) (1921, 1923), Serie trigonometriche (1928), and (with E Lindner) Corso di matematica per la Scuola media (3 volumes) (1941, 1942).*SAU

1972 Louis Joel Mordell (28 January 1888 – 12 March 1972) was a U.S. born British mathematician, known for pioneering research in number theory. He was born in Philadelphia, USA, in a Jewish family of Lithuanian extraction. He came in 1906 to Cambridge to take the scholarship examination for entrance to St John's College, and was successful in gaining a place and support.
Having taken third place in the Mathematical Tripos, he began independent research into particular diophantine equations: the question of integer points on the cubic curve, and special case of what is now called a Thue equation, the Mordell equation

y^2 = x^3 + k.

During World War I he was involved in war work, but also produced one of his major results, proving in 1917 the multiplicative property of Ramanujan's tau-function. The proof was by means, in effect, of the Hecke operators, which had not yet been named after Erich Hecke; it was, in retrospect, one of the major advances in modular form theory, beyond its status as an odd corner of the theory of special functions.
In 1920 he took a teaching position in Manchester College of Technology, becoming the Fielden Reader in Pure Mathematics at the Victoria University of Manchester in 1922 and Professor in 1923. There he developed a third area of interest within number theory, geometry of numbers. His basic work on Mordell's theorem is from 1921/2, as is the formulation of the Mordell conjecture.
In 1945 he returned to Cambridge as a Fellow of St. John's, when elected to the Sadleirian Chair, and became Head of Department. He officially retired in 1953. It was at this time that he had his only formal research students, of whom J. W. S. Cassels was one. His idea of supervising research was said to involve the suggestion that a proof of the transcendence of the Euler–Mascheroni constant was probably worth a doctorate. *Wik
An example of a Mordell curve y^2 = x^3 + 1

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

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