## Friday 22 March 2024

### On This Day in Math - March 22

 1727 Eclipse Map *greatamericaneclipse.com

We [he and Halmos] share a philosophy about linear algebra:
we think basis-free,
we write basis-free,
but when the chips are down
we close the office door and compute with matrices like fury.

~Irving Kaplansky

The 81st day of the year; 81 is the only integer (except 1) which is the square of the sum of its digits.

Multiples of nine seem to have powers whose digits sum to the original, look at 9^2, 18^3, 27^3, 36^4, 45^6, 54^6, 63^8 and 81^9 even 90^19, but I couldn't find 72,

81 is a square number(9^2) and the sum of its divisors is also a square, 1 + 3 + 9 + 27 + 81= 121 = 11^2.
There are no other year dates with this property.  A generous reader contributed a list of the few under 10^8, and here are the only ones less than 1000, 1,1; 81, 121 ;  400, 961 .**more at bottom of page.

The smallest 10 digit pandigital number is 1023456789, 81 or  34 is a factor.  The other two factors are both four digit numbers. Can you find the smallest which is prime?    ;-}

81 is one of only three non-trivial numbers for which the sum of the digits * the reversal of the sum yields the original number (8+1 = 9;  9*9 = 81).  The other two are the famous Hardy-Ramanujan taxicab # 1729, which is the smallest number which is the sum of two positive cubes in two ways.(1+7+2+9 = 19; 19*91 = 1729), and 1458 (1+4+5+8 = 18; 18*81=1458) which is also unique for being the maximum determinant possible for a 11x11 matrix with only ones and zeros.  The Hardy-Ramanujan number's properties were first noted by  Frénicle de Bessy in 1657(without mention of a taxicab).That is, he knew it was the sum of two cubes in two ways, not sure if he knew the sum of the digits property above... anyone?

EVENTS

1129 Chinese accounts state “there was a Black spot within the Sun” on March 22, 1129, which “died away” on April 14th. This may well have been one of the sunspots John of Worcester had observed 104 days earlier (8 December, 1128), on the other side of the world. Worcester's observation prompted the earliest known drawing of sunspots, which appear in his Chronicle recorded in 1128. *Joe Hanson

1638 In a letter to Descartes, Mersenne reports that Fermat is able to prove that no number of the form 4n − 1 is a sum of two integral or rational squares. *Lemmermeyer, Euler, Goldbach, and" Fermat's Theorem"

1675. John Evelyn records in his diary a visit with William Petty and the story of the rejuvenation of Anne Greene after she was hanged until dead. "Supped at Sir William Petty's, with the Bishop of Salisbury, and divers honorable persons. ..grown famous...for his recovering a poor wench that had been hanged for felony; and her body having been begged (as the custom is) for the anatomy lecture, he bled her, put her to bed to a warm woman, and, with spirits and other means, restored her to life." *The Diary of John Evelyn

1727 The first detailed documentation and map of an eclipse in the New World came from Mexico in 1727. (At Top of page)
This map in the pamphlet Spherographia de la Obscuration de la Tierra en el Eclypse de Sol de 22. de Marzo de 1727 has several interesting features. It predates the earliest eclipse map from the United States by 104 years. Curiously, it also seems to predate any known eclipse map from Spain. Of special interest to historians of cartography, this map shows California as an island. *http://www.greatamericaneclipse.com

1818 The last time that Easter fell on this date, the earliest possible. It will not happen again until the year 2285. By definition Easter is the ﬁrst Sunday after the ﬁrst full moon on or after the vernal equinox. Since the Roman Catholic Church defined the vernal equinox to be 21 March and uses a tabulated moon, not the real moon, this is a mathematical issue, not an astronomical event. *VFR

1880 The New York Times comments, somewhat tongue-in-cheek, on the Fifteen Puzzle that was sweeping the country, “No pestilence has ever visited this or any other country which has spread with the awful celerity of what is popularly called the ‘Fifteen Puzzle.’ ...it now threatens our free institutions, inasmuch as from every town and hamlet there is coming up a cry for a ‘strong man’ who will stamp out this terrible puzzle at any cost of Constitution or freedom” *Jerry Slocum, Dic Sonneveld, The 15 Puzzle

1851 Edward Walter Maunder (12 Apr 1851, 21 Mar 1928 at age 76) English astronomer who was the first to take the British Civil Service Commission examination for the post of photographic and spectroscopic assistant at the Royal Observatory, Greenwich. For the next forty years that he worked there, he made extensive measurements of sunspots. Checking historical records, he found a period from 1645 to 1715 that had a remarkable lack of reports on sunspots. Although he might have questioned the accuracy of the reporting, he instead attributed the shortage of report to an actual dearth of sunspots during that period. Although his suggestion was not generally accepted at first, accumulating research has since indicated there are indeed decades-long times when the sun has notably few sunspots. These periods are now known as Maunder minima.*TIS

On the far side of the Moon lies the Maunder crater, named after two British astronomers - Annie and Walter Maunder.
Annie worked alongside her husband at the end of the 19th Century, recording the dark spots that pepper the Sun.
The name Maunder is still known in scientific circles, yet Annie has somehow slipped from history.
"I think the name Maunder is there and we have all rather forgotten that that's two people," says Dr Sue Bowler, editor of the Royal Astronomical Society magazine, Astronomy and Geophysics.
"She was acknowledged on papers, she published in her own name as well as with her husband, she wrote books, she was clearly doing a lot of work but she also clearly kept to the conventions of the day, I think." *By Helen Briggs BBC News
She is known to have worked closely with her husband on the study of sunspots, and she is often credited with discovering the butterfly pattern. *LH
Annie Scott Dill Maunder (née Russell) FRAS (14 April 1868 – 15 September 1947)*PBnotes

1945 On 22 March 1945, the first female Fellows were elected to the Royal Society. This followed a statutory amendment in 1944 that read "Nothing herein contained shall render women ineligible as candidates", and was contained in Chapter 1 of Statute 1. Following approval by the Council, Marjory Stephenson (From Burwell in the Fens of East Anglia, and just west of my old school in Lakenheath,She wrote Bacterial Metabolism (1930), which ran to three editions and was a standard textbook for generations of microbiologists. A founder of the Society for General Microbiology, she also served as its second president.) and Kathleen Lonsdale were elected as Fellows.
Stephenson would die only three years later in 1948.  In 1949 Lonsdale was appointed professor of chemistry and head of the Department of Crystallography at University College London. She was the first tenured woman professor at that college, a position she held until 1968 when she was named professor emeritus. In 1956 she was made Dame Commander of the Order of the British Empire. *Wik

1960 The first laser was patented (U.S. No. 2,929,922) by Arthur Schawlow and Charles Hard Townes under the title “Masers and Maser Communications System.” What distinguished this invention as the first laser is that it was the first to operate in the visible light spectrum. The patent was assigned to the Bell Telephone Laboratories, where they had done the research. *TIS
Townes was awarded half the Nobel Prize in Physics in 1964. Russian physicists Alexander Prokhorov and Nikolay Basov shared the other half “for fundamental work in the field of quantum electronics, which has led to the construction of oscillators and amplifiers based on the maser-laser principle,” according to the Nobel Prize website.
Townes and the development of the laser isn’t without controversy. Columbia University graduate student Gordon Gould had met with Townes in November 1957. It was during this meeting that Gould reportedly confided his idea for the laser with Townes. Gould and his employer Technical Research Group applied for patents relating to his ideas in 1959. Townes and Schawlow got their patent for the laser in 1960, while Gould’s application was shot down. Gould eventually received a patent pertaining to laser technology in 1977 and began receiving money for his work in 1988.

 Townes with prototype Mazer, *EE World OnLine

1993 Intel Begins Shipping "Pentium" Chip":
Intel announces it is shipping its Pentium microprocessor. Engineers Federico Faggin, Ted Hoff, San Mazor, and Matsatoshi Sima, an engineer from the Japanese firm of Busicom, invented the world's first microprocessor at Intel in 1971 -- the Intel 4004. The new processor continued the exponential increase in speed and power for personal computers, also allowing for a smoother incorporation of speech, sound, handwriting, and photographs into documents.*CHM

1997 Comet Hale-Bopp makes its closest approach to the Earth at 1.315 AU. The comet was discovered independently on July 23, 1995 by two observers, Alan Hale and Thomas Bopp, both in the United States. *David Dickinson‏@Astroguyz, *Wik

BIRTHS

1394 Ulugh Beg (22 Mar 1394- 27 Oct 1449) The only important Mongol scientist, mathematician, and the greatest astronomer of his time. His greatest interest was astronomy, and he built an observatory (begun in 1428) at Samarkand. In his observations he discovered a number of errors in the computations of the 2nd-century Alexandrian astronomer Ptolemy, whose figures were still being used. His star map of 994 stars was the first new one since Hipparchus. After Ulugh Beg was assassinated by his son, the observatory fell to ruins by 1500, rediscovered only in 1908. Written in Arabic, his work went unread by the world's next generation of astronomers. When his tables were translated into Latin in 1665, telescopic observations had surpassed them. *TIS

1644 Otto Mencke (22 March (OS) April 2, 1644 – 18 Jan (OS) 29 Jan 1707) was a 17th-century German philosopher and scientist. He obtained his doctorate at the University of Leipzig in 1666 with a thesis entitled: Ex Theologia naturali — De Absoluta Dei Simplicitate, Micropolitiam, id est Rempublicam In Microcosmo Conspicuam.
He is notable as being the founder of the very first scientific journal in Germany, established 1682, entitled: Acta Eruditorum. *Wik

1784 Samuel Hunter Christie (22 March 1784 – 24 January 1865) was a British scientist and mathematician.
He studied mathematics at Trinity College, Cambridge, where he won the Smith's Prize and was second wrangler. It may help to understand the difficulty of this exam by looking at some of the great achievers who did NOT win Senior Wrangler. A short list of Second Wranglers, include Alfred Marshall, James Clerk Maxwell, J. J. Thomson, and Lord Kelvin.
Those who have finished between third and 12th include Karl Pearson and William Henry Bragg (third), George Green and G. H. Hardy (fourth), Adam Sedgwick (fifth), John Venn (sixth), Bertrand Russell and Nevil Maskelyne (seventh), Thomas Malthus (ninth), and John Maynard Keynes (12th).

Christie was particularly interested in magnetism, studying the earth's magnetic field and designing improvements to the magnetic compass. Some of his magnetic research was done in collaboration with Peter Barlow. He became a Fellow of the Royal Society in 1826, delivered their Bakerian Lecture in 1833 and served as their Secretary from 1837 to 1853. In 1833 he published his 'diamond' method, the forerunner of the Wheatstone bridge, in a paper on the magnetic and electrical properties of metals, as a method for comparing the resistances of wires of different thicknesses. However, the method went unrecognized until 1843, when Charles Wheatstone proposed it, in another paper for the Royal Society, for measuring resistance in electrical circuits. Although Wheatstone presented it as Christie's invention, it is his name, rather than Christie's, that is now associated with the device.
Christie taught mathematics at the Royal Military Academy, Woolwich, from 1838 until his retirement in 1854. He died at Twickenham, on 24 January 1865. *Wik

1799 Friedrich Wilhelm August Argelander (22 Mar 1799, 17 Feb 1875 at age 75)
German astronomer who established the study of variable stars as an independent branch of astronomy and is renowned for his great catalog listing the positions and brightness of 324,188 stars of the northern hemisphere above the ninth magnitude. He studied at the University of Königsberg, Prussia, where he was a pupil and later the successor of Friedrich Wilhelm Bessel. In 1837, Argelander published the first major investigation of the Sun's motion through space. In 1844 he began studies of variable stars.*TIS

1868 Robert Andrews Millikan (22 Mar 1868, 19 Dec 1953) American physicist who was awarded the 1923 Nobel Prize for Physics for "his work on the elementary charge of electricity and on the photoelectric effect." Millikan's famous oil-drop experiment (1911) was far superior to previous determinations of the charge of an electron, and further showed that the electron was a fundamental, discrete particle. When its value was substituted in Niels Bohr's theoretical formula for the hydrogen spectrum, that theory was validated by the experimental results. Thus Millikan's work also convincingly provided the first proof of Bohr's quantum theory of the atom. In later work, Millikan coined the term "cosmic rays" in 1925 during his study of the radiation from outer space.*TIS

1868 Nathan Rosen (22 Mar 1909, 18 Dec 1995) U.S.-born Israeli theoretical physicist who in 1935 collaborated with Albert Einstein and Boris Podolsky on a much-debated refutation of the theory of quantum mechanics; he later came to accept the theory. The famous Einstein-Podolsky-Rosen critique of quantum mechanics was published in the 1935 Physical Review. (A New York Times obituary described The Physical Review as "one of the most impenetrable periodicals in the English language.") Rosen founded the Institute of Physics at Technion in Haifa.*TIS
 *LH

1917 Irving "Kap" Kaplansky (22 March 1917 in Toronto, Ontario, Canada - 25 June 2006 in Sherman Oaks, Los Angeles, California) was born in Toronto, Ontario, Canada after his parents emigrated from Poland and attended the University of Toronto as an undergraduate. After receiving his Ph.D from Harvard in 1941 as Saunders Mac Lane's first student, Kaplansky was professor of mathematics at the University of Chicago from 1945 to 1984. He was chair of the department from 1962 to 1967.
"Kap," as his friends and colleagues called him, made major contributions to group theory, ring theory, the theory of operator algebras and field theory. He published over 150 papers with over 20 co-authors. He was a member of the National Academy of Sciences and the American Academy of Arts and Sciences. He was the Director of the Mathematical Sciences Research Institute from 1984 to 1992, and the President of the American Mathematical Society from 1985 to 1986.
Kaplansky also was a noted pianist known to take part in Chicago performances of Gilbert and Sullivan productions. He often composed music based on mathematical themes. One of those compositions, A Song About Pi, is a melody based on assigning notes to the first 14 decimal places of pi.
Kaplansky was the father of singer-songwriter Lucy Kaplansky, who occasionally performs A Song About Pi in her act. In this video she talks about her dad a few years after his death, and sings the song which is amazingly nice, but listen for it, she misses a digit in there I think...

He was among the first five recipients of William Lowell Putnam fellowships in 1938.*Wik

1931 Burton Richter (22 Mar 1931, ) American physicist who was jointly awarded the 1976 Nobel Prize for Physics with Samuel C.C. Ting for the discovery of a new subatomic particle, the J/psi particle. *TIS He led the Stanford Linear Accelerator Center (SLAC) team which co-discovered the J/ψ meson in 1974, alongside the Brookhaven National Laboratory (BNL) team led by Samuel Ting. This discovery was part of the so-called November Revolution of particle physics. He was the SLAC director from 1984 to 1999.*Wik

DEATHS

1772 John Canton (31 Jul 1718, 22 Mar 1772 at age 53) British physicist and teacher, who educated himself about science, and for developing a new method of preparing artificial magnets, won election to the Royal Society (1749). In July 1752, he was the first Englishman to repeat French experiments verifying Franklin's hypothesis that lightning was just a huge electric spark, (as seen from charged Leyden jars). Following this, he studied the polarity of the charge on a cloud. He invented a portable electroscope to detect charge present in a system, and he remains well-known for electrostatic induction experiments. Canton proved that water is slightly compressible (1762). Noting compass needle irregularities during a prominent aurora borealis he made the first observations of magnetic storms (1756-9). *TIS

1840 Étienne Bobillier (April 17, 1798 – March 22, 1840) was a French mathematician.
At the age of 19 he was accepted into the École Polytechnique and studied there for a year. However, due to a shortage of money, in 1818 he became an instructor in mathematics at the École des Arts et Métiers in Châlons-sur-Marne. In 1829, he was sent to Angers to be director of studies. The following year he served in the national guard during the 1830 revolution. In 1832 he returned to Châlons after his post was abolished, and was promoted to professor.
In 1836 he began suffering from health problems, but continued teaching; declining to take a leave to recuperate. As a result he died in Châlons at the relatively early age of 41.
He is noted for his work on geometry, particularly the algebraic treatment of geometric surfaces and the polars of curves. He also worked on statics and the catenary.
The crater Bobillier on the Moon is named after him.*Wik

1926 Joseph Jean Baptiste Neuberg (30 Oct 1840 in Luxembourg City, Luxembourg - 22 March 1926 in Liège, Belgium) Neuberg worked on the geometry of the triangle, discovering many interesting new details but no large new theory. Pelseneer writes, "The considerable body of his work is scattered among a large number of articles for journals; in it the influence of A. Möbius is clear." *SAU

1953 Gustav Herglotz (2 February 1881 – 22 March 1953) was a German mathematician. He is best known for his works on the theory of relativity and seismology. From 1925 (until becoming Emeritus in 1947) he again was in Göttingen as the successor of Carl Runge on the chair of applied mathematics. One of his students was Emil Artin.
Herglotz made contribution in many fields of applied and pure mathematics. The Theorem of Herglotz is known in differential geometry, and he also contributed to number theory. He worked in the fields of celestial mechanics, theory of electrons, special relativity (where he developed a theory of elasticity), general relativity, hydrodynamics, refraction theory. *Wik

1987 Andrew Paul Guinand (3 March 1912 in Renmark, South Australia, - 22 March 1987 in Peterborough, Ontario, Canada) Guinand worked on summation formulae and prime numbers, the Riemann zeta function, general Fourier type transformations, geometry and some papers on a variety of topics such as computing, air navigation, calculus of variations, the binomial theorem, determinants and special functions.  W N Everitt writes,
"As a student of Titchmarsh in Oxford in the years immediately before the second world war it was natural that Guinand's research interests should be directed into the field of Fourier analysis and the Riemann zeta function. ... [In an important paper in 1948] the main application of the general result yields a deep-seated connection between the distribution of the prime numbers and the location of the zeros of the Riemann zeta function on (or near to it if the Riemann hypothesis is false) the critical line in the complex plane... Guinand was convinced that these results could lead to more information about the Riemann zeta function, and he was disappointed that he was not able to advance further in this area and that others did not take up the possibility themselves. "
*SAU

***I calculated a few below 10**8:
1 1 [1]
81 121 [1, 3, 9, 27, 81]
400 961 [1, 2, 4, 5, 8, 10, 16, 20, 25, 40, 50, 80, 100, 200, 400]
32400 116281 [1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 24, 25, 27, 30, 36, 40, 45, 48, 50, 54, 60, 72, 75, 80, 81, 90, 100, 108, 120, 135, 144, 150, 162, 180, 200, 216, 225, 240, 270, 300, 324, 360, 400, 405, 432, 450, 540, 600, 648, 675, 720, 810, 900, 1080, 1200, 1296, 1350, 1620, 1800, 2025, 2160, 2700, 3240, 3600, 4050, 5400, 6480, 8100, 10800, 16200, 32400]
1705636 2989441 [1, 2, 4, 653, 1306, 2612, 426409, 852818, 1705636]
3648100 7958041 [1, 2, 4, 5, 10, 20, 25, 50, 100, 191, 382, 764, 955, 1910, 3820, 4775, 9550, 19100, 36481, 72962, 145924, 182405, 364810, 729620, 912025, 1824050, 3648100]

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