Fourier Series approximation of a square wave, *Mathworld |

True greatness is when your name is like ampere, watt, and fourier—when it's spelled with a lower case letter.

~Richard Hamming (

*creator of the hamming code, with a lower case h*)

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

The smallest 10 digit pandigital number is 1023456789, 81 or 3

^{4}is a factor. The other two factors are both four digit numbers.

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 = 18; 18*81 = 1729), and 1458 (1+4+5+8 = 19; 19*91=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).

EVENTS

---Commonly considered the ﬁrst day of spring, a tradition dating from the Council of Nicaea in A.D. 325. The most recent year in which this was in fact true in the U.S. was 1979, when the vernal equinox occurred at 12:22 a.m. EST. The next time the vernal equinox will be on March 21 is in 2103 when it will occur at 1:09:04 a.m. EST. This computation uses a tropical year of 365 days, 5 hours, 48 minutes, and 46 seconds. [Mathematics Magazine, 55(1982), 46–47] *VFR 1522 Copernicus read the German version of his treatise, Modus cudendi monetam (The Way to Strike Coin), before the Royal Prussian Assembly attended by King Sigismund Is envoys at Grudziądz (Graudenz). Copernicus discusses general issues related to the theory of money and formulates inter alia a law of bad money driving out good. In the second he focused on the current monetary situation in Royal Prussia and in particular on the decline in the value of Prussian coinage, and concluded his presentation with a proposal to mint three Prussian szelągi as an equivalent of one Polish grosz (groshen) and thus to equalize the value of the new Prussian coinage with that issued by the Crown. *Leszek Zygner

Nicolaus Copernicus University (

*Students may not know that, in addition to being a respected astronomer, Copernicus was a respected economist.*)

1543 Copernicus’ De Revolutionibus published, {{{This date seems incorrect, Thony Christie sent me a note that, "in his An Annotated Census of Copernicus' De Revolutionibus Owen Gingerich writes, 'The printing was finished on 20 April 1543 when Rheticus autographed a presentation copy of the completed work. (Copernicus himself did not receive the final pages until a month later, the day on which he died.)' However I have a note from a post by Teresa Borawska of Nicolaus Copernicus University that says, "There is no information whether a copy of the book printed shortly before 21 March 1543 ever reached Warmia before the astronomers death." and gives no other publication date.}}} The book was so technically complex that only true astronomers could read through it so the 400 copies didn't even sale out. In addition Osiander had written a disclaimer (without, it seems, the dying Copernicus' permission) that readers should view it as a useful mathematical fiction with no physical reality, thereby somewhat shielding it from accusations of blasphemy. But eventually it was banned. It was placed on the Index of Forbidden Books by a decree of the Sacred Congregation of March 5, 1616 as part of the Galileo "incident". [

*while I was researching this note I came across a nice bit of information that I am not sure where else I could use. De revolutionibus was printed in Hans Petreiuss printing shop in Nuremberg. The building of Petreiuss former printing shop at 9, Öberg Street, (located near Albrecht Durers birthplace) luckily survived the ravages of WWII. You can see in the banner an image of the shop at The Renaissance Mathematicus blog.]*

**1599**Tycho sends a letter to Longomontanus, in which he reports his revised theory on the movement of the moon. On January 31, During an observation of the lunar eclipse, he had discovered that his predictive theory about the movement of the Moon was wrong since the eclipse started 24 minutes before his calculations predicted.*Wik

**1665-6**Hooke writes to C. Huygens to send him a paper on Gravity he has written and presented to the Royal Society.

**1684**Giovanni Domenico Cassini discovered two moons of Saturn: Tethys and Dione, using a refractor telescope with an aperture of 108mm. He had previously discovered two other satellites of Saturn: Iapetus (Sep 1671) and Rhea (1672). Christiaan Huygens was the first to discover a moon of Saturn, when he viewed Titan (the largest and easiest to see) on 25 Mar 1655.*TIS

**1797**Gauss makes an entry in his diary that the perimeter of the lemniscate can be divided into five equal parts by ruler and compass. Abel would show in 1827 that the division of the lemniscate with classical tools is possible for the same numbers n as the circle. This is an important theorem in elliptic functions. *John Stillwell, Mathematics and Its History

1801 Thomas Jefferson to Joseph Priestly:

DEAR SIR,*The Letters of Thomas Jefferson, http://www.let.rug.nl/

-- I learnt some time ago that you were in Philadelphia, but that it was only for a fortnight; supposed you were gone. It was not till yesterday I received information that you were still there, had been very ill, but were on the recovery. I sincerely rejoice that you are so. Yours is one of the few lives precious to mankind, for the continuance of which every thinking man is solicitous.

1816 John Dalton makes the first entry in the second volume of his meteorological notebook. Dalton came to his views on atomism through his interest in meteorology. The volumes contain daily meteorological observations, vol. 1 covering from 1 Apr 1803 to 20 Mar 1816. Volume II would continue until 31 Aug, 1827

In 1925, Wolfgang Pauli published his “exclusion principle.” At the young age of 24, in an article in Zeitschrift für Physik, Pauli introduced the idea that two nearby electrons cannot be in exactly the same state at the same time. For this, now fundamental, contribution to quantum mechanics, he was awarded a Nobel Prize in 1945. *TIS

1925 The Butler Act is signed into law. A law in Tennessee prohibiting the teaching of Darwin’s theory of evolution passed the state senate on March 13, and was signed into law by Governor Austin Peay (for whom the university in Clarksville, Tennessee is named) on March 21. The Butler Act was a Tennessee law:

That it shall be unlawful for any teacher in any of the Universities, Normals and all other public schools of the State which are supported in whole or in part by the public school funds of the State, to teach any theory that denies the Story of the Divine Creation of man as taught in the Bible, and to teach instead that man has descended from a lower order of animals.It would remain the law in Tennessee until repealed on September 1, 1967. *Wik Within a few months, John Scopes became a willing defendant in the “Scopes Monkey Trial,” which began 10 Jul 1925, and received world attention as the statute was tested. He was convicted and fined $100, which was overturned on appeal. *TIS

1943 Joseph Needham, 43, known at that point as a brilliant biologist, arrives in China for the first time. By the time he left, he would be well on his way to being the foremost student of China in the Western World. His "Science and Civilization in China", would alter the basis and direction of math/science history. *Simon Winchester, The Man Who Loved China

1963 When this date is written in the form 3/21/63, the product of the ﬁrst two numbers is the third. This happens 212 times each century. *VFR (

*you have 211 left to find*)

1989 NCTM released its Curriculum and Evaluation Standards for School Mathematics, a document intended to change fundamentally the way mathematics is taught. *VFR

**2016**France issues stamp honoring Sophie Germain.

2016 Sphere packing for 24 dimensions is solved by Maryna Viazovska. In 1611, Kepler conjectured that here was no way to pack spheres more densly than the way we would normally stack oranges or cannonballs, with every triangle of three supporting another nestled above (and below) tangent to all of the first three. By 1831 Gauss had managed to prove the conjecture for 3d. In her paper on May 14th Viazovska proved no packing of unit balls in Euclidean space R

^{8}has density greater than that of the E8-lattice packing. One week later, (March 21) building on her work, with collaboration of four others, they were able to prove that the Leech lattice is the densest packing of congruent spheres in twenty-four dimensions, and that it is the unique optimal periodic packing. *arxiv.

BIRTHS

1866 Antonia Coetana de Paiva Pereira Maury (21 Mar 1866; 8 Jan 1952 at age 85) was an American astronomer and ornithologist whose painstaking classifications of stars by their spectra included elaborate work on 681 bright stars of the northern skies published in Annals of Harvard College Observatory (1896), a significant early catalog. Yet she was unappreciated by her observatory director, Edward C. Pickering. Her work was important in Ejnar Hertzsprung's verification of the distinction between dwarf stars and giant stars, as now seen in the Hertzsprung-Russell diagram. After Pickering discovered the first spectroscopic binary star, Mizar, she was first to measure its period, 104 days. In 1889, she identified the second such star, Beta Aurigae, with a period of about 4 days. Antonia was the niece of astronomer Henry Draper, and the granddaughter of John William Draper who pioneered in the use of photography in astronomy.*TIS

In 1897, having examined 4,800 photographs, she published her findings on 681 bright northern stars in the Annals of the Harvard College Observatory. It was the first Harvard observatory publication credited to a woman, which she had insisted on, writing to Pickering, “I worked out the theory at the cost of much thought and elaborate comparison and I think that I should have full credit for my theory of the relations of the star spectra.” *Time

1884 George David Birkhoff (21 Mar 1884, 12 Nov 1944) American mathematician, foremost of the early 20th century, who formulated the ergodic theorem. As the first American dynamicist, Birkhoff picked up where Poincaré left off, gaining distinction in 1913 with his proof of Poincaré's Last Geometric Theorem, a special case of the 3-body problem. Although primarily a geometer, he discovered new symbolic methods. He saw beyond the theory of oscillations, created a rigorous theory of ergodic behavior, and foresaw dynamical models for chaos. His ergodic theorem transformed the Maxwell- Boltzmann ergodic hypothesis of the kinetic theory of gases (to which exceptions are known) into a rigorous principle through use of the Lebesgue measure theory. He also produced a mathematical model of gravity. *TIS

1909 Founder of ACM Edmund Berkeley Is Born:

Edmund Berkeley, founder of the Association of Computing Machinery, is born. A graduate of Harvard University, Berkeley participated in the development of Harvard's Mark II while enlisted in the Navy during World War II. In addition to co-founding the ACM in 1947, he wrote one of the first books on computers intended for a general audience, "Giant Brains, or Machines that Think." *CHM

1920 John Michael Hammersley (21 March 1920 in Helensburgh, Dunbartonshire, Scotland - 2 May 2004 in Oxford, England) British mathematician best-known for his foundational work in the theory of self-avoiding walks and percolation theory. (Wikipedia) when introduced to guests at Trinity College, Oxford, he would say he did difficult sums". He believed passionately in the importance of mathematics with strong links to real-life situations, and in a system of mathematical education in which the solution of problems takes precedence over the generation of theory. He will be remembered for his work on percolation theory, subadditive stochastic processes, self-avoiding walks, and Monte Carlo methods, and, by those who knew him, for his intellectual integrity and his ability to inspire and to challenge. Quite apart from his extensive research achievements, for which he earned a reputation as an outstanding problem-solver, he was a leader in the movement of the 1950s and 1960s to re-think the content of school mathematics syllabuses. (Center for Mathematical Sciences, Cambridge)

During his lifetime, great changes were made in the teaching of mathematics at schools, a matter on which he held strong and opposed, but by no means reactionary, views. He published widely and gave many lectures critical of soft theory at the expense of problem-solving and beauty in mathematics. His best known work, `On the enfeeblement of mathematical skills by `Modern Mathematics' and by similar soft intellectual trash in schools and universities' (published in the Bulletin of the Institute of Mathematics and its Applications, 1968), is now regarded as a force for good at a crossroads of mathematics education. *from his Independent obituary

1927 Halton Christian Arp (21 Mar 1927, ) American astronomer noted for challenging the theory that red shifts of quasars indicate their great distance. Arp is one of the key actors in the contemporary debate on the origin and evolution of galaxies in the universe. His landmark compilation of peculiar galaxies led him to challenge the fundamental assumption of modern cosmology, that redshift is a uniform indicator of distance. Astronomers have debated Arp's assertion that quasars are related to peculiar galaxies since the late 1960's. Most astronomers believe that quasars are unrelated to the peculiar galaxies. Yet, no one has been able to explain why the quasars seem to be more numerous around the peculiar galaxies. *TIS

1951 David Nualart (21 March 1951 - ) is a Spanish mathematician working in the field of probability theory, in particular on aspects of stochastic processes and stochastic analysis.

He obtained his PhD titled "Contribución al estudio de la integral estocástica" in 1975 at the University of Barcelona under the supervision of Francesc d'Assís Sales Vallès. After positions at the University of Barcelona and the Polytechnique University of Barcelona he took up a professorship at Kansas University and is currently the Black-Babcock Distinguished Professor in its Mathematics Department.

He published hundreds of scientific articles in his field, served on several scientific committees, has been an associate editor of many journals and from 2006 to 2008 was the Chief Editor of Electronic Communications in Probability.

He has been elected a Fellow of the Institute of Mathematical Statistics in 1997. He received a Doctor Honoris Causa by the University Blaise Pascal of Clermond-Ferrand in 1998. He received the Prize IBERDROLA de Ciencia y Tecnologia in 1999. He has been a Corresponding Member of the Real Academia de Ciencias Exactas Fisicas y Naturales of Madrid since 2003. He has been a member of the Reial Academia de Ciencies i Arts of Barcelona since 2003. He received the Research Prize of the Real Academia de Ciencias de Madrid in 1991.

In March 2011 the International Conference on Malliavin Calculus and Stochastic Analysis in honor of David Nualart took place at University of Kansas. *Wik

DEATHS

1699 Erhard Weigel (December 16, 1625 – March 21, 1699) was a German mathematician, astronomer and philosopher. He earned his Ph.D. from the University of Leipzig. From 1653 until his death he was professor of mathematics at Jena University. He was the teacher of Leibniz in 1663, and other notable students. He also worked to make science more widely accessible to the public, and what would today be considered a populariser of science. Through Leibniz, Weigel is the intellectual forefather of a long tradition of mathematicians that connects a great number of professionals to this day. The Mathematics Genealogy Project lists more than 50,000 "descendants" of Weigel's, including Lagrange, Euler, Poisson and several Fields Medalists. *WikA post at the Renaissance Mathematicus about Weigel and some of his lesser known students

*(*also pointed out that "Another Weigel innovation in celestial cartography was his eclipse map from 1654. An eclipse map is a map that shows the path on the surface of the earth from which a solar eclipse will be visible. Weigel’s was the first such printed map ever produced. This honor is usually falsely accredited to Edmund Halley for his 1715 eclipse map."

**most**student's would be "lesser known" compared to Leibniz)For religious reasons, he wanted to rename all the constellations, and made several globes of the sky with his renamed constellations.

1762 Abbé Nicolas Louis de Lacaille (15 Mar 1713; 21 Mar 1762 at age 48) was a French astronomer who named 15 of the 88 constellations in the sky. He spent 1750-1754 mapping the constellations visible from the Southern Hemisphere, as observed from the Cape of Good Hope, the southernmost part of Africa. In his years there, he was said to have observed over 10,000 stars using just his 1/2-inch refractor. He established the first southern star catalogue containing 9776 stars (Caelum Australe Stelliferum, published partly in 1763 and completely in 1847), and a catalogue of 42 nebulae in 1755 containing 33 true deep sky objects (26 his own discoveries).*TIS

1822 D'Amondans Charles de Tinseau (19 April 1748 in Besançon, France - 21 March 1822 in Montpellier, France) wrote on the theory of surfaces, working out the equation of a tangent plane at a point on a surface, and he generalised Pythagoras's theorem proving that the square of a plane area is equal to the sum of the squares of the projections of the area onto mutually perpendicular planes. He continued Monge's study of curves of double curvature and ruled surfaces, being in a sense Monge's first follower. Taton writes that Tinseau's works, "... deal with topics in the theory of surfaces and curves of double curvature: planes tangent to a surface, contact curves of circumscribed cones or cylinders, various surfaces attached to a space curve, the determination of the osculatory plane at a point of a space curve, problems of quadrature and cubature involving ruler surfaces, the study of properties of certain special ruled surfaces (particularly conoids), and various results in the analytic geometry of space."

Two papers were published in 1772 on infinitesimal geometry Solution de quelques problèmes relatifs à la théorie des surfaces courbes et des lignes à double courbure and Sur quelques proptiétés des solides renfermés par des surfaces composées des lignes droites. He also wrote Solution de quelques questions d'astronomie on astronomy but it was never published. He did publish further political writings, as we mentioned above, but other than continuing to correspond with Monge on mathematical topics, he took no further part in mathematics. *SAU

1864 Luke Howard, FRS (28 November 1772 – 21 March 1864) was a British manufacturing chemist and an amateur meteorologist with broad interests in science. His lasting contribution to science is a nomenclature system for clouds, which he proposed in an 1802 presentation to the Askesian Society.

He has been called "the father of meteorology" because of his comprehensive recordings of weather in the London area from 1801 to 1841 and his writings, which transformed the science of meteorology. *Wik

1915 Frederick Winslow Taylor (20 Mar 1856, 21 Mar 1915 at age 58) was an American engineer and inventor who is known as the father of scientific management. His system of industrial management has influenced the development of virtually every country enjoying the benefits of modern industry. He introduced a scientific approach (1881) to “time and motion study” while chief engineer at Midvale Steel Company, Philadelphia, Pa. Taylor and his associates used stop-watches to time the laborers as they performed various tasks, counted the number of shovel-loads they each moved, and the load per shovel. Thus he was able to determine an optimum shovel size and length. Such careful observations, aimed at recognizing wasted effort and minimizing time used, increased the efficiency of actions of factory workers.*TIS

1928 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

1933 Enrico D'Ovidio (11 Aug 1842 in Campobasso, Italy - 21 March 1933 in Turin, Italy) D'Ovidio was to work for 46 years in the University of Turin. He was chairman of the Faculty of Science in 1879-80 and rector of the University between 1880 and 1885. Another spell as chairman of the Faculty of Science between 1893 and 1907 ended when he was appointed Commissioner of the Polytechnic of Turin.

Euclidean and noneuclidean geometry were the areas of special interest to D'Ovidio. He built on the geometric ideas which had been introduced by Lobachevsky, Bolyai, Riemann and Cayley. D'Ovidio's most important work is probably his paper of 1877 The fundamental metric functions in spaces of arbitrarily many dimensions with constant curvature.

D'Ovidio also worked on binary forms, conics and quadrics. He had two famous assistants, Peano (1880-83) and Corrado Segre (1883-84). D'Ovidio and Corrado Segre built an important school of geometry at Turin. *SAU

1934 Thomas Muir (25 Aug 1844 in Stonebyres, Falls of Clyde, Lanarkshire, Scotland

- 21 March 1934 in Rondebosch, South Africa) He is noted for a four volume work on the history of determinants. *VFR He also proved an important lemma about determinants of skew symmetric matrices

1960 Sheila Scott Macintyre (née Sheila Scott, April 23, 1910 - March 21, 1960) was a Scottish mathematician well known for her work on the Whittaker constant. Macintyre is also well known for creating a multilingual scientific dictionary: written in English, German, and Russian; at the time of her death, she was working on Japanese.*Wik

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