See Events:1897 |

It is a mathematical fact that the casting of this pebble from my hand alters the center of gravity of the universe.

~Thomas Carlyle

In 2017 on this date was the 5th day of the 2nd month, in 2017 teachers can offer their students, \(Sin(2017 \sqrt[5]{2}) = -1 \) (It's not, but it will give that answer on the Ti-84 calculators (mine does at least.) The true answer is

The 36th day of the year; 36 is the smallest non trivial number which is both triangular and square. It's also the largest day number of the year which is both. What's the next? You can find an infinity of them using this beautiful formula from Euler, Hat Tip to Vincent PANTALONI @panlepan

36 is the sum of the first three cubes, \(1 ^3 + 2^3 + 3^3 = 36\) The sums of the first n cubes is always a square number. \(\sum_{k=1}^n k^3 = (\frac{(n)(n+1)}{2}) ^2\) *Note that this sequence and its formula were known to (and possibly discovered by) Nicomachus, 100 CE*) (There are only two year days that are square numbers that are the sum of three distinct cubes, can you find the square, and ir's cube partitions)

The sum of the first 36 integers, \(\sum_{k=1}^{36} k = 666\) the so called "number of the beast."

And Mario Livio pointed out in a tweet that this is 5/2 in European style dating, and 52 is the maximum number of moves needed to solve the "15" sliding puzzle from any solvable position.

The length of an Inch was decreed by King Edward in 1324 to be “three grains of barley, dry and round, placed end to end lengthwise." Which makes a foot the length of 36 such barleycorns.

The Kiwi's seeds divide the circle into 36 equal sections. Nature's protractor. *Matemolivares@Matemolivares

A special historical tribute to 36: The thirty-six officers problem is a mathematical puzzle proposed by Leonhard Euler in 1782. He asked if it were possible to place officers of six ranks from each of six regiments in a 6x6 square so that no row or column would have an officer of the same rank, or the same regiment. Euler suspected that it could not be done. Euler knew how to construct such squares for nxn when n was odd, or a multiple of four, and he believed that all such squares with n = 4m+2 (6, 10, 14...) were impossible ( Euler didn't say it couldn't be done. He just said that his method does not work for numbers of that form.) Proof that he was right for n=6 took a while. French mathematician (and obviously a very patient man) Gaston Tarry proved it in 1901 by the method of exhaustion. He wrote out each of the 9408 6x6 squares and found that none of them worked. Then in 1959, R.C. Bose and S. S. Shrikhande proved that all the others could be constructed. So the thirty-six square is the *only one that can't be done.*

Orthogonal Latin squares have been known to predate Euler. As described by Donald Knuth the construction of 4x4 set was published by Jacques Ozanam in 1725 (in Recreation mathematiques et physiques, Vol. IV) as a puzzle involving playing cards. The problem was to take all aces, kings, queens and jacks from a standard deck of cards, and arrange them in a 4x4 grid such that each row and each column contained all four suits as well as one of each face value. This problem has several solutions known back to 1725, but no one could figure out how many in all.

A common variant of this problem was to arrange the 16 cards so that, in addition to the row and column constraints, each diagonal contains all four face values and all four suits as well.

According to Martin Gardner, who featured this variant of the problem in his November 1959 Mathematical Games column, the number of distinct solutions was incorrectly stated to be 72 by Rouse Ball. This mistake persisted for many years until the correct value of 144 was found by Kathleen Ollerenshaw. Notice both 72 and 144 are multiples of 36.

**EVENTS**

**1575** Jan De Groot entered the University of Leiden, in the Netherlands, on its opening day. With Simon Stevin he later performed an experiment proving that bodies of different weights fall the same distance in the same time (published 1586 by Stevin). This anti-Aristotelian experiment anticipated Galileo’s famous, but apocryphal, experiment at the Leaning Tower of Pisa. His son Hugo De Groot was a famous jurist. *VFR Thony Christie pointed out that "The anti-Aristotle tower and ball experiment was first carried out by Johannes Philiponus in 6th century CE". Philiponus proposed a kinetic theory for motion in place of Aristotle's impetus.

**1673** Robert Hooke writes in his journal that he had, "Told the Society of Arithmetick engine.*@HookesLondon It is said that Newton had this, and other Hooke items, including Hooke's portrait, removed from the Royal Society after Hooke's death but this does not seem to be supported by most math historians

5 Feb **1675** (OS) 15 Feb 1676(NS) Newton wrote Hooke: "What DesCartes did was a good step....If I have seen further it is by standing on ye sholders of Giants." *VFR

The letter is at the Historical Society of Pennsylvania.

**1689 **The Convention Parliament, with Cambridge U. MP Isaac Newton voting in the majority, declared the throne of England vacant after James II escaped to France with the permission of his Son-in-Law and daughter, William and Mary, who were offered the crown jointly. The only record of a comment by Newton during the Parliament except to ask for a servant to close a drafty window. *Thomas Levenson, Newton and The Counterfeiter.

**1772** Laplace presented his ﬁrst probability memoir to the Acad´emie des Sciences. *VFR

**1796** Schiller (1759–1815) wrote to Goethe (1749–1832): “Wo es die Sache leidet, halte ich es immer f¨ur besser, nicht mit dem Anfang anzufangen, der immer das Schwerste ist.” (I always think it better, whenever possible, not to begin at the beginning, as it is always the most difficult part). Although this is advice from one poet to another, it seems to apply to mathematics, especially the foundations of mathematics. Quoted from Numbers (1990) by H.-D. Ebinghaus et al., p. 6. *VFR

**1835** A ceremony to honor "The Genius and Discoveries of Sir Isaac Newton" was organized by the citizens of the Lincolnshire, his area of birth, a few years after the centennial of his death. By unanimous choice, the committee selected as the speaker, the 19 yr old George Boole. "All present were struck by the youthful age of the speaker and not a little amazed by both his knowledge of the subject and his confident lecturing style."

*Desmond MacHale, The Life and Work of George Boole

**1840** The American Statistical Association held its ﬁrst annual meeting, in Boston. "On November 27, 1839, five men held a meeting in the rooms of the American Education Society at No. 15 Cornhill in Boston, Massachusetts, to organize a statistical society. Its purpose, as stated in the society's first constitution, was to "collect, preserve, and diffuse statistical information in the different departments of human knowledge." Originally called the American Statistical Society, the organization's name was changed to the American Statistical Association (ASA) at its first annual meeting, held in Boston on February 5, 1840. " *Robert L. Mason, ASA: The First 160 Years

**1843** The great comet of 1843, A night-time view showing an eyewitness account of the Great Comet of 1843, painted by the astronomer Charles Piazzi Smyth. The earliest observation occurred on the evening of 5 of February, 1843 and Smyth recorded its appearance at the Royal Observatory, Cape of Good Hope, South Africa between 3 and 6 of March. When at its greatest brilliance, it was visible only from southern latitudes. The view in the painting is probably taken from the Observatory. It shows Table Bay with Table Mountain visible in the background on the left. A large sailing ship sits in the foreground on the right, with other shipping in the distance. One of the great British astronomers, Smyth was 42 years Astronomer Royal for Scotland. *Royal Museums Greenwich

**1850** D. D. Parmalee issued a patent (US Patent # 7074) for the ﬁrst key-driven adding machine. *VFR

While this was the first US patent, an earlier key-driven machine had been patented "as early as 1844 by Jean-Baptiste Schwilgue´ (1776– 1856), together with his son Charles. Jean-Baptiste Schwilgue´ was the architect of Strasbourg’s third astronomical clock during the years 1838–1843. He was trained as a clockmaker, but also became professor of mathematics,weights and measures controller, and an industry man, whose particular focus was on improving scales." *Denis Roegel, An Early (1844) Key-Driven Adding Machine, IEEE Annals of the History of Computing, Volume 30, Number 1, January-March 2008, pp. 59-65

In **1897**, the Indiana State House legislature presented Bill No.246 which in effect gave 3.2 exactly as the value of pi. It stated, in part, "the ratio of the diameter and circumference [pi] is as five-fourths to four." That is (4 divided by 5/4) = 16/5 = 3.2 exactly. It was introduced by Representative Taylor I. Record, a farmer and lumber merchant, on behalf of a mathematical hobbyist, Dr. Edwin J. Goodwin, M.D. Neither they, nor the House politicians, understood it was mathematically incorrect. That was shortly recognized by Clarence A. Waldo, mathematics professor at Purdue University, who advised the Indiana Senators. They indefinitely postponed the bill on 12 Feb 1897. Pi is, in fact, an irrational number, approx. 3.141592.*TIS

The Committee on Education, reported favorably and following a motion to suspend the rules, the bill passed on February 6, 1897 without a dissenting vote. Although called the "Pi" bill, it did not use the name. The bill also reported that the square root of two would be 10/7. *Wik

**1901** Loop-the-loop centrifugal RR (roller coaster) patented by Ed Prescot. (I have also seen the date of patent as August 16, 1898. This date is now the National Roller Coaster Day in the US. ) Prescott,an inventor and mechanic from Arlington, Massachusetts. Prescott’s Loop the Loop coaster, a dual-tracked steel roller coaster, was installed at Coney Island, New York from 1901 to 1910. It seems more people came to look, than to ride.

No more looping roller coasters were built until 1976 when Revolution opened at Six Flags Magic Mountain.*Wik

The vertical loop is not a recent roller coaster innovation. Its origins can be traced back to the 1850s when centrifugal railways were built in France and Great Britain. In 1901 Prescott built the Loop-the-Loop at Coney Island.

*Smithsonian Mag

**1920 **Discussion on the theory of relativity by J. H. Jeans – a meeting of the Royal Society, *Royal Society Journal, HT Katharina H Mathsbooks

**1924** The Royal Greenwich Observatory begins broadcasting the time "pips" on BBC, a series of six short tones broadcast at one-second intervals by many BBC Radio stations. The pips were introduced in 1924 and have been generated by the BBC since 1990. The pips were the idea of the Astronomer Royal, Sir Frank Watson Dyson, and the head of the BBC, John Reith.*Wik

This eight-day wall-mounted astronomical regulator by Edward John Dent & Co was originally made for use in observing the Transit of Venus in 1874. In 1923 it was adapted as the primary standard for the new six-pip time signal. The clock sent electrical impulses down a telephone wire to the BBC for conversion into audio pips for radio broadcasts. It has a zinc tube temperature-compensated pendulum and was corrected from 1929 by the Shortt master clock number 16. The three sets of contacts for closing the six-pip circuit every quarter of an hour can be seen in two of the holes within the seconds dial, and halfway down the pendulum, operated by a roller. This clock was in service for the BBC signal at the Observatory from 1924 to 1949, when it was superseded by a quartz clock. *Royal Observatory Greenwich

**1958** Kilby Files a Patent for the Integrated Circuit. Jack Kilby of Texas Instruments files a patent application called miniaturized electronic circuits for his work on a multi-transistor device. The patent was only one of 60 that Kilby holds. While Kilby has the earliest patent on the integrated circuit, it was Robert Noyce, later co-founder of Intel, whose parallel work resulted in a practical device. Kilby's device had several transistors connected by flying wires while Noyce devised the idea of interconnection via a layer of metal conductors. Noyce also adapted Jean Hoerni's planar technique for making transistors to the manufacture of more complex circuits. *CHM

*Wik |

In **1962**, the Sun, the Moon, and the five naked-eye visible planets - Mercury, Venus, Mars, Jupiter, and Saturn - were in conjunction. Though not in a straight line along their orbital paths, as viewed in the sky, they were within 16 degrees of each other (meaning all appeared within a circle just 16 º across). This conjunction coincided with a total solar eclipse, which made viewing Mercury, Venus, Mars, Jupiter, and Saturn possible for a brief period of time from a small stretch of Earth where the eclipse's shadow hit. The five naked-eye visible planets cluster together in the sky within a circle 25 degrees or less in diameter once every 57 years, on average. The next time in the 21st century that this will happen is 8 Sep 2040. *TIS (image...In May of 2011 a planetary conjunction of Mercury, Venus, Mars and Jupiter appeared very close to each other in the sky.) And for St. Valentines day this year (2012) I have ordered up a conjunction with Mercury and Neptune less than 1.5 ^{o} apart for my beautiful Jeannie, but the rest of you may enjoy it as well.

1974 US Mariner 10 returns 1st close-up photos of Venus' cloud structure**2040** The near-Earth asteroid 2011 AG5 currently has an impact probability of 1 in 625 for Feb. 5, 2040, according to Donald Yeomans, head of the Near-Earth Object Observations Program at NASA’s Jet Propulsion Laboratory in Pasadena, California. Made using an ultraviolet filter in its imaging system, the photo has been color-enhanced to bring out Venus's cloudy atmosphere as the human eye would see it. Venus is perpetually blanketed by a thick veil of clouds high in carbon dioxide and its surface temperature approaches 900 degrees Fahrenheit.

Launched on Nov. 3, 1973 atop an Atlas-Centaur rocket, Mariner 10 flew by Venus in 1974.

**BIRTHS**

**1608 Caspar Schott **SJ, and Gaspar Schott or Kaspar Schott (February 5 1608 in Königshofen, May 22 1666 in Würzburg) was a scientific author and educator.

Schott attended the Würzburg Jesuit High School and entered the Order in 1627. During his studies in Würzburg one of his teachers was Athanasius Kircher. When the Jesuits fled before the approaching Swedish army in 1631,Schott went to Palermo to complete his studies. He stayed in Sicily 20 years as a teacher of mathematics, philosophy, moral theology at the Jesuit school in Palermo. In 1652 was sent to Rome as support in the scientific work of Kircher. He decided to publish Kircher's work. In 1655, he returned as Professor in the Würzburg school, where he taught mathematics and physics. He was Hofmathematker and confessor of the Elector Johann Philipp von Schönborn who had just purchased the vacuum pump invented by Otto von Guericke and used at Magdeburg.

He corresponded with leading scientists including Otto von Guericke, Christiaan Huygens, and Robert Boyle. The term "technology" was probably invented by Schott in his "Technica curiosa" which inspired Boyle and Hooke's vacuum experiments.

In the posthumously published work Organum mathematicum he describes his Cistula invented by him, a computing device, by Kircher with which you can multiply and divide.

The device described in Schott's book was divided by functionality into 9 main sections, each of which contained approximately 24 rods.

Arithmetic The arithmetic rods included a set of Napier's Bones. They were capable of assisting with the multiplication of multi-digit numbers and producing quotients.

Geometry The rods in this section could aid in determining heights, by use of a geometric square.

Fortifications The rods in this section could aid in determining the design of bulwarks in fortification plans.

ChronologynThe rods in this section could be used to determine the date of Easter and other church holidays which were positioned relative to it. These rods simply contained a table of upcoming dates.

Horography The rods in this section contained information needed to construct sundials.

Astronomy This compartment had tablets which resembled those found in an almanac. For each day of the year, the length of the day and night, the times for sunrise and sunset, and the duration of morning and evening twilight were provided. All the information was based on measurements taken at 48 degrees latitude (Vienna).

Astrology This section had tables describing movements for the visible planets, and the constellation Draco, and also provided astrological interpretations for the 12 zodiac signs.

Cryptography The rods in this section could be used to encrypt and decrypt text using a cyclic transposition cypher, based on a keyword.

Music The rods in this section could be used by non musicians to compose church music. The system used was the same as that used for Kircher's previous device, the Arca Musarithmica. They contained sets of musical phrases which could be combined randomly to set verses to music, producing millions of hymns in 4-part harmony.*Wik

the Organum Mathematicum at the Museo Galileo in Florence, Italy.

**1797 Jean-Marie-Constant Duhamel** (5 Feb 1797; 29 Apr 1872) French mathematician and physicist who proposed a theory dealing with the transmission of heat in crystal structures based on the work of the French mathematicians Jean-Baptiste-Joseph Fourier and Siméon-Denis Poisson. *TIS

**1836 Alexander Stewart Herschel** (5 February 1836 – 18 June 1907) was a British astronomer, born in Feldhausen, South Africa.

He was the son of John Herschel and the grandson of William Herschel. Although much less well known than either of them, he did pioneering work in meteor spectroscopy. He also worked on identifying comets as the source of meteor showers. The Herschel graph, the smallest non-Hamiltonian polyhedral graph, is named after Herschel due to his pioneering work on Hamilton's Icosian game. *Wik

The image of the graph at right is from Christian Perfect at the Aperiodical Blog. You can’t draw a path on it that visits each vertex exactly once, but you can make a polyhedron whose vertices and edges correspond with the graph exactly. It’s also bipartite – you can color the vertices using two colors so that edges only connect vertices of different colors.

I think the polyhedron is the only enneahedron (9 faces children) that has all quadrilateral faces. You can see the solid here.

**1907 Wilhelm Magnus** (February 5, 1907, Berlin, Germany – October 15, 1990, New York City) made important contributions in combinatorial group theory, Lie algebras, mathematical physics, elliptic functions, and the study of tessellations.*Wik

**1915 Robert Hofstadter** (5 Feb 1915, 17 Nov 1990) American scientist who was a joint recipient of the Nobel Prize for Physics in 1961 for his investigations in which he measured the sizes of the neutron and proton in the nuclei of atoms. He revealed the hitherto unknown structure of these particles and helped create an identifying order for subatomic particles. He also correctly predicted the existence of hte omega-meson and rho-meson. He also studied controlled nuclear fission. Hofstadter was one of the driving forces behind the creation of the Stanford Linear Accelerator. He also made substantial contributions to gamma ray spectroscopy, leading to the use of radioactive tracers to locate tumors and other disorders.*TIS

**1930 Urbanik Kazimierz** (born 5 February 1930 in Krzemieniec - 29 May 2005 in Wrocław ) - Polish mathematician, rector of the University of Wroclaw ( 1975 - 1981 ), Doctor Honoris Causa of the University of Lodz and the Technical University of Wroclaw. He dealt with problems from different fields of mathematics, but his research interests were focused on the theory of probability . He obtained several important results in the theory of stochastic processes , information theory , theoretical physics , universal algebra , topology and measure theory . He published about 180 scientific papers. *Wik

**DEATHS**

**1881 Thomas Carlyle** (4 Dec 1795 in Ecclefechan, Dumfriesshire, Scotland - 5 Feb 1881 in Chelsea, London, England) was a Scottish writer who was also interested in mathematics. He translated Legendre's work.*SAU

**1939 Gheorghe Ţiţeica** ((October 4, 1873–February 5, 1939) publishing as George or Georges Tzitzeica) was a Romanian mathematician with important contributions in geometry. He is recognized as the founder of the Romanian school of differential geometry.*Wik

**1977 Oskar Benjamin Klein** (September 15, 1894 – February 5, 1977) was a Swedish theoretical physicist. Klein retired as professor emeritus in 1962. He was awarded the Max Planck medal in 1959. He is credited for inventing the idea, part of Kaluza–Klein theory, that extra dimensions may be physically real but curled up and very small, an idea essential to string theory / M-theory. *Wik

**1980 Nachman Aronszajn **(26 July 1907, Warsaw, Poland – 5 February 1980 Corvallis, Oregon, U.S) was a Polish American mathematician of Ashkenazi Jewish descent. Aronszajn's main field of study and expertise was mathematical analysis. He also contributed to mathematical logic.

He received his Ph.D. from the University of Warsaw, in 1930, in Poland. Stefan Mazurkiewicz was his thesis advisor. He also received a Ph.D. from Paris University, in 1935; this time Maurice Fréchet was his thesis advisor. He joined the Oklahoma A&M faculty, but moved to the University of Kansas in 1951 with his colleague Ainsley Diamond after Diamond, a quaker, was fired for refusing to sign a newly-instituted loyalty oath. Aronszajn retired in 1977. He was a Summerfield Distinguished Scholar from 1964 to his death.

He introduced, together with Prom Panitchpakdi, the injective metric spaces under the name of "hyperconvex metric spaces". Together with Kennan T. Smith, Aronszajn offered proof of the Aronszajn–Smith theorem. Also, the existence of Aronszajn trees was proven by Aronszajn; Aronszajn lines, also named after him, are the lexicographic orderings of Aronszajn trees.

He also has a fundamental contribution to the theory of reproducing kernel Hilbert space, the Moore–Aronszajn theorem is named after him. *Wik

**1988 Dorothy Lewis Bernstein** (April 11, 1914 – February 5, 1988) was an American mathematician known for her work in applied mathematics, statistics, computer programming, and her research on the Laplace transform.

Dorothy Bernstein was born in Chicago, the daughter of Russian immigrants to the US. She was a member of the American Mathematical Society and the first woman elected president of the Mathematical Association of America. Due in great part to Bernstein's ability to get grants from the National Science Foundation, Goucher College (where she taught for decades) was the first women's university to use computers in mathematics instruction in the 1960s.*Wik

**1997 Frederick Justin Almgren**,(3 July 1933 in Birmingham, Alabama, USA - 5 Feb 1997 in Princeton, USA) Almost certainly Almgren's most impressive and important result was only published in 2000, three years after his death. Why was this? The paper was just too long to be accepted by any journal. Brian Cabell White explains the background in a review of the book published in 2000 containing the result:

By the early 1970s, geometric analysts had made spectacular discoveries about the regularity of mass-minimizing hypersurfaces. (Mass is area counting multiplicity, so that if k sheets of a surface overlap, the overlap region is counted k times.) In particular, the singular set of an m-dimensional mass-minimizing hypersurface was known to have dimension at most m - 7. By contrast, for an m-dimensional mass-minimizing surface of codimension greater than one, the singular set was not even known to have m-measure 0. Around 1974, Almgren started on what would become his most massive project, culminating ten years later in a three-volume, 1700-page preprint containing a proof that the singular set not only has m-dimensional measure 0, but in fact has dimension at most (m - 2). This dimension is optimal, since by an earlier result of H Federer there are examples for which the dimension of the singular set is exactly (m - 2). ...

Now, thanks to the efforts of editors Jean Taylor and Vladimir Scheffer, Almgren's three-volume, 1700-page typed preprint has been published as a single, attractively typeset volume of less than 1000 pages.

Fred Almgren received many honours for his outstanding contributions. He was an Alfred P Sloan Fellow in 1968-70, an Exchange Visitor at the Steklov Mathematical Institute in Leningrad in 1970, a John Simon Guggenheim Memorial Fellow in 1974-75, and Earle Raymond Hedrick Lecturer for the Mathematical Association of America in1975. He was elected a fellow of the American Association for the Advancement of Science in 1982, was awarded a medallion by Brown University in 1988:-

... in recognition of distinguished contributions to society through scholarship and professional activity ...

and he received the Class of 55 Public Service Award from Princeton University in 1988:-

... for contributions to society beyond the bounds of occupation.

Among his service we should mention he was an editor of three journals: the Journal of Experimental Mathematics, the Journal of Geometric Algebra, and Differential Geometry and its Applications. He administered the Geometry Supercomputer Project for the Geometry Computing Group and served on the American Mathematical Society Committee on Applications of Mathematics.*SAU

Photograph by Paul Halmos

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

## No comments:

Post a Comment