## Saturday 9 March 2024

### On This Day in Math - March 9

 Waldsemuller 1507 first map to use the name "America" *Wik

Don't worry about people stealing your ideas. If your ideas are any good, you'll have to ram them down people's throats.
~Howard Aiken

The 68th day of the year; if you searched through pi for all the two digit numbers, the last one you would find is 68. The string 68 begins at position 605 counting from the first digit after the decimal point. (What is the last single digit numeral to appear? One might wonder how far out the string would you have to go to find all possible three digit numbers? )

68 is the largest known number to be the sum of two primes in exactly two different ways: 68=7+61=31+37.

68 is a stobogrammatic number, rotated it is 89. Some consider only invertible numbers (rotated they form the same value, like 181) as strobograms. HT to Paul O'Malley

There are exactly 68 ten digit binary numbers in which each digit is the same as one of it's adjacent digits.

The numbers on the two diagonals of Durer's Melencolia add up to 68.  All the numbers not on the two main diagonals also add up to 68, but that's just the teaser.  The sum of the squares of the numbers in each group sum to 748.....Not impressed?  Try the sum of the cubes of each group...Yep also equal, their sums are each 9248....Now That's Magic...Math Magic!

$2^{68} = 295147905179352825856$, notice anything? Every digit 0 through 9 is included. There is no smaller power of two for which this is true.*@fermatslibrary

68 is the smallest composite number that can be read as a prime number when it is rotated 180o HT Jim Wilder @wilderlab.

And a historical oddity, in 46 BCE, as a result of Julius Caesar's Calendar adjustment, there were 68 days inserted between November and December.

EVENTS

1497 Copernicus, then a student of canon law at the University of Bologna, made his ﬁrst recorded astronomical observation. Working with Domenica Maria Novara, a professor of astronomy at the university, from whom he rented a room, they observed an occultation of the star aldebaran by the moon. He will later mention this as one of the influential experiences in shaping his new theory.

In 1611, (Mar 9 (NS),Feb 27 (OS)) Johannes Fabricius, a Dutch astronomer, observed the rising sun through his telescope, and observed several dark spots on it. This was perhaps the first ever observation of sunspots. (This is not true, see below) He called his father to investigate this new phenomenon with him. The brightness of the Sun's center was very painful, and the two quickly switched to a projection method by means of a camera obscura. Johannes was the first to publish information on such observations. He did so in his Narratio de maculis in sole observatis et apparente earum cum sole conversione. ("Narration on Spots Observed on the Sun and their Apparent Rotation with the Sun"), the dedication of which was dated 13 Jun 1611. *TIS
In 1611 Fabricius’ son Johannes brought home a telescope from the University of Leiden where he was studying medicine. With this instrument the father and son, with the son this time in the leading role, discovered the sunspots. Although they were not the first European astronomers to make this discovery, this honor goes to Thomas Harriot, Johannes Fabricius was the first to publish it in his De Maculis in Sole in 1611. Unfortunately his publication went largely unnoticed and is not mentioned at all by Galileo and Christoph Scheiner in their monumental argument as to who first discovered the sunspots. *RMAT (correct answer, neither of them)
(though unclear statements in East Asian annals suggest that Chinese and Korean astronomers may have discovered them with the naked eye previously, and Fabricius may have noticed them himself without a telescope a few years before).
The first known drawing of sunspots dates back to John of Worcester in 1128.

 John of Wooster drawing

1671 Hooke demonstrates vibration due to sound. For the benefit of two visiting Italian noblemen, Hooke shows how flour "moves like a liquid" when placed in a broad shallow glass when it is struck or vibrated. The flour would rise up the edge of the glass and run over. *Stephen Inwood, The Forgotten Genius

1736 Euler receives a letter challenging him to solve the Konigsburg Bridge Problem.
"Carl Leonhard Gottlieb Ehler was the mayor of Danzig in Prussia (now Gdansk in Poland), some 80 miles west of Kinigsberg. He corresponded with Euler from 1735 to 1742, acting as intermediary for Heinrich Kuhn, a local mathematics professor. Their initial communication has not been recovered, but a letter of 9 March 1736 indicates they had discussed the problem and its relation to the 'calculus of position':
You would render to me and our friend Kiihn a most valuable service, putting us greatly in your debt, most learned Sir, if you would send us the solution, which you know well, to the problem of the seven Kinigsberg bridges, together with a proof. It would prove to be an outstanding example of the calculus of position [Calculi Situs], worthy of your great genius. I have added a sketch of the said bridges ... "
*Brian Hopkins, Robin Wilson; The Truth About Konigsberg

1832 Wolfgang Bolyai made a corresponding member of the mathematics section of the Magyar Academy. *Bonola, Non-Euclidean Geometry, Appendix 1, p. xxv

In 1893, Professor James Dewar communicated to the meeting of the Royal Society that he had succeeded in freezing air into a clear, transparent solid. The precise nature of this solid was not known, and needed further research. It was speculated that it may be “a jelly of solid nitrogen containing liquid oxygen, much as calves'foot jelly contains water diffused in solid gelatine. Or it may be a true ice of liquid air, in which both oxygen and nitrogen exist in the solid form.” At this time, Dewar had not been able to solidify pure oxygen, although nitrogen had been frozen with comparative ease. It also had already been proved that in the evaporation of liquid air, nitrogen boils off first.*TIS

1914  The Mining and Metallurgical Society held a dinner to bestow its first gold medal  on future President Herbert Hoover, and his wife Lou Henry Hoover for their joint translation of Georgius Agricola's De Re Metallica.(1556)  Both Hovers had earned bachelor degrees in geology from Stanford.  It is said that the future First Lady bore most of the "heavy lifting" in the translation. The President was poor at languages.

1951 Edward Teller and Stanislaw Ulam submit a classified paper at the Los Alamos lab, in which they proposed their revolutionary new design, staged implosion, for a practical megaton-range hydrogen bomb.

1961 Korabl-Sputnik 4 or Vostok-3KA No.1, also known as Sputnik 9 in the West, was a Soviet spacecraft which was launched on 9 March 1961. Carrying the mannequin Ivan Ivanovich, a dog named Chernushka, some mice and the first guinea pig in space, it was a test flight of the Vostok spacecraft. *Wik

1993 PowerOpen Association Formed: Apple Computer Inc., Motorola Inc., IBM Corp. and four other computer companies form the PowerOpen Association Inc., intended to promote new computer chip technology in preparation for the release of the next generation of personal computers. The association also tested conformance to the PowerOpen environment, which led to computers such as Apple's Power PC. *CHM

BIRTHS

1451 Amerigo Vespucci (9 Mar 1451; died 22 Feb 1512 at age 60. ), Italian navigator, who claimed to have reached North and South America in 1498. It is after him that the continents are named. *VFR
Waldsemuller 1507 first map to use the name "America" *Wik

1564 David Fabricius(9 Mar 1564; died 7 May 1617 at age 53) A German astronomer, friend of Tycho Brahe and Kepler, and one of the first to follow Galileo in telescope observation of the skies. He is best known for a naked-eye observation of a star in Aug 1596, subsequently named Omicron Ceti, the first variable star to be discovered, and now known as Mira. Its existence with variable brightness contradicted the Aristotelian dogma that the heavens were both perfect and constant. With his son, Johannes Fabricius, he observed the sun and noted sunspots. For further observations they used a camera obscura and recorded sun-spot motion indicating the rotation of the Sun. (David Fabricius wrote to Michael Maestlin (Kepler's old teacher) that he did not believe the spots were on the Sun's body, although the center of their motions clearly lay in the Sun. *Galileo Project)
Kepler had studied the stars and planets with a camera obscura that had a lens to sharpen the view in 1600.(he coined the term camera obscura in 1604 from the Latin for dark chamber or dark room. Before the term camera obscura was first used, other terms were used to refer to the devices: cubiculum obscurum, cubiculum tenebricosum, conclave obscurum, and locus obscurus.)
Fabricius, a Protestant minister, was killed by a parishioner angered upon being accused by him as a thief. *TIS (after denouncing a local goose thief from the pulpit, the accused man struck him in the head with a shovel and killed him.. *Wik)
 *Wik

[re: invented, The Camera Obscura (Latin for dark room) was a dark box or room with a hole in one end. If the hole was small enough, an inverted image would be seen on the opposite wall. Such a principle was known by thinkers as early as Aristotle (c. 300 BC). It is said that Roger Bacon invented the camera obscura just before the year 1300, but this has never been accepted by scholars; more plausible is the claim that he used one to observe solar eclipses. In fact, the Arabian scholar Hassan ibn Hassan (also known as Ibn al Haitam), in the 10th century, described what can be called a camera obscura in his writings..]  The image is the first published picture of camera obscura in Gemma Frisius' 1545 book De Radio Astronomica et Geometrica

1818 Ferdinand Joachimsthal (9 March 1818 in Goldberg, Prussian Silesia (now Złotoryja, Poland) - 5 April 1861 in Breslau, Germany (now Wrocław, Poland)) Influenced by the work of Jacobi, Dirichlet and Steiner, Joachimsthal wrote on the theory of surfaces where he made substantial contributions, particularly to the problem of normals to conic sections and second degree surfaces.
Joachimsthal applied the theory of determinants to geometry. He made the important step of introducing oblique coordinates. Joachimsthal surfaces are named after him, these have a family of plane lines of curvature within the plane of a pencil. He has a theorem named after him which concerns the intersection of surfaces. He is also remembered for another theorem on the four normals to an ellipse from a point inside it. *SAU  His name is derived from the region in Silesia which was rich in Silver.  Coins made with the silver were called "daler", from German T(h)aler, short for Joachimsthaler, a coin from the silver mine of Joachimsthal (‘Joachim's valley’), now Jáchymov in the Czech Republic. The term was later applied to a coin used in the Spanish American colonies, which was also widely used in the British North American colonies at the time of the American War of Independence, hence adopted as the name of the US monetary unit in the late 18th century.

1824 Birthdate of Leland Stanford, the American railroad builder and capitalist who founded Stanford University in 1885. *VFR

1852 Constantin Marie Le Paige (9 March 1852 in Liège, Belgium - 26 Jan 1929 in Liège, Belgium) worked on the theory of algebraic forms, a topic whose study was initiated by Boole in 1841 and then developed by Cayley, Sylvester, Hermite, Clebsch and Aronhold. In particular Le Paige studied the geometry of algebraic curves and surfaces, building on this earlier work. He is best known for his construction of a cubic surface given by 19 points.
Le Paige studied the generation of plane cubic and quartic curves, developing further Chasles's work on plane algebraic curves and Steiner's results on the intersection of two projective pencils.
The history of mathematics was another topic which interested Le Paige. He published Sluze's correspondence with Pascal, Huygens, Oldenburg and Wallis. *SAU

1900 Howard Hathaway Aiken (9 Mar 1900; 14 Mar 1973 at age 72) American mathematician who invented the Harvard Mark I, forerunner of the modern electronic digital computer. While a graduate student and instructor Harvard University, Aiken's research had led to a system of differential equations which could only be solved using numerical techniques, for which he began planning large computer. His idea was to use an adaptation of Hollerith's punched card machine. When eventually built, (1943) it weighed 35 tons, had 500 miles of wire and could compute to 23 significant figures. There were 72 storage registers and central units to perform multiplication and division. It was controlled by a sequence of instructions on punched paper tapes, and used punched cards to enter data and give output from the machine. *TIS

1923 Walter Kohn (March 9, 1923 – April 19, 2016)  Austrian-American physicist who shared (with John A. Pople) the 1998 Nobel Prize in Chemistry. The award recognized their individual work on computations in quantum chemistry. Kohn's share of the prize acknowledged his development of the density-functional theory, which made it possible to apply the complicated mathematics of quantum mechanics to the description and analysis of the chemical bonding between atoms. *TIS
"Paris somehow lends itself to conceptual new ideas. There is a certain magic to that city." (Thanks to Arjen Dijksman)

1948 László Lovász (March 9, 1948 - ) is a Hungarian mathematician, best known for his work in combinatorics, for which he was awarded the Wolf Prize and the Knuth Prize in 1999, and the Kyoto Prize in 2010.*Wik

DEATHS
886 Abu masar (10 Aug 787, 9 Mar 886 at age 98)Persian astrologer, a.k.a. Abu Ma'shar al-Balkhi, or Ja'far ibn Muhammad, who was the leading astrologer of the Muslim world. He is known primarily for his theory that the world, created when the seven planets were in conjunction in the first degree of Aries, will come to an end at a like conjunction in the last degree of Pisces. *TIS
His discourses incorporated and expanded upon the studies of earlier scholars of Islamic, Persian, Greek, and Mesopotamian origin. His works were translated into Latin in the 12th century and, through their wide circulation in manuscript form, had a great influence on Western scholars. Kitab al-Mudkhal al-Kabīr (Great introduction) is his most important work and the one most frequently cited by scholars in the West. It contains an astrological theory on the nature of the moon's influence on the tides and was the key work on the subject during the Middle Ages. This edition is the 1140 translation into Latin by Hermann of Carinthia, first printed by Erhard Ratdolt in Augsburg, Germany, in 1489. The woodcut title vignette of a black-faced astronomer reading the stars with an astrolabe and dividers is one of the best-known Renaissance representations of an astronomer. *Library of Congress

1833 Jacques Frédéric Français (20 June 1775 in Saverne, Bas-Rhin, France - 9 March 1833 in Metz, France) In September 1813 Français published a work in which he gave a geometric representation of complex numbers with interesting applications. This was based on Argand's paper which had been sent, without disclosing the name of the author, by Legendre to François Français. Although Wessel had published an account of the geometric representation of complex numbers in 1799, and then Argand had done so again in 1806, the idea was still little known among mathematicians. This changed after Français' paper since a vigorous discussion between Français, Argand and Servois took place in Gergonne's Journal. In this argument Français and Argand believed in the validity of the geometric representation, while Servois argued that complex numbers must be handled using pure algebra. *SAU
Argand diagram

1851 Hans Christian Oersted (14 Aug 1777, 9 Mar 1851 at age 73) Danish physicist and chemist whose discovery (1820) that an electric current in a wire causes a nearby magnetized compass needle to deflect, indicating the electric current in a wire induces a magnetic field around it, marks the starting point for the development of electromagnetic theory. For this, he can be called “the father of electromagnetism,” for which his name was adopted for the magnetic field strength in the CGS system of units (for which the SI system now uses the henry unit). Philosophically, he had believed nature's forces had a common origin. Oersted was the first to isolate aluminum as a metal (1825). He also made the first accurate determination of the compressibility of water (1822). Late in his career, he researched diamagnetism. In his final years, he turned back to philosophy, and started writing The Soul in Nature. *TIS

1866 Edmond Bour (19 May 1832 in Gray, Haute-Saône, France - 9 March 1866 in Paris, France)Bour made many significant contributions to analysis, algebra, geometry and applied mechanics despite his early death from an incurable disease. His remarkable achievements were cut short at the age of 33 and as a consequence Bour is hardly known in the history of mathematics whereas one feels that if he had been given the chance to continue his outstanding work he would today be remembered as one of the major figures in the subject. *SAU

1917 Agnes Sime Baxter (Hill) (18 March 1870 – 9 March 1917) was a Canadian-born mathematician. She studied at Dalhousie University, receiving her BA in 1891, and her MA in 1892. She received her Ph.D. from Cornell University in 1895; her dissertation was “On Abelian integrals, a resume of Neumann’s ‘Abelsche Integrele’ with comments and applications." *Wik
It must have been a difficult time for a woman such as Baxter taking what were considered at that time to be men's subjects. Although few women studied mathematics, Baxter was not the only one studying mathematics at Dalhousie; for example there were two other women in the class of 24 that studied second level mathematics with her. Her performance at university was outstanding and she was awarded a distinction and received the Sir William Young Gold Medal. With the award of her B.A. degree Baxter became the first ever woman to graduate with honours from Dalhousie University. But more than this, she had been clearly the best student in both mathematics and mathematical physics.
When she graduated in 1895, Baxter became only the second Canadian woman to be awarded Ph.D. in Mathematics. On a wider scale, she was only the fourth woman to receive such a degree in the whole of North America.*SAU

1923 Johannes Diederik van der Waals (23 Nov 1837; 9 Mar 1923) Dutch physicist, winner of the 1910 Nobel Prize for Physics for his research on the gaseous and liquid states of matter. He was largely self-taught in science and he originally worked as a school teacher. His main work was to develop an equation (the van der Waals equation) that - unlike the laws of Boyle and Charles - applied to real gases. Since the molecules do have attractive forces and volume (however small), van der Waals introduced into the theory two further constants to take these properties into account. The weak electrostatic attractive forces between molecules and between atoms are called van der Waals forces in his honour. His valuable results enabled James Dewar and Heike Kamerlingh-Onnes to work out methods of liquefying the permanent gases. *TIS

1931 Ivan Vladislavovich Sleszynski (23 July 1854 in Lysianka, Cherkasy, Kiev gubernia, Ukraine - 9 March 1931 in Kraków, Poland)Sleszynski's main work was on continued fractions, least squares and axiomatic proof theory based on mathematical logic. In a paper of 1892, based on his doctoral dissertation, he examined Cauchy's version of the Central Limit Theorem using characteristic function methods, and made several significant improvements and corrections. Because of the work, he is recognised as giving the first rigorous proof of a restricted form of the Central Limit Theorem. *SAU

1942 Mykhailo Pilipovich Krawtchouk (27 Sept 1892 in Chovnitsy, (now Kivertsi) Ukraine - 9 March 1942 in Kolyma, Siberia, USSR) In 1929 Krawtchouk published his most famous work, Sur une généralisation des polynômes d'Hermite. In this paper he introduced a new system of orthogonal polynomials now known as the Krawtchouk polynomials, which are polynomials associated with the binomial distribution.
However his mathematical work was very wide and, despite his early death, he was the author of around 180 articles on mathematics. He wrote papers on differential and integral equations, studying both their theory and applications. Other areas he wrote on included algebra (where among other topics he studied the theory of permutation matrices), geometry, mathematical and numerical analysis, probability theory and mathematical statistics. He was also interested in the philosophy of mathematics, the history of mathematics and mathematical education. Krawtchouk edited the first three-volume dictionary of Ukrainian mathematical terminology. *SAU
Mykhailo Krawtchouk was arrested on February 21, 1938. He was charged with a
membership in an underground Ukrainian nationalist and terrorist organization and spying.
The accusation of a membership in such fictitious organizations was a typical charge
against the country’s intellectuals during the Great Terror. The allegations of stemmed
from the fact that Krawtchouk closely identified with Ukrainian culture, playing a major
role in developing Ukrainian mathematical terminology and mathematical education.
On September 23, 1938, in a trial lasting one half-hour, the Military Collegium of the Supreme Court of the USSR sentenced Krawtchouk to 20 years in prison and 5 years in exile. Mykhailo Krawtchouk
was assigned to perform heavy manual work in a gold mine in Kolyma region, one of the coldest and most uninhabitable places on the planet. Like a large proportion of political prisoners, Krawtchouk did not survive the Kolyma camps.

1954 V(agn) Walfrid Ekman (3 May 1874, 9 Mar 1954 at age 79) Swedish physical oceanographer and mathematical physicist whose research into the dynamics of ocean currents led to his name remaining associated with terms for particular phenomena of the ocean or atmosphere, including Ekman spiral, Ekman transport and Ekman layer. Fridtjof Nansen pointed out to Ekman that he had noticed that icebergs drift at an angle of 20°-40° to the prevailing wind, rather than directly with the wind. In 1902, Ekman published an explanation, known now as the Ekman spiral, describing movement of ocean currents influenced by the Earth's rotation. He also developed experimental techniques and instruments such as the Ekman current meter and Ekman water bottle.*TIS

1962 Dr. Howard T. Engstrom (23 Jun 1902, 9 Mar 1962 at age 59) American computer designer who promoted the first commercially available digital computer, the Univac. As a Yale professor he had written a paper on the mathematical basis for cryptanalysis techniques. During WW II he was called to the Navy and placed in command of the OP-20-G automated machines "Research Section" for message decryption. After the war, he was a co-founder of Engineering Research Associates, a private company to work on electronic digital circuit technology for the Navy on a contract basis, with former Navy researchers. ERA delivered its first Atlas computer to the National Security Agency in Dec 1950. As vice president for research, Engstrom took the initiative to make a commercial version, renamed Univac. *TIS

1981 Max Ludwig Henning Delbrück (September 4, 1906 – March 9, 1981)
Delbrück was a German-American biophysicist and Nobel laureate.
Delbrück studied astrophysics, shifting towards theoretical physics, at the University of Göttingen. After receiving his Ph.D. in 1930, he traveled through England, Denmark, and Switzerland. He met Wolfgang Pauli and Niels Bohr, who got him interested in biology.
In 1937, he moved to the United States to pursue his interests in biology, taking up research in the Biology Division at Caltech on genetics of the fruit fly Drosophila melanogaster.
Delbrück was one of the most influential people in the movement of physical scientists into biology during the 20th century. Delbrück's thinking about the physical basis of life stimulated Erwin Schrödinger to write the highly influential book, What Is Life?. Schrödinger's book was an important influence on Francis Crick, James D. Watson and Maurice Wilkins who won a Nobel prize for the discovery of the DNA double helix. *TIA

1993 Max August Zorn (6 June 1906 in Krefeld, Germany - 9 March 1993 in Bloomington, Indiana, USA) To his chagrin, he is most famous for discovering something yellow and equiv­alent to the Axiom of Choice. *VFR (with a smile, I'm sure) He was an algebraist, group theorist, and numerical analyst. He is best known for Zorn's lemma, a powerful tool in set theory that is applicable to a wide range of mathematical constructs such as vector spaces, ordered sets, etc. Zorn's lemma was first discovered by K. Kuratowski (see June 18) in 1922, and then independently by Zorn in 1935.*Wik Today we know that the Axiom of Choice, the well-ordering principle, and Zorn's Lemma (the name now given to Zorn's maximum principle by Tukey and now the standard name) are equivalent. *SAU

1916 Richard Kenneth Guy (born September 30, 1916, Nuneaton, Warwickshire -  March 9,  2020 ) is a British mathematician, and Professor Emeritus in the Department of Mathematics at the University of Calgary.
He is best known for co-authorship (with John Conway and Elwyn Berlekamp) of Winning Ways for your Mathematical Plays and authorship of Unsolved Problems in Number Theory, but he has also published over 100 papers and books covering combinatorial game theory, number theory and graph theory.
He is said to have developed the partially tongue-in-cheek "Strong Law of Small Numbers," which says there are not enough small integers available for the many tasks assigned to them — thus explaining many coincidences and patterns found among numerous cultures.
Additionally, around 1959, Guy discovered a unistable polyhedron having only 19 faces; no such construct with fewer faces has yet been found. Guy also discovered the glider in Conway's Game of Life.
Guy is also a notable figure in the field of chess endgame studies. He composed around 200 studies, and was co-inventor of the Guy-Blandford-Roycroft code for classifying studies. He also served as the endgame study editor for the British Chess Magazine from 1948 to 1951.
Guy wrote four papers with Paul Erdős, giving him an Erdős number of 1. He also solved one of Erdős problems.
Many number theorists got their start trying to solve problems from Guy's book Unsolved problems in number theory.
His son, Michael Guy, is also a computer scientist and mathematician.
Guy died on 9 March 2020 at the age of 103.
*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