## Friday 31 March 2023

### On This Day in Math -- March 31

God runs electromagnetics on Monday, Wednesday, and Friday by the wave theory, and the devil runs it by quantum theory on Tuesday, Thursday, and Saturday.
~Sir Lawrence Bragg  (apparently there is no electricity on Sundays)

The 90th day of the year; 90 is the only number that is the sum of its digits plus the sum of the squares of its digits. (Is there any interesting distinction to the rest of the numbers for which this sum is more (or less) than the original number?)

$\frac{90^3 - 1}{90 - 1}$ is a Mersenne prime.

90 is the smallest number having 6 representations as a sum of four positive squares

90 is the number of degrees in a right angle. Moreover, as a compass direction, 90 degrees corresponds to east.
Which reminds me of a fun math joke:"The number you have dialed is imaginary. Please rotate you phone by 90 degrees and dial again."

And 90 is the sum of the first 9 consecutive even numbers,

the sum of its divisors,
the sum of consecutive integers in two different ways,
the sum of two consecutive primes,
and of six consecutive primes,
and the sum of five consecutive squares.
(all proofs left to the reader.)

EVENTS

1638 Descartes, in a letter to Mersenne, Gives explicit rules for how to find amicable numbers, and then illustrates his rule by finding the third known pair of amicable numbers.  Fermat had found the second.

In 1851, Leon Foucault demonstrated his pendulum experiment at the Pantheon of Paris at the request of Napoleon III, who had been informed of Foucault's recent discovery on 6 Jan 1851. He had installed a pendulum in his cellar in the Arras Street of Paris. It was made from 2 m (6.5-ft) long wire supporting a 5-kg weight. He observed a small movement of the oscillation plane of the pendulum - showing that the Earth was rotating underneath the swinging pendulum. A month later, he repeated the experiment at the observatory of Paris, with a 11-m pendulum which gave longer swings and a more clearly visible deviation. His March demonstration at the Pantheon used a 28-kg sphere on a 67-m (220-ft) wire. *TIS (The first date of this demonstration seems to have been on March 28,

1854 The University of Konigsberg awarded Weierstrass an honorary doctorate. Previously he was a Gymnasium teacher without a university degree. *VFR The award was the result of the attention his 1854 paper, Zur Theorie der Abelschen Functionen, which appeared in Crelle's Journal. This paper did not give the full theory of inversion of hyperelliptic integrals that Weierstrass had developed but rather gave a preliminary description of his methods involving representing abelian functions as constantly converging power series. With this paper Weierstrass burst from obscurity.*SAU

1876  Alexander Graham Bell and his assistant, Thomas A Watson,  talked by telephone over a two-mile wire stretched between Boston and Cambridge Massachusetts. The message was a simple statement, "Mr Watson, come here, I want to see you."  The common story is that he had invented the device by accident and would not have one in his home because he saw it as a distraction.

Whatever his objections, years later on January 25 of 1915, he place another call to his former assistant, between Bell in New York and Watson in San Francisco, and they repeated the exact same dialogue as their first message.  The call was a public relations stunt by A T & T to demonstrate their ability to make transcontinental calls, a 3,400 mile communication.  The call was timed to agree with the opening of the 1915 Panama–Pacific International Exposition in San Francisco which would open on Feb 20. A telephone line was also established to New York City so people across the continent could hear the Pacific Ocean.

The transcontinental line was completed on June 17, of 1914 and successfully voice tested in July. A postage stamp commemerating the completion was released in 1914 also.

1899 The EIFFEL TOWER, was built in 26 months and opened in Mar 1889 for the Universal Exposition. it is 320.75 m (1051 ft) high and only weighs 7000 tons – less than the air around it! The tower was inaugurated on 31 March 1889, and opened on 6 May. *VFR

Eiffel had a permit for the tower to stand for 20 years. It was to be dismantled in 1909, when its ownership would revert to the City of Paris. The city had planned to tear it down (part of the original contest rules for designing a tower was that it should be easy to dismantle) but as the tower proved to be valuable for radio telegraphy, it was allowed to remain after the expiry of the permit, and from 1910 it also became part of the International Time Service

Eiffel had the names of 72 scholars inscribed on the border encircling the first floor of the Tower. All disciplines are represented : mathematics (Cauchy, Fourier), physics, the most represented discipline with 17 names (Lavoisier, Fresnel, Laplace), mechanics (Navier), astronomy (Le Verrier), agronomy (Chaptal), electricity (Coulomb), natural sciences (Cuvier), chemistry (Lavoisier), mineralogy (Haüy), medicine (Bichat) and even photography (Daguerre) and ballooning (Giffard).

1959 Sof'ja Janovskaja became the first chairperson of the newly created department of mathematical logic at the Moscow State University. *Women of Mathematics

1918 Daylight Savings Time for the USA first applied. Standard time was adopted throughout the United States. 'An Act to preserve daylight and provide standard time for the United States' was enacted on March 19, 1918. It both established standard time zones and set summer DST to begin on March 31, 1918. *WebExhibits.org
I understand that at least three states are trying to repeal daylight savings in their states as of 2014.

1936 The Last day of service of the US Post Office in Eight, West Va. (It Seems the PO in nearby Six, W. Va lasted a little longer, but I can't find it now in Post Office Listings)  Eight was an unincorporated community located in McDowell County, West Virginia.

1939 Harvard and IBM Agree to Build The Mark I "Giant Brain":
Harvard and IBM sign an agreement to build the Mark I, also known as the IBM Automatic Sequence Controlled Calculator (ASCC). Project leader Howard Aiken developed the original concept of the machine: a series of switches, relays, rotating shafts and clutches. The Mark I weighed about five tons and contained more than 750,000 components. It read instructions from paper tape and data from punch cards.*CHM

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1952, Alan Turing was tried as a homosexual, offering no defense other than that he saw nothing wrong in his actions. Found guilty, he was given the alternatives of prison or oestrogen injections for a year. He accepted the latter and returned to a wide range of academic pursuits.

Turing's work was fundamental in the theoretical foundations of computer science.  *MacTutor

1981 Time (p. 51) reported that Educational Testing Service had to change the scores on 250,000 PSAT and 19,000 SAT papers because a student had successfully challenged a mathematical question about polyhedrons with no right answer. Mathematics Magazine 54 (1981), pp 152 and 277. *VFR Daniel Lowen, 17, a junior at Cocoa Beach High School in Florida was the first to call the ETS attention to their error. The problem involved putting two pyramids together and determining the number of faces on the new figure. The ETS had failed to allow for the fact that when two faces are joined, other faces meeting at the edges of the union might meld into one face.

1984 Science News reports that Persi Diaconis, a statistician at Stanford, can do a perfect riffle shuffle eight times in a row, thereby returning the 52-card deck to its original order. He has also proved that seven ordinary shuffles is enough to randomize a deck of cards. *VFR

1993 The birth of Spamming, A bug in a program written by Richard Depew sends an article to 200 newsgroups simultaneously. The term spamming is coined by Joel Furr (a writer and software trainer notable as a Usenet personality in the early and mid 1990s.) to describe the incident. *Wik

2011 The first ever "On This Day in Math"... thanks to hundreds of you for all the help.

BIRTHS

1596 René Descartes (31 March 1596 in La Haye (now Descartes),Touraine, France
- 11 Feb 1650 in Stockholm, Sweden)was a French philosopher whose work, La géométrie, includes his application of algebra to geometry from which we now have Cartesian geometry. His work had a great influence on both mathematicians and philosophers. La Géométrie is by far the most important part of this work. Scott summarises the importance of this work in four points:

He makes the first step towards a theory of invariants, which at later stages derelativises the system of reference and removes arbitrariness.
Algebra makes it possible to recognise the typical problems in geometry and to bring together problems which in geometrical dress would not appear to be related at all.
Algebra imports into geometry the most natural principles of division and the most natural hierarchy of method.
Not only can questions of solvability and geometrical possibility be decided elegantly, quickly and fully from the parallel algebra, without it they cannot be decided at all.

*SAU His lifelong habit of laying abed till noon was interrupted by Descartes’ new employer, the athletic, nineteen-year-old Queen Christiana of Sweden, who insisted he tutor her in philosophy in an unheated library early in the morning. This change of lifestyle caused the illness that killed him. [Eves, Circles, 177◦]*VFR

1730 – Étienne Bézout (31 March 1730 in Nemours, France - 27 Sept 1783 in Basses-Loges (near Fontainbleau), France) His most famous and well used book "including an incorrect proof that the quintic was solvable by radicals. In the early nineteenth century some of his in influential textbooks were translated into English. One translator, John Farrah, used
them to teach calculus at Harvard." *VFR
Bezout's theorem was essentially stated by Isaac Newton in his proof of lemma 28 of volume 1 of his principia, where he claims that two curves have a number of intersection points given by the product of their degrees. The theorem was later published in 1779 in Étienne Bézout's Théorie générale des équations algébriques. Bézout, who did not have at his disposal modern algebraic notation for equations in several variables, gave a proof based on manipulations with cumbersome algebraic expressions. From the modern point of view, Bézout's treatment was rather heuristic, since he did not formulate the precise conditions for the theorem to hold. This led to a sentiment, expressed by certain authors, that his proof was neither correct nor the first proof to be given.

1795 Louis Paul Emile Richard (31 March 1795 in Rennes, France - 11 March 1849 in Paris, France) Richard perhaps attained his greatest fame as the teacher of Galois and his report on him which stated, "This student works only in the highest realms of mathematics.... "
It is well known. However, he also taught several other mathematicians whose biographies are included in this archive including Le Verrier, Serret and Hermite. He fully realised the significance of Galois' work and so, fifteen years after he left the college, he gave Galois' student exercises to Hermite so that a record of his school-work might be preserved. It is probably fair to say that Richard chose to give them to Hermite since in many ways he saw him as being similar to Galois. Under Richard's guidance, Hermite read papers by Euler, Gauss and Lagrange rather than work for his formal examinations, and he published two mathematics papers while a student at Louis-le-Grand.
Despite being encouraged by his friends to publish books based on the material that he taught so successfully, Richard did not wish to do so and so published nothing. This is indeed rather unfortunate since it would now be very interesting to read textbooks written by the teacher of so many world-class mathematicians.*SAU

1806 Thomas Penyngton Kirkman FRS (31 March 1806 – 3 February 1895) was a British mathematician. Despite being primarily a churchman, he maintained an active interest in research-level mathematics, and was listed by Alexander Macfarlane as one of ten leading 19th-century British mathematicians. Kirkman's schoolgirl problem, an existence theorem for Steiner triple systems that founded the field of combinatorial design theory, is named after him.
Kirkman's first mathematical publication was in the Cambridge and Dublin Mathematical Journal in 1846, on a problem involving Steiner triple systems that had been published two years earlier in the Lady's and Gentleman's Diary by Wesley S. B. Woolhouse. Despite Kirkman's and Woolhouse's contributions to the problem, Steiner triple systems were named after Jakob Steiner who wrote a later paper in 1853. Kirkman's second research paper paper, in 1848, concerned hypercomplex numbers.
In 1850, Kirkman observed that his 1846 solution to Woolhouse's problem had an additional property, which he set out as a puzzle in the Lady's and Gentleman's Diary:

Fifteen young ladies in a school walk out three abreast for seven days in succession: it is required to arrange them daily, so that no two shall walk twice abreast.

This problem became known as Kirkman's schoolgirl problem, subsequently to become Kirkman's most famous result. He published several additional works on combinatorial design theory in later years. Kirkman also studied the Pascal lines determined by the intersection points of opposite sides of a hexagon inscribed within a conic section. Any six points on a conic may be joined into a hexagon in 60 different ways, forming 60 different Pascal lines. Extending previous work of Steiner, Kirkman showed that these lines intersect in triples to form 60 points (now known as the Kirkman points), so that each line contains three of the points and each point lies on three of the lines. *Wik

1847 – Yegor Ivanovich Zolotarev, (March 31, 1847, Saint Petersburg – July 19, 1878, Saint Petersburg) In 1874, Zolotarev become a member of the university staff as a lecturer and in the same year he defended his doctoral thesis “Theory of Complex Numbers with an Application to Integral Calculus”. The problem Zolotarev solved there was based on a problem Chebyshev had posed earlier. His steep career ended abruptly with his early death. He was on his way to his dacha when he was run over by a train in the Tsarskoe Selo station. On July 19, 1878 he died from blood poisoning. *Wik

1890 Sir William Lawrence Bragg (31 Mar 1890; 1 Jul 1971 at age 81) was an Australian-English physicist and X-ray crystallographer who at the early age of 25, shared the Nobel Prize for Physics in 1915 (with his father, Sir William Bragg). Lawrence Bragg formulated the Bragg law of X-ray diffraction, which is basic for the determination of crystal structure: nλ = 2dsinθ which relates the wavelength of x-rays, λ, the angle of incidence on a crystal, θ, and the spacing of crystal planes, d, for x-ray diffraction, where n is an integer (1, 2, 3, etc.). Together, the Braggs worked out the crystal structures of a number of substances. Early in this work, they showed that sodium chloride does not have individual molecules in the solid, but is an array of sodium and chloride ions. *TIS

1906 Shin'ichiro Tomonaga (31 Mar 1906; 8 Jul 1979 at age 73)Japanese physicist who shared the Nobel Prize for Physics in 1965 (with Richard P. Feynman and Julian S. Schwinger of the U.S.) for independently developing basic principles of quantum electrodynamics. He was one of the first to apply quantum theory to subatomic particles with very high energies. Tomonaga began with an analysis of intermediate coupling - the idea that interactions between two particles take place through the exchange of a third (virtual particle), like one ship affecting another by firing a cannonball. He used this concept to develop a quantum field theory (1941-43) that was consistent with the theory of special relativity. WW II delayed news of his work. Meanwhile, Feynman and Schwinger published their own independent solutions.*TIS

When he sent a letter explaining his theory to Oppenheimer in Princeton, it came out of the blue. Everyone was astonished: somehow Tomonaga had developed his theory in bombed-out wartime Japan, isolated from colleagues and journals, while sitting in the ashes and rubble of Tokyo.

Freeman Dyson wrote about him to his parents, "He is more able than either Schwinger or Feynman to talk about ideas other than his own...He is an exceptionally unselfish person."

*Ash Jogalekar

DEATHS

1624 Joao Baptista Lavanha (1550 in Portugal - 31 March 1624 in Madrid, Spain)Lavanha is said to have studied in Rome. He was appointed by Philip II of Spain to be professor of mathematics in Madrid in 1582.
Philip had sent the Duke of Alba with an army to conquer Portugal in 1580 and soon realized that Portugal was more advanced in studies of navigation than Spain. In an attempt to correct this, Philip founded an Academy of Mathematics in Madrid with Lavanha as its first professor.
From 1587 Lavanha became chief engineer to Philip II. He was appointed cosmographer to the king in 1596 and about the same time he moved to Lisbon where he taught mathematics to sailors and navigators.
Lavanha is best known for his contributions to navigation. His book Regimento nautico gives rules for determining latitude and tables of declination of the Sun. He also worked on maps, producing some interesting new ideas. He produced a map of Aragon in about 1615. Among his publications was a translation of Euclid.
Lavanha also studied instruments used in navigation, constructing astrolabes, quadrants and compasses. *SAU

1726/7 Isaac Newton (25 December 1642 – 20 March 1727 [NS: 4 January 1643 – 31 March 1727) English physicist and mathematician, who made seminal discoveries in several areas of science, and was the leading scientist of his era. His study of optics included using a prism to show white light could be split into a spectrum of colors. The statement of his three laws of motion are fundamental in the study of mechanics. He was the first to describe the moon as falling (in a circle around the earth) under the same influence of gravity as a falling apple, embodied in his law of universal gravitation. As a mathematician, he devised infinitesimal calculus to make the calculations needed in his studies, which he published in Philosophiae Naturalis Principia Mathematica (Mathematical Principles of Natural Philosophy, 1687)*TIS
Newton died intestate. Immediately his relatives began to quarrel over the division of his estate, which amounted to a considerable fortune. Thomas Pellet examined Newton’s manuscript holdings in hopes of turning a quick proﬁt. His “thick clumsy annotations ‘Not ﬁt to be printed,’ now seem at once pitiful and ludicrous.” See Whiteside, Newton Works, I, xvii ﬀ for details. *VFR

1776 John Bird (1709 – March 31, 1776), the well known mathematical instrument maker, was born at Bishop Auckland. He worked in London for Jonathan Sisson, and by 1745 he had his own business in the Strand. Bird was commissioned to make a brass quadrant 8 feet across for the Royal Observatory at Greenwich, where it is still preserved. Soon after, duplicates were ordered for France, Spain and Russia.

Bird supplied the astronomer James Bradley with further instruments of such quality that the commissioners of longitude paid him £500 (a huge sum) on condition that he take on a 7-year apprentice and produce in writing upon oath, a full account of his working methods. This was the origin of Bird's two treatises The Method of Dividing Mathematical Instruments (1767) and The Method of Constructing Mural Quadrants (1768). Both had a foreword from the astronomer-royal Nevil Maskelyne. When the Houses of Parliament burned down in 1834, the standard yards of 1758 and 1760, both constructed by Bird, were destroyed.

Bird was an early influence in the life of Jerimiah Dixon, and in all probability it was he who recommended Dixon as a suitable companion to accompany Mason. *Wik

1841 George Green (14 Jul 1793, 31 Mar 1841 at age 47) was an English mathematician, born near Nottingham, who was first to attempt to formulate a mathematical theory of electricity and magnetism. He was a baker while, remarkably, he became a self-taught mathematician. He became an undergraduate at Cambridge in October 1833 at the age of 40. Lord Kelvin (William Thomson) subsequently saw, was excited by the Essay. Through Thomson, Maxwell, and others, the general mathematical theory of potential developed by an obscure, self-taught miller's son heralded the beginning of modern mathematical theories of electricity.*TIS His most famous work, An Essay on the Application of Mathematical Analysis to the Theory of Electricity and Magnetism was published, by subscription, in March 1828. Most of the ﬁfty-two subscribers were friends and patrons. The work lay unnoticed until William Thomson rediscovered it and showed it to Liouville and Sturm in Paris in 1845. The Theory of Potential it developed led to the modern mathematical theory of electicity. *VFR

1877 Antoine-Augustin Cournot (28 Aug 1801; 31 Mar 1877) French economist and mathematician, who was the first economist who applied mathematics to the treatment of economic questions. In 1838, he published Recherches sur les principes mathématiques de la théorie des richesses (Researches into the Mathematical Principles of the Theory of Wealth) which was a treatment of mathematical economics. In particular, he considered the supply-and-demand functions. Further, he studied the conditions for equilibrium with monopoly, duopoly and perfect competition. He included the effect of taxes, treated as changes in production costs, and discussed problems of international trade. His definition of a market is still the basis for that presently used in economics. In other work, he applied probability to legal statistics *TIS

1997 Friedrich (Hermann) Hund (4 Feb 1896 - 31 Mar 1997) was a German physicist known for his work on the electronic structure of atoms and molecules. He introduced a method of using molecular orbitals to determine the electronic structure of molecules and chemical bond formation. His empirical Hund's Rules (1925) for atomic spectra determine the lowest energy level for two electrons having the same n and l quantum numbers in a many-electron atom. The lowest energy state has the maximum multiplicity consistent with the Pauli exclusion principle. The lowest energy state has the maximum total electron orbital angular momentum quantum number, consistent with rule. They are explained by the quantum theory of atoms by calculations involving the repulsion between two electrons. *TIS

Harold Scott MacDonald Coxeter (9 Feb 1907 in London, England - 31 March 2003 in Toronto, Canada) graduated from Cambridge and worked most of his life in Canada. His work was mainly in geometry. In particular he made contributions of major importance in the theory of polytopes, non-euclidean geometry, group theory and combinatorics. Among his most famous geometry books are The real projective plane (1955), Introduction to geometry (1961), Regular polytopes (1963), Non-euclidean geometry (1965) and, written jointly with S L Greitzer, Geometry revisited (1967). He also published a famous work on group presentations, which was written jointly with his first doctoral student W O J Moser, Generators and relations for discrete groups.
His 12 books and 167 published articles cover more than mathematical research. Coxeter met Escher in 1954 and the two became lifelong friends. Another friend, R Buckminister Fuller, used Coxeter's ideas in his architecture. In 1938 Coxeter revised and updated Rouse Ball's Mathematical recreations and essays, a book which Rouse Ball first published in 1892. *SAU

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 & Campbel

## Thursday 30 March 2023

### Complimentary, Supplementary, and Explementary, Math Terms Notes

Most Students learn Supplementary and complimentary in geometry.  They may even use the same mnemonic I do to remember which is which.  90 degree angles are crooked, (Complimentary ),180 degree angles are straight, (Supplementary).

Supplement The supplement of an angle is the angle that must be added to "fill up" a semi-circle. The sup root is a variation of the common sub for below or under. The ple is the same root that gives us the math word plus for "to increase or add to" something. Together they suggest the addition of something to fill the "low" amount. Several other English words are formed from the same roots. Supply is an alternative of the same word. The word supplicate, meaning beg or implore, if from one who needs to be supplied. Supple, for limber, is perhaps and early variation of "beggars can't be choosers"; those who need should remain flexible.

Jeff Miller's website gives the first use of the term (in this use) as:

In 1796 Hutton Math. Dict. has "The complement to 180° is usually called the supplement.

In 1798 Hutton in Course Math. has "supplemental arc" (one of two arcs which add to a semicircle) [OED].

He also gives"Supplement of a parallelogram" appears in English in 1570 in Sir Henry Billingsley’s translation of Euclid’s Elements. Maybe because the adjacent angles of a parallelogram are supplementary.

Complementary The Latin word complere means to complete. The ple root is the same root that gives us the word plus. Most mathematical uses of complement can be understood from this origin. A complement to an angle is the amount needed to complete a right angle. The "tens complement" of six is four, the amount that is needed to complete a ten. The word compliment, for an expression of praise or admiration, is from the same root. It came from a Spanish term for the gift that was given to repay someone for a favor. The gift that would complete the exchange.

Explementary I first heard of the word explementary in July of 1999. It was "re-created" by Steve Wells of a company called think3 while working on a new CAD program, thinkdesign. The word was needed to represent the angle required to complete a 360 degree circle. They wanted a word that would be a natural sounding extension of complement, and supplement. The Latin explementum means "filling" or "stuffing" (as reported by Ken Pledger, and other sources) and it is "explement" that is reported to be in the O.E.D. as "that which fills up". This is very much the same meaning as complement and supplement. After a couple of days, he found the word was not as new to mathematics as we had thought. Several days later he wrote to tell me that the word already appeared on the DICTIONARY OF TECHNICAL TERMS FOR AEROSPACE USE (Web edition edited by Daniel R. Glover, Jr.) NASA Lewis Research Center, Cleveland, Ohio. Here is their definition, as sent to me by Mr Wells:

"Explement -- An angle equal to 360 degrees minus a given angle. Thus, 150 ° is the explement of 210° and the two are said to be explementary. See complement, supplement.

Explementary angles -- Two angles whose sum is 360°."

My thanks to Mr Wells for his advice and corrections as much of this content came directly from his letters.  But, it seems to have existed well before either of these.  EXPLEMENT is found in 1827 in Mathematical and astronomical tables by William Galbraith: "...the explement, or difference from four right angles" [Google print search].

The term conjugate angles is also sometimes used. This may come from the polar representation of complex conjugates. Two complex numbers a + bi and a - bi are called conjugates, and the polar representations using the Argand diagram will have angles that sum to 360 degrees

### On This Day in Math - March 30

 Jaime Escalante *Wik

A mathematician is a person who can find analogies between theorems; a better mathematician is one who can see analogies between proofs and the best mathematician can notice analogies between theories. One can imagine that the ultimate mathematician is one who can see analogies between analogies.
~Stefan Banach

The 89th day of the year; 89 is the fifth Fibonacci prime and the reciprocal of 89 starts out 0.011235... (generating the first five Fibonacci numbers) *Prime Curios  It actually generates many more, but the remainder are hidden by the carrying of digits from the two digit Fibonacci numbers. (The next digit, for instance is a 9 instead of an eight because it includes the tens digit of the next Fibonacci number, 13.)

and 89 can be expressed by the first 5 integers raised to the first 5 Fibonacci numbers: 11 + 25 + 33 + 41+ 52

$\sqrt(81) = 8+1$  81 is the only multidigit number whose square root is equal to the sum of its digits.
If you write any integer and sum the square of the digits, and repeat, eventually you get either 1, or 89
(ex:  16; $1^2 + 6^2 = 37; 3^2 + 7^2 = 58; 5^2 + 8^2 = 89$

An Armstrong (or Pluperfect digital invariant) number is a number that is the sum of its own digits each raised to the power of the number of digits. For example, 371 is an Armstrong number since $3^3+7^3+1^3 = 371$. There are exactly 89 such numbers, including two with 39 digits. (115,132,219,018,763,992,565,095,597,973,522,401 is the largest) (Armstrong numbers are named for Michael F. Armstrong who named them for himself as part of an assignment to his class in Fortran Programming at the University of Rochester \)

89 is a numeric ambigram (a number that rotates to form a different number), and is the sum of four  strobogrammatic numbers (rotate and stay the same) , 1+8+11+69 = 89.

And from our strange measures category, A Wiffle, also referred to as a WAM for Wiffle (ball) Assisted Measurement, is equal to a sphere 89 millimeters (3.5 inches) in diameter – the size of a Wiffle ball, a perforated, light-weight plastic ball frequently used by marine biologists as a size reference in photos to measure corals and other objects. The spherical shape makes it omnidirectional and perfect for taking a speedy measurement, and the open design also allows it to avoid being crushed by water pressure. Wiffle balls are a much cheaper alternative to using two reference lasers, which often pass straight through gaps in thin corals. A scientist on the research vessel EV Nautilus is credited with pioneering the technique *Wik

EVENTS

In 239, B.C., was the first recorded perihelion passage of Halley's Comet by Chinese astronomers in the Shih Chi and Wen Hsien Thung Khao chronicles. Its highly elliptical, 75-year orbit carries it out well beyond the orbit of Neptune and well inside the orbits of Earth and Venus when it swings in around the Sun, traveling in the opposite direction from the revolution of the planets. It was the first comet that was recognized as being periodic. An Englishman, Edmond Halley predicted in 1705 that the comet that appeared over London in 1682 would reappear again in 1759, and that it was the same comet that appeared in 1607 and 1531. When the comet did in fact reappear again in 1759, as correctly predicted, it was named (posthumously) after Halley. *TIS
Comets have been observed and recorded in China since the Shang Dynasty (1600-1046 BC). The set of comet illustrations shown below is from a silk book written during the western Han period.

 * Marilyn Shea,umf.maine.edu

1612 The Jesuit astronomer Christoph Scheiner thought he had discovered a 5th Jupiter moon He was mistaken. *Thony Christie, @rmathematicus

In 1791, after a proposal by the Académie des sciences (Borda, Lagrange, Laplace, Monge and Condorcet), the French National Assembly finally chose that a metre would be a 1/10 000 000 of the distance between the north pole and the equator. *TIS (although at the time, this distance was not known. To determine the distance from the North Pole to the equator it was assumed that a portion of a meridian could be measured accurately and the whole distance could then be estimated from this sample. The meridian chosen went from Barcelona in Spain, to Dunquerque in France; this choice was an early example of the intended international nature of the metric system. Two astronomers, Borda and Méchain, were appointed to carry out the measurement. )

1796 The nineteen year old Gauss began his scientific diary with his construction of the regular, heptadecagon (17-gon). The Greeks had ruler-and-compass constructions for the regular polygons with 3, 4, 5 and 15 sides, and for all others obtainable from these by doubling the number of sides. Here the problem rested until Gauss completely solved it: A regular n-gon is constructable IFF n is a product of a power of 2 and one or more distinct Fermat primes, i.e., primes of the form 22n +1. This discovery led Gauss to devote his life to mathematics rather than philology. *VFR Gauss told his close friend Bolyai that the regular 17-gon should adorn his tombstone, but this was not done. There is a 17 pointed star on the base of a monument to him in Brunswick because the stonemason felt everyone would mistake the 17-gon for a circle. Gauss gave the tablet on which he had made the discovery to Bolyai, along with a pipe, as a souvenir. (I have been unable to find any later trace of the pipe or tablet, but if anyone has knowledge of the I would appreciate any information.)

 *Genial Gauss Gottingen

1818 Physicist Augustin Fresnel reads a paper on optical rotation to the Academy of Sciences, reporting that when polarized light is "depolarized" by a Fresnel rhomb its properties are preserved in subsequent passage through an optically-rotating crystal or liquid.  (A Fresnel rhomb is an optical prism that introduces a 90° phase difference between two perpendicular components of polarization)

==============================================================

1858 Pencil with attached eraser patented. It has benefited generations of mathematics students. The first patent for attaching an eraser to a pencil was issued to a man from Philadelphia named Hyman Lipman. This patent was later held to be invalid because it was merely the combination of two things, without a new use. I found a note at about.com that said that "Before rubber, breadcrumbs had been used to erase pencil marks."

 *Wik

1866 The New York Daily-Tribune carries front page information on the Super Blue Moon Lunar Eclipse happening on that evening. It would be the last visible in the US until Jan 31, 2018. *Library of Congress

1867 The U. S. purchases Alaska from Russia for $7,200,000 in gold. The most prominent American mathematician of the time, Benjamin Peirce, then superintendent of the Coast Survey, played a role in the acquisition by sending out a reconnaissance party whose reports were important aids to proponents of the purchase. *VFR ================================================================ 1877 The article "The Electroscope" was published in The New York Sun of 30 March 1877. Written under the pseudonym "Electrician", the New York Sun article claimed that "an eminent scientist", whose name had to be withheld, had invented a device whereby objects or people anywhere in the world "could be seen anywhere by anybody". According to the article, the device would allow merchants to transmit pictures of their wares to their customers, the contents of museum collections would be made available to scholars in distant cities, and (combined with the telephone) operas and plays could be broadcast into people's homes. An illustration of the Telectroscope appeared in Scientific American in 1881.  *Wik 1951 UNIVAC I turned over to Census Bureau. During ENIAC project, Mauchly met with several Census Bureau officials to discuss non-military applications for electronic computing devices. In 1946, with ENIAC completed, Mauchly and Eckert were able to secure a study contract from the National Bureau of Standards (NBS) to begin work on a computer designed for use by the Census Bureau. This study, originally scheduled for six months, took about a year to complete. The final result were specifications for the Universal Automatic Computer (UNIVAC). UNIVAC was, effectively, an updated version of ENIAC. Data could be input using magnetic computer tape (and, by the early 1950's, punch cards). It was tabulated using vacuum tubes and state-of-the-art circuits then either printed out or stored on more magnetic tape. Mauchly and Eckert began building UNIVAC I in 1948 and delivered the completed machine to the Census Bureau in March 1951. The computer was used to tabulate part of the 1950 population census and the entire 1954 economic census. Throughout the 1950's, UNIVAC also played a key role in several monthly economic surveys. The computer excelled at working with the repetitive but intricate mathematics involved in weighting and sampling for these surveys. UNIVAC I, as the first successful civilian computer, was a key part of the dawn of the computer age *US CENSUS Bureau Web page In 1953, Albert Einstein announced his revised unified field theory.*TIS 1985 M.I.T. computer science graduate students Robert W. Baldwin and Alan T. Sherman successfully decode a cipher consisting of a series of numbers separated by commas. They failed to share in the$116,000 prize oﬀered by Decipher Inc. since they misread the contest rules—the contest ended the previous evening. [Burlington Free Press, 5 April 1985.]

2010 A Blue moon - The second full moon of the month of March. The next month with a blue moon will be in 2012: August 2, August 31

BIRTHS

1862 Leonard James Rogers (30 March 1862, 12 Sept 1933) Rogers was a man of extraordinary gifts in many fields, and everything he did, he did well. Besides his mathematics and music he had many interests; he was a born linguist and phonetician, a wonderful mimic who delighted to talk broad Yorkshire, a first-class skater, and a maker of rock gardens. He did things well because he liked doing them. Music was the first necessity in his intellectual life, and after that came mathematics. He had very little ambition or desire for recognition.
Rogers is now remembered for a remarkable set of identities which are special cases of results which he had published in 1894. Such names as Rogers-Ramanujan identities, Rogers-Ramanujan continued fractions and Rogers transformations are known in the theory of partitions, combinatorics and hypergeometric series. *SAU

1864 Helen Abbot Merrill born in Llewellyn Park, Orange, New Jersey. She graduated from Wellesley College in 1886, taught school for several years and then returned to teach at Wellesley from 1893 until her retirement in 1932. She studied function theory with Heinrich Maschke at Chicago, descriptive geometry with G. F. Shilling at G¨ottingen, and function theory with James Pierpont at Yale, where she received her Ph.D. in 1903. She wrote a popular book about mathematics, Mathematical Excursions (1933), that has been reprinted by Dover.*WM
A rare collectors favorite

1879 Bernhard Voldemar Schmidt (30 Mar 1879, 1 Dec 1935) Astronomer and optical instrument maker who invented the telescope named for him. In 1929, he devised a new mirror system for reflecting telescopes which overcame previous problems of aberration of the image. He used a vacuum to suck the glass into a mold, polishing it flat, then allowing in to spring back into shape. The Schmidt telescope is now widely used in astronomy to photograph large sections of the sky because of its large field of view and its fine image definition. He lost his arm as a child while experimenting with explosives. Schmidt spent the last year of his life in a mental hospital.*TIS

1886 Stanisław Leśniewski (March 30, 1886, Serpukhov – May 13, 1939, Warsaw) was a Polish mathematician, philosopher and logician. Leśniewski belonged to the first generation of the Lwów-Warsaw School of logic founded by Kazimierz Twardowski. Together with Alfred Tarski and Jan Łukasiewicz, he formed the troika which made the University of Warsaw, during the Interbellum, perhaps the most important research center in the world for formal logic. *Wik

1892 Stefan Banach (30 Mar 1892, 31 Aug 1945) Polish mathematician who founded modern functional analysis and helped develop the theory of topological vector spaces. In addition, he contributed to measure theory, integration, the theory of sets, and orthogonal series. In his dissertation, written in 1920, he defined axiomatically what today is called a Banach space. The idea was introduced by others at about the same time (for example Wiener introduced the notion but did not develop the theory). The name 'Banach space' was coined by Fréchet. Banach algebras were also named after him. The importance of Banach's contribution is that he developed a systematic theory of functional analysis, where before there had only been isolated results which were later seen to fit into the new theory. *TIS
His doctoral dissertation, which was published in Fundamenta Mathematicae in 1922, marks the birth of functional analysis. *VFR

1921 Alfréd Rényi (20 March 1921 – 1 February 1970) was a Hungarian mathematician who made contributions in combinatorics, graph theory, number theory but mostly in probability theory. He proved, using the large sieve, that there is a number K such that every even number is the sum of a prime number and a number that can be written as the product of at most K primes. See also Goldbach conjecture.
In information theory, he introduced the spectrum of Rényi entropies of order α, giving an important generalisation of the Shannon entropy and the Kullback-Leibler divergence. The Rényi entropies give a spectrum of useful diversity indices, and lead to a spectrum of fractal dimensions. The Rényi–Ulam game is a guessing game where some of the answers may be wrong.
He wrote 32 joint papers with Paul Erdős, the most well-known of which are his papers introducing the Erdős–Rényi model of random graphs. Rényi, who was addicted to coffee, invented the quote: "A mathematician is a device for turning coffee into theorems.", which is generally ascribed to Erdős. The sentence was originally in German, being a wordplay on the double meaning of the word Satz (theorem or residue of coffee). *Wik

Renyi's wife Catherine (she went by Kato') was also a mathematician and co-authored at least one paper with him on counting K trees.  She died during the completion of this work which carried this footnote.

1929 Ilya Piatetski-Shapiro (30 March 1929 – 21 February 2009) During a career that spanned 60 years he made major contributions to applied science as well as theoretical mathematics. In the last forty years his research focused on pure mathematics; in particular, analytic number theory, group representations and algebraic geometry. His main contribution and impact was in the area of automorphic forms and L-functions.
For the last 30 years of his life he suffered from Parkinson's disease. However, with the help of his wife Edith, he was able to continue to work and do mathematics at the highest level, even when he was barely able to walk and speak.*Wik

DEATHS
1559 Adam Ries (23 Dec 1492 in Staffelstein (near Bamberg), Upper Franconia (now Germany) - 30 March 1559 in Annaberg, Saxony (now Annaberg-Buchholz, Germany) Ries's income came mainly from his arithmetic textbooks. The first of these was Rechnung auff der linihen written while he was in Erfurt and printed in that city in 1518 by Mathes Maler. The book was intended to teach people how to use a calculating board similar to an abacus. This type of device is described by the Money Museum,

Four horizontal and five vertical lines were painted or carved on the calculating boards to represent the decimal values in ascending order. The arithmetical sums were worked out with the help of coin-like counters. They were placed on the respective lines according to the values of the numbers and then, depending on the calculation, these were moved, removed or added to the lines until the final result could be read off. No numbers were printed on the counters; they amounted to as much as the line on which they were placed.

No copy of the first edition of this book has survived, the earliest that we have is the second of the four editions which was published in 1525.
Dirk Struik writes,

Adam Ries has remained in German memory because of his Rechenbücher -schoolbooks on arithmetic, popular for a century and a half. It is less known that he also wrote an algebra, called the Cosz, but this work has remained in manuscript form. Three of these manuscripts were bound together in 1664 by the Dresden Rechenmeister Martin Kupffer. They were thought to be lost until they were found in 1855, and are now kept at the Erzgebirgsmuseum Annaberg-Buchholz, Annaberg being the Saxonian mining town where Ries lived as a respected citizen and teacher for many years until his death. The impressive folio facsimile, published on the occasion of the 500th birthday of Ries, contains three manuscripts: Cosz I (pp. 1-325) was finished in 1524, Cosz II (pp. 329-499) was written between 1545 and 1550 ...

*SAU
Thony Christie pointed out to me that the German Wikipedia gives his date of death as April 2. He also has confirmed that the phrase "das macht nach Adam Ries" (That's according to Adam Ries) is still used in Germany to indicate something is done correctly, sort of like the American idiom, "according to Hoyle."

And here is the amazing story of how he was billed for his television license over 450 years after his death.

1832 Stephen Groombridge (7 Jan 1755; 30 Mar 1832) English astronomer and merchant, who compiled the Catalogue of Circumpolar Stars (corrected edition published 1838), often known as the Groombridge Catalog. For ten years, from 1806, he made observations using a transit circle, followed by another 10 years adjusting the data to correct for refraction, instrument error and clock error. He retired from the West Indian trade in 1815 to devote full time to the project. He was a founder of the Astronomical Society (1820). His work was continued by others when he was struck (1827) with a "severe attack of paralysis" from which he never fully recovered. The catalog eventually listed 4,243 stars situated within 50° of the North Pole and having apparent magnitudes greater than 9. Editions of the catalog were published posthumously. The 1833 edition was withdrawn due to errors, and corrected in 1838 by A Catalog of Circumpolar Stars, Reduced to January 1, 1810, edited by G. Biddell Airy. *TIS

1914 John Henry Poynting (9 Sep 1852; 30 Mar 1914)British physicist who introduced a theorem (1884-85) that assigns a value to the rate of flow of electromagnetic energy known as the Poynting vector, introduced in his paper On the Transfer of Energy in the Electromagnetic Field (1884). In this he showed that the flow of energy at a point can be expressed by a simple formula in terms of the electric and magnetic forces at that point. He determined the mean density of the Earth (1891) and made a determination of the gravitational constant (1893) using accurate torsion balances. He was also the first to suggest, in 1903, the existence of the effect of radiation from the Sun that causes smaller particles in orbit about the Sun to spiral close and eventually plunge in.*TIS

1944 Sir Charles Vernon Boys (15 Mar 1855; 30 Mar 1944 at age 88) English physicist and inventor of sensitive instruments. He graduated in mining and metallurgy, self-taught in a wide knowledge of geometrical methods. In 1881, he invented the integraph, a machine for drawing the antiderivative of a function. Boys is known particularly for his utilization of the torsion of quartz fibres in the measurement of minute forces, enabling him to elaborate (1895) on Henry Cavendish's experiment to improve the values obtained for the Newtonian gravitational constant. He also invented an improved automatic recording calorimeter for testing manufactured gas (1905) and high-speed cameras to photograph rapidly moving objects, such as bullets and lightning discharges. Upon retirement in 1939, he grew weeds.*TIS

1954 Fritz Wolfgang London (7 Mar 1900; 30 Mar 1954 at age 53) German-American physicist who, with Walter Heitler, devised the first quantum mechanical treatment of the hydrogen molecule, while working with Erwin Schrödinger at the University of Zurich. In a seminal paper (1927), they developed a wave equation for the hydrogen molecule with which it was possible to calculate approximate values of the molecule's ionization potential, heat of dissociation, and other constants. These predicted values were reasonably consistent with empirical values obtained by spectroscopic and chemical means. This theory of the chemical binding of homopolar molecules is considered one of the most important advances in modern chemistry. The approach is later called the valence-bond theory. *TIS

1995 John Lighton Synge (March 23, 1897–March 30, 1995) was an Irish mathematician and physicist. Synge made outstanding contributions to different fields of work including classical mechanics, general mechanics and geometrical optics, gas dynamics, hydrodynamics, elasticity, electrical networks, mathematical methods, differential geometry, and Einstein's theory of relativity. He studied an extensive range of mathematical physics problems, but his best known work revolved around using geometrical methods in general relativity.
He was one of the first physicists to seriously study the interior of a black hole, and is sometimes credited with anticipating the discovery of the structure of the Schwarzschild vacuum (a black hole).
He also created the game of Vish in which players compete to find circularity (vicious circles) in dictionary definitions. *Wik

2000 George Keith Batchelor FRS (8 March 1920 – 30 March 2000) was an Australian applied mathematician and fluid dynamicist. He was for many years the Professor of Applied Mathematics in the University of Cambridge, and was founding head of the Department of Applied Mathematics and Theoretical Physics (DAMTP). In 1956 he founded the influential Journal of Fluid Mechanics which he edited for some forty years. Prior to Cambridge he studied in Melbourne High School.
As an applied mathematician (and for some years at Cambridge a co-worker with Sir Geoffrey Taylor in the field of turbulent flow), he was a keen advocate of the need for physical understanding and sound experimental basis.
His An Introduction to Fluid Dynamics (CUP, 1967) is still considered a classic of the subject, and has been re-issued in the Cambridge Mathematical Library series, following strong current demand. Unusual for an 'elementary' textbook of that era, it presented a treatment in which the properties of a real viscous fluid were fully emphasized. He was elected a Foreign Honorary Member of the American Academy of Arts and Sciences in 1959.*Wik

2010 Jaime Alfonso Escalante Gutierrez (December 31, 1930 — March 30, 2010) was a Bolivian educator well-known for teaching students calculus from 1974 to 1991 at Garfield High School, East Los Angeles, California. Escalante was the subject of the 1988 film Stand and Deliver, in which he is portrayed by Edward James Olmos.

In 1974, he began to teach at Garfield High School. Shortly after Escalante came to Garfield, its accreditation became threatened. Instead of gearing classes to poorly performing students, Escalante offered AP Calculus.

The school administration opposed Escalante frequently during his first few years. He was threatened with dismissal by an assistant principal because he was coming in too early, leaving too late, and failing to get administrative permission to raise funds to pay for his students' Advanced Placement tests. The opposition changed with the arrival of a new principal, Henry Gradillas. Aside from allowing Escalante to stay, Gradillas overhauled the academic curriculum at Garfield, reducing the number of basic math classes and requiring those taking basic math to take algebra as well. He denied extracurricular activities to students who failed to maintain a C average and to new students who failed basic skills tests. One of Escalante's students remarked, "If he wants to teach us that bad, we can learn.

*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

## Wednesday 29 March 2023

### Rhombus from Math Terms Notes

The rhombus is a quadrilateral with four sides of congruent length(and whether you include squares, or don't, is a matter of taste.) It is sometimes called a rhomb, and sometimes a diamond and sometimes, if you are French especially, a lozenge. In classical Latin, a rhombus was a diamond shaped instrument that was whirled on a string to make a whirring sound, aha, but why.

If you have ever been to a rodeo, you have probably been impressed with the agility and courage of the rodeo clowns as they distract the bull after the rider departs from the bull. You may even think it was a sport created by cowboys of the old American west. The truth however, is that playing tag with a bull may date back to the ancient Greek civilizations around 2000 BC. Archiologists working on Minoan ruins found pots with illustrations that seemed to show that taunting a bull was a popular pastime for young males of that culture. The picture below is from a fresco found when the castle of King Minos was excavated.

It seems that sometimes, however, the bull was bored by the whole routine. It is hard to be macho if the bull is doing his "Ferdinand" routine and smelling the daisies so, to prod the animal into more ferocious activity, the young men began twirling an object on a string around their heads that made a roaring noise.

You may have seen other objects used to make a sound in a similar manner. Hopi Indians use something like that in their dances and you may have seen your science teacher twirl a length of plastic tube to make various "roaring" sounds. Such objects today are called bull roarers. I always thought it was because they were presumed to sound like a bull. Now I am less sure. The ancient Minoan object that twisted as it twirled and made the roaring sound was called a rhomb. The root began to be used in words that suggested rotation or twisting motions, such as spinning tops, but none of the others seem to have made it into modern language. The use that did prevail was for shapes that looked like the four sided object that they swung on the end of the string. This is how we came to call the equilateral quadrilateral a rhombus... and that's no bull.

Euclid uses the word rombos and in his translation Heath says it is apparently drawn from the Greek word rembw, to turn round and round. He also points out that Archimedes used the term solid rhombus for two right circular cones sharing a common base. Euclid extended the idea in using rhomboid to name the shape we more commonly call a parallelogram. Since the definition of rhomboid (romboeides) comes before the definition of parallel lines, Euclid defines the rhomboid as (in Heath's words)," that which has its opposite sides and angles equal to one another but is neither equilateral nor right-angled."

The term rhomb is often used for the same shape, and many people, particularly young students, refer to a rhombus as a diamond. Some use the term only for non-squre rhombi (or rhombuses). It is especially interesting to work with early elementary students who will identify a shape as a square when the sides are horizontal and vertical, and then call it a diamond when the shape is rotated 45 degrees, even while they watch. The word diamond seems to be a mutation of the word adamant. A person is adamant if they are firm or unyielding in their attitude or position. The origin seems to be from the common root anti and the Greek word deme which meant to force or break (as in training an animal) which is the root of our present word domesticate. Together the two roots meant unbreakable, and the word was commonly used for hard metals and gems, and extremely difficult people.

The French word lozenge is also used for the non-square rhombus by some people, although I have never seen the term in a current math book. The word comes from the Gaulish word lausa for "flat stone".
Lozenge was used by Robert Recorde in 1551 in Pathway to Knowledge: "Defin., The thyrd kind is called losenges or diamondes whose sides bee all equall, but it hath neuer a square corner" *J Miller

As with many geometric terms, there are two common definitions that are still in use for a rhombus. Some think of geometric names with an inclusive approach, and they usually define rhombus as it is defined in The Concise Oxford English Dictionary, "rhombus n. ( pl. rhombuses or rhombi / -b / ) Geometry a quadrilateral whose sides all have the same length." Notice that in this definition, a square would be a rhombus also. Others, who want definitions to describe how things are different from each other will define it the way it is defined in The Oxford American Dictionary of Current English, "rhombus n. a parallelogram with oblique angles and equal sides." Note that the Oblique angles rules out the case of a square.

The word Rhomboid which means rhom-like was commonly used in the 19th century for a parallelogram which was neither a rectangle nor a rhombus. Today it is more often used for a solid figure with six faces in which each face is a parallelogram and opposite faces in pairs lie in parallel planes. Some crystals are formed in 3D rhomboids. It is also sometimes called a rhombic prism. The term shows up frequently in science terminology referring to both its two and three dimensional meaning.
My thanks to Mary O'Keeffe for the suggestions to explore the origins of this word.

### On This Day in Math - March 29

Natural selection is a mechanism for generating an exceedingly high degree of improbability.
~R. A. Fisher

The 88th day of the year; 882 = 7744, it is one of only 5 numbers known whose square has no isolated digits. (Can you find the others?) [Thanks to Danny Whittaker @nemoyatpeace for a correction on this.]

There are only 88 narcissistic numbers  in base ten, (an n-digit number that is the sum of the nth power of its digits, 153=13 + 53 + 33

88 is also a chance to introduce a new word.  88 is strobogrammatic, a number that is the same when it is rotated 180o about its center... 69 is another example. If they make a different number when rotated, they are called invertible (109 becomes 601 for example). *Prime Curios (Note that this rule is not strictly enforced.

And with millions (billions?) of stars in the sky, did you ever wonder how many constellations there are?  Well, according to the Internationals Astronomical Union, there are 88.

Currently, 14 men and women, 9 birds, two insects, 19 land animals, 10 water creatures, two centaurs, one head of hair, a serpent, a dragon, a flying horse, a river and 29 inanimate objects are represented in the night sky (the total comes to more than 88 because some constellations include more than one creature.)

And if you chat with Chinese friends, the cool way to say bye-bye is with 88, from Mandarin for 88, "bā ba".

Not too far from my home near Possum Trot, Ky, there is a little place called Eighty-eight, Kentucky. One story of the naming (there could be as many as 88 of them) is that the town was named in 1860 by Dabnie Nunnally, the community's first postmaster. He had little faith in the legibility of his handwriting, and thought that using numbers would solve the problem. He then reached into his pocket and came up with 88 cents.
In the 1948 presidential election, the community reported 88 votes for Truman and 88 votes for Dewey, which earned it a spot in Ripley's Believe It or Not.

And expanding the "88 is strobogrammatic" theme, INDER JEET TANEJA came up with this beautiful magic square with a constant of 88 that was used in a stamp series in Macao in 2014 and 2015. This image shows the reflections both horizontally and vertically, as well as the 180 degree rotation, each is a magic square.

The stamps had denominations of 1 through 9 pataca and when  two sheets were  printed you could do your own Luo Shu magic square with the denominations. The Luo Shu itself was featured on the 12 pataca stamp.

EVENTS

1796 Gauss achieved the construction of the 17-gon and a week later he would obtain his first proof of the quadratic reciprocity law. These two accomplishments mark the emergence from the ingenious manipulations of his youth, to the polished proofs of the mature mathematician. *Merzbach, An Early Version of Guass' Disquisitiones Arithmeticae, Mathematical Perspectives Academic Press 1981

 first image obtained by NASA’s Dawn spacecraft .

In 1807, Vesta 4, the only asteroid visible to the naked eye, thus the brightest on record, was first observed by the amateur astronomer Heinrich Wilhelm Olbers from Bremen. Vesta is a main belt asteroid with a diameter of 525-km and a rotation period of 5.34 hours. Pictures taken by the Hubble Space Telescope in 1995 show Vesta's complex surface, with a geology similar to that of terrestrial worlds - such as Earth or Mars - a surprisingly diverse world with an exposed mantle, ancient lava flows and impact basins. Though no bigger than the state of Arizona, it once had a molten interior. This contradicts conventional ideas that asteroids essentially are cold, rocky fragments left behind from the early days of planetary formation. *TIS Since the discovery of Ceres (by Giuseppe Piazzi) in 1801,  and the asteroid Pallas (also discovered by Olbers) in 1802, he had corresponded and became close friends with Gauss.  For that reason he allowed Gauss to name the new "planet".

1933 Italy issued the world’s ﬁrst postage stamp portraying Galileo. [Scott #D16] *VFR
Galileo Galilei (1564–1642) made his first appearance on this stamp in 1933 for use in pneumatic postal systems (hence the wording “Posta Pneumatica” on the stamp). Pneumatic post involved placing letters in canisters which were then shot along pipes by compressed air from one Post Office to another. Pneumatic postal systems were set up in several European and American cities, including Rome, Naples, and Milan. Italy was the only country to issue stamps specifically for pneumatic postal use. Two of the designs showed Galileo – this one and a modified version with different face value and colour issued in 1945. The portrait is based on one by Justus Sustermans painted in 1636 when Galileo was aged 72. *Ian Ridpath, World's Oldest Astro Stamps page.

1938  In 1922 Issai Schur was elected to the Prussian Academy, proposed by Planck, the secretary of the Academy. Planck's address which listed Schur's outstanding achievements had been written by Frobenius, at least five years earlier, as Frobenius died in 1917.

On 29 March 1938 Bieberbach wrote below Schur's signature on a document of the Prussian Academy:- "I find it surprising that Jews are still members of academic commissions."

Just over a week later, on 7 April 1938, Schur resigned from Commissions of the Academy. However, the pressure on him continued and later that year he resigned completely from the Academy. Schur left Germany for Palestine in 1939, broken in mind and body, having the final humiliation of being forced to find a sponsor to pay the 'Reichs flight tax' to allow him to leave Germany. Without sufficient funds to live in Palestine he was forced to sell his beloved academic books to the Institute for Advanced Study in Princeton. He died two years later on his 66th birthday.

Only five years earlier  "On 7 April 1933 the Nazis passed a law which, under clause three, ordered the retirement of civil servants who were not of Aryan descent, with exemptions for participants in World War I and pre-war officials. Schur had held an appointment before World War I which should have qualified him as a civil servant, but the facts were not allowed to get in the way, and he was 'retired'. M M Schiffer wrote :-When Schur's lectures were cancelled there was an outcry among the students and professors, for Schur was respected and very well liked. The next day Erhard Schmidt started his lecture with a protest against this dismissal and even Bieberbach, who later made himself a shameful reputation as a Nazi, came out in Schur's defence. Schur went on quietly with his work on algebra at home."  #SAU

=====================================================================

1989 Pixar Wins Academy Award for "Tin Toy":

Pixar wins an Academy Award for "Tin Toy," the first entirely computer-animated work to win in the best animated short film category. Pixar, now a division of Disney, continued its success with a string of shorts and the first entirely computer-animated feature-length film, the best-selling "Toy Story." *CHM

2012 Buzz Lightyear that flew in space joins Smithsonian collection. Launched May 31, 2008, aboard the space shuttle Discovery with mission STS-124 and returned on Discovery 15 months later with STS-128, the 12-inch action figure is the longest-serving toy in space. Disney Parks partnered with NASA to send Buzz Lightyear to the International Space Station and create interactive games, educational worksheets and special messages encouraging students to pursue careers in science, technology, engineering and mathematics (STEM). The action figure will go on display in the museum’s "Moving Beyond Earth" gallery in the summer. The Toy Story character became part of the National Air and Space Museum’s popular culture collection. *http://airandspace.si.edu [I still have a Buzz Lightyear toy on my book case given to me by some students because I used to use his trademark quote in (my very questionable) Latin, "ad infinitum, et ultra." ]

BIRTHS

1825 Francesco Faà di Bruno (29 March 1825–27 March 1888) was an Italian mathematician and priest, born at Alessandria. He was of noble birth, and held, at one time, the rank of captain-of-staff in the Sardinian Army. He is the eponym of Faà di Bruno's formula. In 1988 he was beatified by Pope John Paul II. Today, he is best known for Faà di Bruno's formula on derivatives of composite functions, although it is now certain that the priority in its discovery and use is of Louis François Antoine Arbogast: Faà di Bruno should be only credited for the determinant form of this formula. However, his work is mainly related to elimination theory and to the theory of elliptic functions.
He was the author of about forty original articles published in the "Journal de Mathématiques" (edited by Joseph Liouville), Crelle's Journal, "American Journal of Mathematics" (Johns Hopkins University), "Annali di Tortolini", "Les Mondes", "Comptes rendus de l'Académie des sciences", etc.*Wik

1830 Thomas Bond Sprague (29 March 1830 in London, England - 29 Nov 1920 in Edinburgh, Scotland) studied at Cambridge and went on to become the most important actuary of the late 19th Century. He wrote more than 100 papers including many in the Proceedings of the EMS. *SAU

1873 Tullio Levi-Civita (29 Mar 1873, 29 Dec 1941) Italian mathematician who was one of the founders of absolute differential calculus (tensor analysis) which had applications to the theory of relativity. In 1887, he published a famous paper in which he developed the calculus of tensors. In 1900 he published, jointly with Ricci, the theory of tensors Méthodes de calcul différentiel absolu et leurs applications. in a form which was used by Einstein 15 years later. Weyl also used Levi-Civita's ideas to produce a unified theory of gravitation and electromagnetism. In addition to the important contributions his work made in the theory of relativity, Levi-Civita produced a series of papers treating elegantly the problem of a static gravitational field. *TIS

1890 Sir Harold Spencer Jones (29 Mar 1890, 3 Nov 1960) English astronomer who was 10th astronomer royal of England (1933–55). His work was devoted to fundamental positional astronomy. While HM Astronomer at the Cape of Good Hope, he worked on poper motions and parallaxes. Later he showed that small residuals in the apparent motions of the planets are due to the irregular rotation of the earth. He led in the worldwide effort to determine the distance to the sun by triangulating the distance of the asteroid Eros when it passed near the earth in 1930-31. Spencer Jones also improved timekeeping and knowledge of the Earth’s rotation. After WW II he supervised the move of the Royal Observatory to Herstmonceux, where it was renamed the Royal Greenwich Observatory.*TIS

1893 Jason John Nassau (29 March 1893 in Smyrna, (now Izmir) Turkey - 11 May 1965 in Cleveland, Ohio, USA) was an American astronomer.
He performed his doctoral studies at Syracuse, and gained his Ph.D. mathematics in 1920. (His thesis was Some Theorems in Alternants.) He then became an assistant professor at the Case Institute of Technology in 1921, teaching astronomy. He continued to instruct at that institution, becoming the University's first chair of astronomy from 1924 until 1959 and chairman of the graduate division from 1936 until 1940. After 1959 he was professor emeritus.
From 1924 until 1959 he was also the director of the Case Western Reserve University (CWRU) Warner and Swasey Observatory in Cleveland, Ohio. He was a pioneer in the study of galactic structure. He also discovered a new star cluster, co-discovered 2 novae in 1961, and developed a technique of studying the distribution of red (M-class or cooler) stars.*Wik

1896 Wilhelm Friedrich Ackermann (29 March 1896 – 24 December 1962) was a German mathematician best known for the Ackermann function, an important example in the theory of computation.*Wik

1912 Martin Eichler (29 March 1912 – 7 October 1992) was a German number theorist. He received his Ph.D. from the Martin Luther University of Halle-Wittenberg in 1936.
Eichler once stated that there were five fundamental operations of mathematics: addition, subtraction, multiplication, division, and modular forms. He is linked with Goro Shimura in the development of a method to construct elliptic curves from certain modular forms. The converse notion that every elliptic curve has a corresponding modular form would later be the key to the proof of Fermat's last theorem.*Wik

1912 Caius Jacob (29 March 1912 , Arad - 6 February 1992 , Bucharest ) was a Romanian mathematician and member of the Romanian Academy. He made ​​contributions in the fields of fluid mechanics and mathematical analysis , in particular vigilance in plane movements of incompressible fluids, speeds of movement at subsonic and supersonic , approximate solutions in gas dynamics and the old problem of potential theory. His most important publishing was Mathematical introduction to the mechanics of fluids. *Wik

1941 Joseph Hooton Taylor, Jr. (March 29, 1941, ) is an American astrophysicist and Nobel Prize in Physics laureate for his discovery with Russell Alan Hulse of a "new type of pulsar, a discovery that has opened up new possibilities for the study of gravitation." *Wi

DEATHS

1772 Emanuel Swedenborg (29 Jan 1688; 29 Mar 1772) Swedish scientist, philosopher and theologian. While young, he studied mathematics and the natural sciences in England and Europe. From Swedenborg's inventive and mechanical genius came his method of finding terrestrial longitude by the Moon, new methods of constructing docks and even tentative suggestions for the submarine and the airplane. Back in Sweden, he started (1715) that country's first scientific journal, Daedalus Hyperboreus. His book on algebra was the first in the Swedish language, and in 1721 he published a work on chemistry and physics. Swedenborg devoted 30 years to improving Sweden's metal-mining industries, while still publishing on cosmology, corpuscular philosophy, mathematics, and human sensory perceptions. *TIS

1806 John Thomas Graves (4 December 1806, Dublin, Ireland–29 March 1870, Cheltenham, England) was an Irish jurist and mathematician. He was a friend of William Rowan Hamilton, and is credited both with inspiring Hamilton to discover the quaternions and with personally discovering the octonions, which he called the octaves. He was the brother of both the mathematician Charles Graves and the writer and clergyman Robert Perceval Graves.
In his twentieth year (1826) Graves engaged in researches on the exponential function and the complex logarithm; they were printed in the Philosophical Transactions for 1829 under the title An Attempt to Rectify the Inaccuracy of some Logarithmic Formulæ. M. Vincent of Lille claimed to have arrived in 1825 at similar results, which, however, were not published by him till 1832. The conclusions announced by Graves were not at first accepted by George Peacock, who referred to them in his Report on Algebra, nor by Sir John Herschel. Graves communicated to the British Association in 1834 (Report for that year) on his discovery, and in the same report is a supporting paper by Hamilton, On Conjugate Functions or Algebraic Couples, as tending to illustrate generally the Doctrine of Imaginary Quantities, and as confirming the Results of Mr. Graves respecting the existence of Two independent Integers in the complete expression of an Imaginary Logarithm. It was an anticipation, as far as publication was concerned, of an extended memoir, which had been read by Hamilton before the Royal Irish Academy on 24 November 1833, On Conjugate Functions or Algebraic Couples, and subsequently published in the seventeenth volume of the Transactions of the Royal Irish Academy. To this memoir were prefixed A Preliminary and Elementary Essay on Algebra as the Science of Pure Time, and some General Introductory Remarks. In the concluding paragraphs of each of these three papers Hamilton acknowledges that it was "in reflecting on the important symbolical results of Mr. Graves respecting imaginary logarithms, and in attempting to explain to himself the theoretical meaning of those remarkable symbolisms", that he was conducted to "the theory of conjugate functions, which, leading on to a theory of triplets and sets of moments, steps, and numbers" were foundational for his own work, culminating in the discovery of quaternions.
For many years Graves and Hamilton maintained a correspondence on the interpretation of imaginaries. In 1843 Hamilton discovered the quaternions, and it was to Graves that he made on 17 October his first written communication of the discovery. In his preface to the Lectures on Quaternions and in a prefatory letter to a communication to the Philosophical Magazine for December 1844 are acknowledgments of his indebtedness to Graves for stimulus and suggestion. After the discovery of quaternions, Graves employed himself in extending to eight squares Euler's four-square identity, and went on to conceive a theory of "octaves" (now called octonions) analogous to Hamilton's theory of quaternions, introducing four imaginaries additional to Hamilton's i, j and k, and conforming to "the law of the modulus".
Graves devised also a pure-triplet system founded on the roots of positive unity, simultaneously with his brother Charles Graves, the bishop of Limerick. He afterwards stimulated Hamilton to the study of polyhedra, and was told of the discovery of the icosian calculus. *Wik

The icosian calculus is a non-commutative algebraic structure discovered by the Irish mathematician William Rowan Hamilton in 1856. In modern terms, he gave a group presentation of the icosahedral rotation group by generators and relations.

Hamilton's discovery derived from his attempts to find an algebra of "triplets" or 3-tuples that he believed would reflect the three Cartesian axes. The symbols of the icosian calculus can be equated to moves between vertices on a dodecahedron. Hamilton's work in this area resulted indirectly in the terms Hamiltonian circuit and Hamiltonian path in graph theory. He also invented the icosian game as a means of illustrating and popularizing his discovery.

1873 Francesco Zantedeschi (born 1797, 29 Mar 1873) Italian priest and physicist, who published papers (1829, 1830) on the production of electric currents in closed circuits by the approach and withdrawal of a magnet, preceding Faraday's classic experiment of 1831. Studying the solar spectrum, Zantedeschi was among the first to recognize the marked absorption by the atmosphere of the red, yellow, and green light. Though not confirmed, he also thought he detected a magnetic action on steel needles by ultra-violet light (1838), at least suspecting a connection between light and magnetism many years before Clerk-Maxwell's announcement (1867) of the electromagnetic theory of light. He experimented on the repulsion of flames by a strong magnetic field.*TIS

1912 Robert Falcon Scott, (6 June 1868 - 29 March 1912) was a Royal Navy officer and explorer who led two expeditions to the Antarctic regions: the Discovery Expedition, 1901–04, and the ill-fated Terra Nova Expedition, 1910–13. During this second venture, Scott led a party of five which reached the South Pole on 17 January 1912, only to find that they had been preceded by Roald Amundsen's Norwegian expedition. On their return journey, Scott and his four comrades all died from a combination of exhaustion, starvation and extreme cold.  *Wik

1944 Grace Chisholm Young (née Chisholm; 15 March 1868 – 29 March 1944) was an English mathematician. She was educated at Girton College, Cambridge, England and continued her studies at Göttingen University in Germany. Her early writings were published under the name of her husband, William Henry Young, and they collaborated on mathematical work throughout their lives. For her work on calculus (1914–16), she was awarded the Gamble Prize.
Her son, Laurence Chisholm Young, was also a prominent mathematician. One of her living granddaughters, Sylvia Wiegand (daughter of Laurence), is also a mathematician (and a past president of the Association for Women in Mathematics.)*Wik

1980 William Gemmell Cochran (15 July 1909, Rutherglen – 29 March 1980, Orleans, Massachusetts)In 1934 R A Fisher left Rothamsted Experimental Station to accept the Galton chair at University College, London and Frank Yates became head at Rothamsted. Cochran was offered the vacant post but he had not finished his doctoral course at Cambridge. Yates later wrote:-
... it was a measure of good sense that he accepted my argument that a PhD, even from Cambridge, was little evidence of research ability, and that Cambridge had at that time little to teach him in statistics that could not be much better learnt from practical work in a research institute.
Cochran accepted the post at Rothamsted where he worked for 5 years on experimental designs and sample survey techniques. During this time he worked closely with Yates. At this time he also had the chance to work with Fisher who was a frequent visitor at Rothamsted.
Cochran visited Iowa Statistical Laboratory in 1938, then he accepted a statistics post there in 1939. His task was to develop the graduate programe in statistics within the Mathematics Department. In 1943 he joined Wilks research team at Princeton.
At Princeton he was involved in war work examining probabilities of hits in naval warfare. By 1945 he was working on bombing raid strategies.
He joined the newly created North Carolina Institute of Statistics in 1946, again to develop the graduate programe in statistics. From 1949 until 1957 he was at Johns Hopkins University in the chair of biostatistics. Here he was more involved in medical applications of statistics rather than the agricultural application he had studied earlier.
From 1957 until he retired in 1976 Cochran was at Harvard. His initial task was to help set up a statistics department, something which he had a great deal of experience with by this time. He had almost become a professional at starting statistics within universities in the USA. *SAU

1983 Sir Maurice George Kendall, FBA (6 September 1907 – 29 March 1983) was a British statistician, widely known for his contribution to statistics. The Kendall tau rank correlation is named after him.*Wik He was involved in developing one of the first mechanical devices to produce (pseudo-) random digits, eventually leading to a 100,000-random-digit set commonly used until RAND's (once well-known) "A Million Random Digits With 100,000 Normal Deviates" in 1955.
Kendall was Professor of Statistics at the London School of Economics from 1949 to 1961. His main work in statistics involved k-statistics, time series, and rank-correlation methods, including developing the Kendall's tau stat, which eventually led to a monograph on Rank Correlation in 1948. He was also involved in several large sample-survey projects. For many, what Kendall is best known for is his set of books titled The Advanced Theory of Statistics (ATS), with Volume I first appearing in 1943 and Volume II in 1946. Kendall later completed a
rewriting of ATS, which appeared in three volumes in 1966, which were updated by collaborator Alan Stuart and Keith Ord after Kendall's death, appearing now as "Kendall's Advanced Theory of Statistics". *David Bee

1999 Boris A. Kordemsky ( 23 May 1907 – 29 March, 1999) was a Russian mathematician and educator. He is best known for his popular science books and mathematical puzzles. He is the author of over 70 books and popular mathematics articles.
Kordemsky received Ph.D. in education in 1956 and taught mathematics at several Moscow colleges.
He is probably the best-selling author of math puzzle books in the history of the world. Just one of his books, Matematicheskaya Smekalka (or, Mathematical Quick-Wits), sold more than a million copies in the Soviet Union/Russia alone, and it has been translated into many languages. By exciting millions of people in mathematical problems over five decades, he influenced generations of solvers both at home and abroad. *Age of Puzzles, by Will Shortz and Serhiy Grabarchuk (mostly)

1908 John Bardeen (23 May 1908; 30 Jan 1991 at age 82) American physicist who was cowinner of the Nobel Prize for Physics in both 1956 and 1972. He shared the 1956 prize with William B. Shockley and Walter H. Brattain for their joint invention of the transistor. With Leon N. Cooper and John R. Schrieffer he was awarded the 1972 prize for development of the theory of superconductors, usually called the BCS-theory (after the initials of their names). *TIS

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