## Sunday 28 May 2023

### On This Day in Math - May 28

Twice two makes four seems to me
simply a piece of insolence.
Twice two makes four is a pert coxcomb who stands
with arms akimbo barring your path and spitting.
I admit that twice two makes four is an excellent thing,
but if we are to give everything its due,
twice two makes five is sometimes
a very charming thing too.
~Fyodor Mikhailovich Dostoevsky

The 148th day of the year;  148 is a Palindrome in base 6(404) and base 36 (44).

$e^{\pi\sqrt{148}}$   is an integer..... almost, 39660184000219160.00096667...

148 is also a Loeschian number, a number of the form a2 + ab + b2. These numbers and the triples (a,b,L) formed by points in space are used, among other places in locations of spheres under hexagonal packing.
Voodooguru informed me that the Loeschian numbers are named after August Lösch,
according to https://en.wikipedia.org/wiki/Loeschian_number. He was an economist:

"Overall, Lösch made a plenitude of significant findings in the world of economics, but his main contributions were to regional economics, specifically, pioneering the location theory, spatial equilibrium analysis and hierarchical spatial systems displaying a hexagonal pattern."
The Loeschian numbers are the norms of the Eisenstein integers that form a triangular lattice on the complex plane.

If you let x and y be both be greater than 1, then x + xy + y will never equal 148.  And that means that the product of the first 148 integers is not divisible by the sum of the first 148 integers.

A Vampire number is a number whose digits can be regrouped into two smaller numbers that multiply to make the original (1260 = 21*60).  There are 148 vampire numbers with six digits.   (***How many with four digits?)

EVENTS

585 BC Thales predicted the total eclipse of the sun that took place on this date. See Herschel, Outline of Astronomy (1902), pp. 833 and 839. [Eves, Circles, 33◦] *VFR  WW Rouse Ball says it is uncertain whether the date is the 585 date, or Sep 30, 609 BC.  Heath, and most others, seem to settle on the 585 BC date.

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1555  On this day in 1555, John Dee   was arrested and charged with "calculating"  because he had cast horoscopes of Queen Mary and Princess Elizabeth. The charges were raised to treason against Mary. At this time mathematics in England was considered to be equivalent to the possession of magical powers. Aubrey writes that the authorities had:-

... burned mathematical books for conjuring books.

Although he was guilty of the charges brought against him, Dee was released in August after being held for three months.  *MacTutor

Dee appeared in the Star Chamber and exonerated himself, but was turned over to the Catholic bishop Edmund Bonner for religious examination. His strong, lifelong penchant for secrecy may have worsened matters. The episode was the most dramatic in a series of attacks and slanders that dogged Dee throughout his life. Clearing his name yet again, he soon became a close associate of Bonner

John Dee memorial plaque installed in 2013 inside the church of St Mary the Virgin, Mortlake
 *Wik

1607  Kepler used his newly devised camera obscura, which he named, to observe the solar disk and saw a sunspot, which he mistook for a transit of Mercury, to the amazement of later astronomers who all agreed that of all people, Kepler really should have known better. The first recorded mention of what was surely sunspots.

One year after the introduction of the telescope astronomers identified spots on the Sun. Fabricius was the first to print a book on sunspots at the end of 1611, but this book had little diffusion. Fabricius rightly thought that the spots belonged to the Sun. The Jesuit C. Scheiner independently observed sunspots on the Sun and he announced his discovery at the end of 1611 in three letters under the pseudonym Apelles. Scheiner failed to observe the returning of the spots and hence did not recognize the solar rotation. Therefore he preferred to see the spots as caused by little bodies orbiting the Sun. Based on Scheiner’s observations, Kepler concluded that the spots were on the solar surface like dross floating on melted metal.

 Scheiner drawings

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1684   Robert Hooke delivered some of his most perceptive and far sighted views of the geology of what he called this "terraqueous globe"  in lectures beginning on May 28 and published posthumously.  In these lectures he shared ideas novel to his contemporaries, including "the organic origin, and significance of fossils; cyclicity of the processes of sedimentation,  erosion, consolidation, uplift, and denudation; various processes of petrifacation; subterraneous eruptions  and earthquakes; biologic evolution; the oblate spheroid shape of the Earth; Polar wandering, and universal gravitation. "  *Ellen Tan Drake; Hooke's Ideas of the Terraqueous  Globe and a Theory of Evolution

1765 The Longitude Board at Greenwich awards Leonhard Euler an amount of 300 Pounds, "Reward for Theorems furnished by him to assist Professor Mayer in the Construction of Lunar Tables upon the Principles of Gravitation laid down by Sir Isaac Newton."
Tobias Mayer had died in 1762, but his widow received an amount of 3000 Pounds for his work in the same meeting for his construction of the tables, which she signed over to the Committee. *Derek Howse, Britain's Board of Longitude:The Finances, 1714-1828

1783, Benjamin Franklin receives a letter at his hotel in Paris from Wolfgang von Kempelen, creator of the Turk chess playing automaton, inviting him to see and play his automaton as well as inspect the half-finished talking machine.
Franklin accepted the challenge, played the Turk a few days later at the Café de la Regence and lost. Although Franklin was a lover of chess, he does not mention this event in any of his recorded correspondence, perhaps, some explain, because he was known to be a very poor loser. *Tom Standage, The Turk, 2002 Walker Publishing

The Turk was in fact a mechanical illusion that allowed a human chess master hiding inside to operate the machine. With a skilled operator, the Turk won most of the games played during its demonstrations around Europe and the Americas for nearly 84 years, playing and defeating many challengers including statesmen such as Napoleon Bonaparte and Benjamin Franklin. The device was later purchased in 1804 and exhibited by Johann Nepomuk Mälzel. *Wik

 *Bibliophilia ‏@Libroantiguo

1890  The Harvard Observatory distributed the “Henry Draper Memorial far and wide, including publication in Nature and other scientific journals. The report found one of its most appreciative audiences in England, at the home of astronomer and military engineer Colonel John Herschel. As a grandson of William Herschel (discoverer of the planet Uranus) and a son of Sir John Herschel (thrice president of the Royal Astronomical Society), the colonel had seen his share of important leaps in celestial knowledge.

“I have just rec’d your last H. D. Mem. report,” he wrote to Pickering on May 28, 1890. “It is very like a pudding all plums—but I will ask you to convey to Miss Maury ( Antonia Maury  was an American astronomer who was the first to detect and calculate the orbit of a spectroscopic binary. She published an important early catalog of stellar spectra using her own system of stellar classification, which was later adopted by the International Astronomical Union) congratulations on having connected her name with one of the most notable advances in physical astronomy ever made.” Like the colonel’s much celebrated great-aunt, Caroline Herschel, Miss Maury had entered a field of discovery dominated by men, yet she stood among the first astronomers to detect an entirely new group of objects through the upstart method of spectral photography. Its future—and hers—seemed full of promise.”  *The Glass Universe: How the Ladies of the Harvard Observatory Took the Measure of the Stars by Dava Sobel

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1936  Alan Turing submitted his paper ‘On Computable Numbers’, #OnThisDay in 1936.  His idea was not turned into a reality for more than ten years – when he would make a vital contribution to the Allied victory in the Second World War. *History Today

One Historian said his paper had no relation to his work at Bletchley Park.

In 1937, the Golden Gate Bridge, San Francisco was ceremonially opened to vehicles by President Franklin Delano Roosevelt who pressed a telegraph key in the White House. Within the first hour after the toll gates opened, 1,800 cars crossed the bridge. By day's end, 32,300 vehicles and 19,350 pedestrians had paid to pass over the bridge. A firework display that night celebrated the opening of the bridge. The previous day, a Pedestrian Day had been held which first opened the bridge for public use. The building and design of the bridge had been supervised by chief engineer Joseph B. Strauss. Construction had started on 5 Jan 1933. It was the first bridge to span the mouth of a major U.S. ocean harbour.*TIS

 "Gentlemen, Start your engines!"

1959 Committee formed which developed COBOL. COBOL is one of the oldest programming languages. Its name is an acronym for COmmon Business-Oriented Language, defining its primary domain in business, finance, and administrative systems for companies and governments.
The COBOL specification was created by a committee of researchers from private industry, universities, and government during the second half of 1959. The specifications were to a great extent inspired by the FLOW-MATIC language invented by Grace Hopper - commonly referred to as "the mother of the COBOL language." The IBM COMTRAN language invented by Bob Bemer was also drawn upon, but the FACT language specification from Honeywell was not distributed to committee members until late in the process and had relatively little impact. FLOW-MATIC's status as the only language of the bunch to have actually been implemented made it particularly attractive to the committee.*Wik

1981 The New Scientist (pp 506-507) describes a mathematical theory of how coloration develops in animals. Zebras have stripes rather that spots because coloring is determined at an early stage of the development of the fetus. [Mathematics Magazine 54 (1981), p 215.] *VFR

In 1998, NASA released a picture of what California astronomer Susan Terebey said may be the first extrasolar planet ever seen, dubbed TMR-1C. Digitized pictures taken by the Hubbell Space Telescope seemed to show an image of a planet apparently flung from a pair of young stars in the constellation Taurus, 450 light years from Earth. Located at one end of a bright trail that led from the newborn stars, the faint object appeared as if it was their offspring, a planet a few times as massive as Jupiter that had been expelled from its birthplace. However, by the following year, scrutiny of its spectrum suggested to other astronomers that it could be merely a background star. Telescopic tracking for several years should resolve the answer.*TIS

2013 David L. Donoho has been awarded the 2013 Shaw Prize in Mathematical Sciences for his profound contributions to modern mathematical statistics and in particular the development of optimal algorithms for statistical estimation in the presence of noise and of efficient techniques for sparse representation and recovery in large data-sets.
The Anne T and Robert M Bass Professor of the Humanities and Sciences, and Professor of Statistics at Stanford University, Dr. Donoho is well known for his role in developing new mathematical and statistical tools to deal with problems ranging from large data-sets in high dimensions to contamination with noise. *SIAM

BIRTHS

1676 Jacopo Riccati (28 May 1676 – 15 April 1754) was an Italian mathematician who wrote on philosophy, physics and differential equations. He is chiefly known for the Riccati differential equation. *SAU   The general Riccati diferential equation is of the form dy/dx = A+ By + Cy2 where A, B, and C represent functions of x..(there are actually several types of diff equations known by this term..)  He had two sons who also contributed to mathematics.  Vincenzo was a professor in Bologna, and Giordano published works in Geometry and on Newton's works.  Jacopo (and both sons) died in Treviso.

1710 Johann(II) Bernoulli (28 May 1710 in Basel, Switzerland - 17 July 1790 in Basel, Switzerland)
was a member of the Swiss mathematical family. He worked mainly on heat and light. He was one of three sons of Johann Bernoulli. In fact he was the most successful of the three. He originally studied law and in 1727 he obtained the degree of doctor of jurisprudence. He worked on mathematics both with his father and as an independent worker. He had the remarkable distinction of winning the Prize of the Paris Academy on no less than four separate occasions. On the strength of this he was appointed to his father's chair in Basel when Johann Bernoulli died. *Wik

1850 Wooster Woodruff Beman (May 28, 1850 - January 1, 1922). He attended school in Valparaiso, Ind., and entered the University of Michigan in 1866, receiving his B.A. degree in 1870. After teaching for a year at Kalamazoo College as instructor in Greek and mathematics, he returned to the University of Michigan as an instructor while also working for his master's degree, which he received in 1873. In 1874, he became assistant professor, in 1882 associate professor, and in 1887 full professor.
In addition to his teaching, Beman wrote books and articles on the history and teaching of elementary mathematics. Among his works are "Nature and Meaning of Numbers" (from the German), and "Continuity and Irrational Numbers." He was the joint author, with D. E. Smith, of "Plane and Solid Geometry," "Higher Arithmetic," "New Plane and Solid Geometry," "Elements of Algebra," "Academic Algebra," translations of "Famous Problems of Elementary Geometry," and "A Brief History of Mathematics." *Michigan Historical Collections. They also were editors of T. Sundara Row's Geometric Exercises in Paper Folding:

1888 Jim Thorpe (May 28, 1888 – March 28, 1953) World-class athlete He was born in a one-room cabin near Prague in Indian Territory, now Oklahoma. Thorpe's versatile talents earned him the distinction of being chosen, in 1950, the greatest football player and the greatest American athlete of the first half of the twentieth century by American sports writers and broadcasters. Thorpe won the gold medal in both the decathlon and pentathlon events at the Stockholm Olympics, but was stripped of his medals when a reporter revealed he had played semi-professional baseball. It was not until after his death that Thorpe's amateur status was restored, and his name reentered in the Olympic record book. (Library of Congress web page)
So why is this on a math page…Well it seems that Jim Thorpe may have indirectly influenced the naming of the # key on the telephone. One of several stories for how it is named is this one: In the 1960's when Bell Telephone added two new buttons for push button telephones, they used the * symbol and the # symbol. Although most people call the * an asterisk, the telephone folks decided to use "star". The other symbol, #, has been called lots of different names such as crosshatch, and now the common term on twitter seems to be "hashtag".  Others have  referred to it as tic-tac-toe, the pound sign, and the number sign (leave it to the telephone company to put the number sign on one of the two keys without a number); but the term now "officially" used by the American telephone industry for the symbol is octothorpe although it is more often called the pound key in conversations with the public.
It seems that the name was made up more or less spontaneously by Bell Engineer Don MacPherson while meeting with their first potential customer. The octo part was chosen because of the eight points at the ends of the line segments, and the thorpe was in honor of Jim Thorpe, the great Native American athlete. Why honor Thorpe? At the time MacPherson was working with a group that was trying to restore Thorpe's Olympic medals, which had been taken from him when it was found he had played semi-professional baseball prior to his track victories in the Olympics in Sweden. [It's not math, but I love the story that when the King of Sweden gave him the gold medal, the king said, "You are surely the greatest athlete on the earth". The modest Thorpe smiled and replied, "Thanks, King."]
There are a host of other names for the # symbol, and many of them can be found at this page from Wikipedia which includes several different stories about the creation of "octothorpe" or "octothorn" and also has this rather interesting clip:
"The pronunciation of # as pound' is common in the US but a bad idea. The British Commonwealth has its own, rather more apposite, use of pound sign. On British keyboards the UK pound currency symbol once frequenlty replaced #, with # being elsewhere on the keyboard. The US usage derives from an old-fashioned commercial practice of using a # suffix to tag pound weights on bills of lading. The character is usually pronounced hash' outside the US. There are more culture wars over the correct name of this character than any other, which has led to the “ha-ha” only serious suggestion that it be pronounced shibboleth' (see Judges 12:6 in the Old Testament)." (pballew Etymology page)

The Cincinnati Reds bought Jim Thorpe from the New YorkGiants in 1917

1908 Egbert van Kampen, In 1908 he left Europe and traveled to the United States to take up the position which he had been offered at Johns Hopkins University in Baltimore, Maryland. There he met Oscar Zariski who had taught at Johns Hopkins University as a Johnston Scholar from 1927 until 1929 when he had joined the Faculty. Zariski had been working on the fundamental group of the complement of an algebraic curve, and he had found generators and relations for the fundamental group but was unable to show that he had found sufficient relations to give a presentation for the group. Van Kampen solved the problem, showing that Zariski's relations were sufficient, and the result is now known as the Zariski–van Kampen theorem. This led van Kampen to formulate and prove what is nowadays known as the Seifert–van Kampen theorem. *Wik

1912 Ruby Violet Payne-Scott, (28 May 1912 – 25 May 1981) was an Australian pioneer in radiophysics and radio astronomy, and was the first female radio astronomer.
One of the more outstanding physicists that Australia has ever produced and one of the first people in the world to consider the possibility of radio astronomy, and thereby responsible for what is now a fundamental part of the modern lexicon of science, she was often the only woman in her classes at the University of Sydney.
Her career arguably reached its zenith while working for the Australian government's Commonwealth Scientific and Industrial Research Organisation (then called CSIR, now known as CSIRO) at Dover Heights, Hornsby and especially Potts Hill in Sydney. Some of her fundamental contributions to solar radio astronomy came at the end of this period. She is the discoverer of Type I and Type III bursts and participated in the recognition of Type II and IV bursts.
She played a major role in the first-ever radio astronomical interferometer observation from 26 January 1946, when the sea-cliff interferometer was used to determine the position and angular size of a solar burst. This observation occurred at either Dover Heights (ex Army shore defence radar) or at Beacon Hill, near Collaroy on Sydney's north shore (ex Royal Australian Air Force surveillance radar establishment - however this radar did not become active until early 1950).[4]
During World War II, she was engaged in top secret work investigating radar. She was the expert on the detection of aircraft using PPI (Plan Position Indicator) displays. She was also at the time a member of the Communist Party and an early advocate for women's rights. The Australian Security Intelligence Organisation (ASIO) was interested in Payne-Scott and had a substantial file on her activities, with some distortions.
*Wik

 *Wik

1912 Hans Zassenhaus, algebraist. (28 May 1912–21 November 1991) was a German mathematician, known for work in many parts of abstract algebra, and as a pioneer of computer algebra.
He was born in Koblenz–Moselweiss, and became a student and then assistant of Emil Artin. He was subsequently a professor at McGill University, the University of Notre Dame, and Ohio State University, and was one of the founding editors of the Journal of Number Theory. He died in Columbus, Ohio. *Wik

1930 Frank Donald Drake ( May 28, 1930 -  ) is an American astronomer who formulated the Drake Equation (1961) to estimate the number of technological civilizations that may exist in our galaxy. In 1960, Drake led the first search, the two-month Project Ozma to listen for patterns in radio waves with a complex, ordered pattern that might be assumed to represent messages from some extraterrestrial intelligence. Carl Sagan and Drake designed the plaques on Pioneer 10 and Pioneer 11 for the purpose of greeting and informing any extraterrestrial life that might find the vessels after they left the solar system. *TIS

The equation was formulated in 1961 by Frank Drake, not for purposes of quantifying the number of civilizations, but as a way to stimulate scientific dialogue at the first scientific meeting on the search for extraterrestrial intelligence (SETI)

N = the number of civilizations in the Milky Way galaxy with which communication might be possible (i.e. which are on the current past light cone);  was the product of these seven terms.

R∗ = the average rate of star formation in our Galaxy

fp = the fraction of those stars that have planets

ne = the average number of planets that can potentially support life per star that has planets

fl = the fraction of planets that could support life that actually develop life at some point

fi = the fraction of planets with life that actually go on to develop intelligent life (civilizations)

fc = the fraction of civilizations that develop a technology that releases detectable signs of their existence into space

L = the length of time for which such civilizations release detectable signals into space

Inserting the minimum estimates for each value produced a value of 20 civilizations in the Milky Way.

 Allen Telescope for SETI

DEATHS

1997 Ronald Vernon Book (April 1937 – May 28, 1997 in Santa Barbara, California) worked in theoretical computer science. He published more than 150 papers in scientific journals.

2003 Ilya Prigogine (25 Jan 1917; 28 May 2003) Russian-born Belgian physical chemist who received the Nobel Prize for Chemistry in 1977 for contributions to nonequilibrium thermodynamics, or how life could continue indefinitely in apparent defiance of the classical laws of physics. The main theme of Prigogine's work was the search for a better understanding of the role of time in the physical sciences and in biology. He attempted to reconcile a tendency in nature for disorder to increase (for statues to crumble or ice cubes to melt, as described in the second law of thermodynamics) with so-called "self-organisation", a countervailing tendency to create order from disorder (as seen in, for example, the formation of the complex proteins in a living creature from a mixture of simple molecules). *TIS

***  There are 7 four-digit vampire numbers, 1260, 1395, 1435, 1530, 1827, 2187, 6880,***

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