## Tuesday 16 July 2024

### On This Day in Math - July 16

Pure mathematics is the world's best game.
It is more absorbing than chess, more of a gamble than poker,
and lasts longer than Monopoly.
It's free. It can be played anywhere
- Archimedes did it in a bathtub.

-Richard J. Trudeau

The 197th day of this year; 197 is the sum of all digits of all two-digit prime numbers: 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97.  It is simple to show that the sum of one-digit primes is 17. Do the sum of the digits of n-digit primes always end in seven? (http://oeis.org/A130817) Or perhaps we ask, are there any others that do?  A nice problem for students, look at the sum of all the primes of n digits and decide are there an odd or even number of primes with n digits.For example, the sum of all the four-digit primes is 19879, is the total number of four-digit primes odd or even?

197 is the smallest prime number that is the sum of 7 consecutive primes: 17 + 19 + 23 + 29 + 31 + 37 + 41 (student challenge: can there be a prime that is the sum of eight consecutive primes?)

197 is the seventh, and last, year-day that will be a Keith number   created in 1987 by Michael Keith.  (they are also repfigit numbers, the term he originally used for them. )

197 is the sum of the first twelve prime numbers: 2 + 3 + 5 + 7 + 11 + 13 + 17 + 19 + 23 + 29 + 31 + 37

More Math facts for every year date here

EVENTS

433 B.C. The Metonic 19-year cycle of the moon enacted. This masterpiece of approximation (19 solar years = 235 lunations) is still used today in the computation of the date of Easter. [See A. Philip, The Calendar: Its History, Structure and Improvement, p. 8]*VFR  (I have also seen June 27, 432 BC given for this event.  Purist may choose up sides and argue for their choice)

The cycle was introduced in ancient Greece by Athenian astronomer Meton around 432 BC. The cycle consists of 235 lunations, or synodic months, and seven intercalated months. After this cycle, the moon's phases return on the same days of the solar year.

Depiction of the 19 years of the Metonic cycle as a wheel, with the Julian date of the Easter New Moon, from a 9th-century computistic manuscript made in St. Emmeram's Abbey (Clm 14456, fol. 71r)

1661 Europe’s earliest modern-style banknotes, available to all and sundry with each note worth a fixed sum, were introduced by the Bank of Stockholm. The bank had been started in 1657 by Johan Palmstruch in close collaboration with the royal government which pocketed half the profits. It was Palmstruch who suggested the kreditivsedlar (credit notes) and they provided a welcome alternative to Sweden’s massive copper coins, which were dismayingly heavy and clumsy. Colloquially known as Palmstruchers the notes were printed on thick, white watermarked paper with the word banco as the watermark and carried the date, the bank’s seal and eight signatures, headed by Palmstruch’s, as an assurance of reliability. They were in stated denominations and payable to the bearer and anybody who had one was promised payment by the bank.  (*History Today )

1669  Wallis writes to Oldenburg complaining about the public perception of the Royal Society after Doctor Robert Smith's dedication of the New Theater consisted of only, "Satyrical invectives against Cromwell, Fanaticks, the Royal Society and Philosophy." *The mathematical work of John Wallis, D.D., F.R.S., (1616-1703) By Joseph Frederick Scott, pg 11

1730 The famous lines of Alexander Pope (1688–1744) which were intended as an epitaph for Newton:
Nature and Nature’s Laws lay hid in night: God said, Let Newton be! and all was light.
were published in the Grub-Street Journal, the ﬁrst time they appeared in print. *VFR

The Grub-Street Journal, published from 8 January 1730 to 1738,was a satire on popular journalism and hack-writing as it was conducted in Grub Street in London.It was largely edited by the nonjuror Richard Russel and the botanist John Martyn. While he disclaimed it, Alexander Pope was one of its contributors, continuing his satire which he had started with The Dunciad.

1828 James Ryan recorded his copyright for The Differential and Integral Calculus, the ﬁrst calculus book written by a U.S. citizen.*VFR

1848 Exactly 50 years earlier, Gauss received his doctorate. As part of the show at the golden jubilee Gauss was to light his pipe with a manuscript page from his Disquisitiones Arithmeticae. His student Dirichlet was outraged by this sacrilege and boldly snatched the paper as a treasured memento. [Eves, History of Mathematics, p. 370]*VFR

1945 The ﬁrst atomic bomb explosion was carried out in a test at Alamogordo Air Base in New Mexico, at 12:29:15 G.C.T.  *VFR The atomic bomb was invented by two refugee German scientists in Britain, Professor Rudolph Peierls and Otto Frisch, of Birmingham University. They designed a "blue-print" for making an atom bomb in 1940. It actually began when the Italian-born physicist Enrico Fermi, working in the United States, invented an apparatus which produced the first atomic chain reactions. In 1940 both the Americans and British were researching the atom bomb and when the United States entered WW2, the British joined the American "Manhattan Project" and production of the bomb went on ahead in the US.*TIS

1969  Apollo 11 lifts off.  Launched by a Saturn V rocket from Kennedy Space Center in Merritt Island, Florida on July 16, Apollo 11 was the fifth manned mission of NASA's Apollo program. It would result in the first astronauts to land on the Moon on July 20, 1969. *Wik

In 1994, the first of 21 asteroids, major fragments of the comet Shoemaker-Levy 9 broken-up 2 years earlier, hit Jupiter, creating a 1200-mile wide fireball 600 miles high to the joy of astronomers awaiting the celestial fireworks, giving scientists their first chance to observe such a collision as it happened, and others through July 22. Jupiter is a gas giant, made up mostly of hydrogen and helium in gas and liquid form.When we observe Jupiter, we are looking not at a solid surface, but a banded atmosphere with swirling clouds and huge storms.*TIS

1995 Amazon.com, incorporated a year earlier by Jeff Bezos in Washington (state) as an online bookstore, sells its first book, Douglas Hofstadter's Fluid Concepts and Creative Analogies: Computer Models of the Fundamental Mechanisms of Thought. *Wik

2186 (In case you live a really long time) will be the Closest approach to maximum possible duration of totality with 7 min 29 sec in the Atlantic Ocean. Maximum theoretical
duration is 7 min 31 sec. During the 4th millennium there are only 2 solar eclipses with maximum duration of totality longer than 7 min. In the years 3973 and 3991. There are none in 21st century. *NSEC

BIRTHS

1678 Jakob Hermann (16 July 1678, Basel – 11 July 1733, Basel) was a Swiss mathematician who made contributions to dynamics.*SAU In 1729, he proclaimed that it was as easy to graph a locus on the polar coordinate system as it was to graph it on the Cartesian coordinate system. However, no one listened. He was a distant relative of Leonhard Euler.

He appears to have been the first to show that the Laplace–Runge–Lenz vector is a constant of motion for particles acted upon by an inverse-square central force.*Wik

1689 Samuel Molyneux FRS (16 July 1689 – 13 April 1728) was an amateur astronomer and politician who sat in the British House of Commons between 1715 and 1728 and in the Irish House of Commons from 1727 to 1728. His work with James Bradley attempting to measure stellar parallax led to the discovery of the aberration of light. The aberration was the first definite evidence that the earth moved and that Copernicus and Kepler were correct. In addition to his astronomical works, Molyneux wrote about the natural history and other features of Ireland.

Bradley and Molyneux began their work in 1725, and they never did observe stellar parallax – it was too small for even their instrument to detect. But they did observe another unexpected slight annual motion of their target star, known as gamma Draconis. Bradley ultimately realized that it was a result of the fact that light moves with a finite speed, so that if the earth is moving across the path of the light, the result is a slight sideways deflection of the light. He called this new phenomenon the "aberration of light," and he announced it in a paper of 1729. It was one of the very first proofs that the earth moves through space. It is unfortunate that Molyneux, who should have shared in the approbation, had collapsed and died the previous year, at the age of only 38. Molyneux’s original telescope has disappeared, but Bradley ordered another from the same instrument maker for himself, just 12 feet long, and that one does survive, in the National Maritime Museum

He died in suspicious circumstances.  Molyneux had married Lady Elizabeth Capel, daughter of Algernon Capell, 2nd Earl of Essex, on 5 April 1717. In 1728, he suffered a fit while in the House of Commons. He was treated by court anatomist Nathaniel St André, but the treatment did not prove successful, and Molyneux died in Kew in April. On the night of the death, St André eloped with Molyneux's wife, Elizabeth, the two marrying in 1730. Samuel Madden, a relative of Molyneux's, claimed that St André had poisoned the MP. Although St André won an action for defamation, he found himself unable to secure regular work.

Molyneux’s telescope replacement

1746 Giuseppe Piazzi (July/June? 16, 1746 – July 22, 1826) Italian astronomer and author, born in Valtellina, discovered the first asteroid - Ceres. He established an observatory at Palermo and mapped the positions of 7,646 stars. He also discovered that the star 61 Cygni had a large Proper Motion, which led Bessel to chose it as the object of his parallax studies. He discovered Ceres on 1 Jan 1801, but was able to make only three observations. The term "asteroid," meaning "star-like" was coined (1803) by Herschel. Fortuitously, Gauss had recently developed mathematical techniques that allowed the orbit to be calculated. Within the next few years, astronomers discovered three more asteroids: Pallas, Juno, and Vesta. The thousandth Asteroid discovered was named Piazzi in his honor.*TIS

Modelled shape of Piazzia from its lightcurve

 *Wik

1801 Julius Plücker (16 June 1801 – 22 May 1868)  German mathematician and physicist whose work suggested the far-reaching principle of duality, which states the equivalence of certain related types of theorems. He also discovered that cathode rays (electron rays produced in a vacuum) are diverted from their path by a magnetic field, a principle vital to the development of modern electronic devices, such as television. At first alone and later with the German physicist Johann W. Hittorf, Plücker made many important discoveries in spectroscopy. Before Bunsen and Kirchhoff, he announced that spectral lines were characteristic for each chemical substance and this had value to chemical analysis. In 1862 he pointed out that the same element may exhibit different spectra at different temperatures. *TIS

1819 Siegfried Heinrich Aronhold (16 July 1819 Angerburg, East Prussia – 13 March 1884, Berlin, Germany) was a German mathematician who worked on invariant theory and introduced the symbolic method.*Wik

1866 Edwin Brant Frost II (July 16, 1866 – May 14, 1935) American astronomer, born in Brattleboro, Vermont. His father, Carlton Pennington Frost, was dean of Dartmouth Medical School.
Frost joined the staff of Yerkes Observatory in 1898 and became its director in 1905 when George Hale resigned. Frost kept the position until his retirement in 1932. He was the editor of the Astrophysical Journal from 1902 to 1932, known for his careful attention to details. In 1915 he lost the use of his right eye and in 1921, his left. Despite his blindness he continued working for eleven more years until his retirement in 1932.
Frost's research focused on the determination of radial velocity using stellar spectroscopy and spectroscopic binaries. In 1902, he discovered the strange behavior of Beta Cephei, which later became the prototype for Beta Cephei variable stars. *TIA

1888 Frits Zernike (16 July 1888 – 10 March 1966) Dutch physicist who was awarded the Nobel Prize for Physics in 1953 for his invention of the phase-contrast microscope, an instrument that permits the study of internal cell structure without the need to stain and thus kill the cells. In addition to its capacity to render colourless and transparent objects visible in the microscope, it also enables one to detect slight flaws in mirrors, telescope lenses, and other instruments indispensable for research. In this connection, Zernike's phase-plate serves as an indicator which locates and measures small surface irregularities to a fraction of a light-wavelength.*TiS

1902 Gheorghe Calugareanu (16 July 1902 - 15 November 1976)As a lecturer, Calugareanu gave simple, clear explanations. He spoke quietly and he would start every lecture by spending ten minutes going over the material from the previous lecture. At the end of the lecture he would explain what was coming in the next lecture. This makes it sound as if he would make little progress, but on the contrary, he was able to go steadily though the material. Students really understood the lectures as he gave them and his lectures were models for the highest quality of teaching. His research was elegant and his personality shone through his mathematical papers as it did in his teaching. Some of his results had applications in molecular biology or fluid mechanics. In fact Calugareanu spoke of about the tension between pure and applied mathematics in his autobiographical paper . He remarks there that, in Communist Romania, the party and the state stress the importance of research which leads to improvements in the conditions of life. However, they also recognize the importance of fundamental research as a foundation for and preliminary to applications. The paper allows us to glimpse other aspects of Calugareanu's approach to mathematics. He addresses younger mathematicians explaining that because of the rapid expansion in mathematics there is great importance in having a guiding thread or theme in one's research. This, he explains, is especially true if one's work spans several fields. His own work did indeed span several fields, and he recognises that his thread was the idea of invariance which ran through his work in complex variables, differential topology, and modern algebra.*SAU

1903 Irmgard Flugge-Lotz (6 July 1903 - 22 May 1974)born in Hameln, Germany. Her father encouraged her in mathematics, but she chose engineering because “I wanted a life which would never be boring—a life in which new things would always occur.” She studied applied mathematics at the Technical University of Hanover and in 1929 she became a Doktor-Ingenieur, the equivalent of an American Ph.D. in Engineering. She made contributions to aerodynamics, control theory, and ﬂuid mechanics. In 1960 she became full professor at Stanford. *WM

1951 Daniel Singer Bricklin (born July 16, 1951; ) is an American businessman and engineer who is the co-creator, with Bob Frankston, of VisiCalc, the first spreadsheet program. He also founded Software Garden, Inc., of which he is currently president, and Trellix,[1] which he left in 2004. He currently serves as the chief technology officer of Alpha Software.

His book, Bricklin on Technology, was published by Wiley in May 2009. For his work with VisiCalc, Bricklin is often referred to as “the father of the Spreadsheet.” He was one of 6 people spotlighted when the Computer was denoted "Machine of the Year" by Time magazine in 1982.

DEATHS

1739 Charles François de Cisternay Du Fay (14 September 1698 – 16 July 1739) was a French chemist who made early experiments in electricity. In 1733, he distinguished electrical fluid in two types he named "vitreous electricity" and "resinous electricity" depending on the objects that produced the charge (subsequently called "positive" and "negative" by Benjamin Franklin). Du Fay discovered that objects with like charges repel each other, but oppositely charged objects repel. He also noted the effect of electricity shock on his body, and visible spark when making contact with a highly charged object. He observed that electricity may be conducted in the gaseous matter (now called plasma) adjacent to a red-hot body. Du Fay was also a pioneer in crystal optics.*TIS

1981 Jacob Wolfowitz (March 19, 1910 – July 16, 1981) was a Polish-born American statistician and Shannon Award-winning information theorist. He was the father of former Deputy Secretary of Defense and World Bank Group President Paul Wolfowitz.
While a part-time graduate student, Wolfowitz met Abraham Wald, with whom he collaborated in numerous joint papers in the field of mathematical statistics. This collaboration continued until Wald's death in an airplane crash in 1950. In 1951, Wolfowitz became a professor of mathematics at Cornell University, where he stayed until 1970. He died of a heart attack in Tampa, Florida, where he was a professor at the University of South Florida.
Wolfowitz's main contributions were in the fields of statistical decision theory, non-parametric statistics, sequential analysis, and information theory.*Wik

1994 Julian Seymour Schwinger (February 12, 1918 – July 16, 1994) American physicist who shared the 1965 Nobel Prize in Physics for his contributions to quantum electrodynamics (with Richard Feynman and Shin-Itiro Tomonaga). Schwinger worked on reconciling quantum mechanics with Albert Einstein's special theory of relativity. He published his first physics paper at the age of sixteen. During WW II, he developed important methods in electromagnetic field theory, which advanced the theory of wave guides. His variational techniques were applied in several fields of mathematical physics. In the 1940's he was one of the inventors of the "renormalization" technique. In 1957, he proposed that theoretically there were two different neutrinos: one associated with the electron and one with the muon. Later experimental work provided verification. He invented source theory. *TIS  Schwinger was Oppenheimer's most brilliant student. Oppenheimer once said of him, "When ordinary people give a talk, they tell you how to do it.  When Julian gives a talk, it is to tell you that only he can do it." *Freeman Dyson, Infinities in all Directions.

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