**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 198th day of the year; 198 is a Harshad number, divisible by the sum of its digits. A Harshad number, or Niven number in a given number base, is an integer that is divisible by the sum of its digits when written in that base. Harshad numbers were defined by D. R. Kaprekar, a mathematician from India. The word "Harshad" comes from the Sanskrit harṣa (joy) + da (give), meaning joy-giver. The Niven numbers take their name from Ivan M. Niven from a paper delivered at a conference on number theory in 1997.

(Students might try to find a pair of consecutive numbers greater than 10 which are harshad numbers)

198 nines followed by a one is prime 9999...... 91. *Derek Orr@Derektionary

198 is between the twin primes 197 and 199. If you multiply 198 by its reversal, 891, you get 176,418 which is between the twin primes 176,417 and 176,419. Is there another example of this curiosity?

**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*)

**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

**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. *Wik

**1746 Giuseppe Piazzi**(July 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

**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

**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 Dan Bricklin**(born 16 July 1951- ) American computer scientist who,with Bob Frankston, created VisiCalc, the first spreadsheet computer program (1979) which created a market beyond hobbyists for the emerging personal computers. Businesses found the program very useful because of the speed and accuracy of its calculations. Originally written in 6502 assembly language to run on a 32K-byte Apple II, it was soon ported to virtually all major 6502- and Z80-based personal computers then available. They did not reap huge financial profits from the spreadsheet program, despite eventually selling over a half-million copies by 1983, because at the time, copyright protection was not generally sought for software, and it was subsequently surpassed by Lotus 1-2-3 *TIS

**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

**1983 Edouard Zeckendorf**(2 May 1901 - 16 May 1983) was a Belgian doctor, army officer and mathematician. In mathematics, he is best known for his work on Fibonacci numbers and in particular for proving Zeckendorf's theorem. Zeckendorf's theorem states that every positive integer can be represented uniquely as the sum of one or more distinct Fibonacci numbers in such a way that the sum does not include any two consecutive Fibonacci numbers.

Zeckendorf was born in Liège in 1901. He was the son of a Dutch dentist. In 1925, Zeckendorf graduated as a medical doctor from the University of Liège and joined the Belgian Army medical corps. When Germany invaded Belgium in 1940, Zeckendorf was taken prisoner and remained a prisoner of war until 1945. During this period, he provided medical care to other allied POWs. *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