**EVENTS**

1444

**Nilakantha**was a mathematician and astronomer from South India who wrote texts on both astronomy and infinite series. The series π/4 = 1 - 1/3 + 1/5 - 1/7 + ... is a special case of the series representation for arctan, namely

tan

^{-1}

*x*=

*x*-

*x*

^{3}/3 +

*x*

^{5}/5 -

*x*

^{7}/7 + ...

It is well known that one simply puts

*x*= 1 to obtain the series for π/4. (

*R Roy, The discovery of the series formula for π by Leibniz, Gregory and Nilakantha, Math. Mag.*) Roy reports on the appearance of these series in the work of Leibniz and James Gregory from the 1670s. The contributions of the two European mathematicians to this series are well known but in (

**63**(5) (1990), 291-306.*his paper, Roy mentions*) the results on this series in the work of Madhava nearly three hundred years earlier as presented by Nilakantha in the

*Tantrasamgraha*is also discussed.

Nilakantha derived the series expansion tan

^{-1}

*x*=

*x*-

*x*

^{3}/3 +

*x*

^{5}/5 -

*x*

^{7}/7 + ...

by obtaining an approximate expression for an arc of the circumference of a circle and then considering the limit. An interesting feature of his work was his introduction of several additional series for π/4 that converged more rapidly than π/4 = 1 - 1/3 + 1/5 - 1/7+ ... . *SAU

1564 The mathematician/magician John Dee returns to England after five years on the continent and presents his new book, Monas Hieroglyphica, to Queen Elizabeth. The book provides Dees conjecture that the astronomical planet symbols were relics of a lost universal language. He also stated that all the symbols could be combined together into a single symbol, or monad, which was a variant on the sign for Mercury. The monad appears in the center of the book's frontispiece He felt this union exemplified the unity of the universe. *Benjamin Wolley, The Queen's Conjuror

1648

**Margaret Jones is hanged in Boston for witchcraft in the first such execution for the Massachusetts colony. * The Great Geek Manual**

**1649**John Wallis (1616–1703) appointed Savilian professor of geometry at Oxford. This came as a surprise to many for the theologian’s only previous accomplishment in mathematics was his skill at deciphering captured coded letters for Parliamentarians. Within a few years he became one of the leading mathematicians of the time. *VFR Wallis created the term "continued fraction" and popularized the ∞ infinity symbol. One aspect of Wallis's mathematical skills has not yet been mentioned, namely his great ability to do mental calculations. He slept badly and often did mental calculations as he lay awake in his bed. One night he calculated in his head the square root of a number with 53 digits. In the morning he dictated the 27-digit square root of the number, still entirely from memory. It was a feat that was rightly considered remarkable, and Henry Oldenburg, the Secretary of the Royal Society, sent a colleague to investigate how Wallis did it. It was considered important enough to merit discussion in the Philosophical Transactions of the Royal Society of 1685.

**1777**the Continental Congress approved the design of a national flag. Since 1916, when

**President Woodrow Wilson**issued a presidential proclamation establishing a national Flag Day on June 14, Americans have commemorated the adoption of the Stars and Stripes by celebrating

**June 14**as Flag Day. Prior to 1916, many localities and a few states had been celebrating the day for years. Congressional legislation designating that date as the national Flag Day was signed into law by President

**Harry Truman**in 1949; the legislation also called upon the president to issue a flag day proclamation every year.

According to legend, in 1776, George Washington commissioned Philadelphia seamstress

**Betsy Ross**to create a flag for the new nation. Scholars debate this legend, but agree that Mrs. Ross most likely knew Washington and sewed flags. To date, there have been twenty-seven official versions of the flag, but the arrangement of the stars varied according to the flag-makers' preferences until 1912 when**President Taft**standardized the then-new flag's forty-eight stars into six rows of eight. The forty-nine-star flag (1959-60), as well as the fifty-star flag, also have standardized star patterns. The current version of the flag dates to July 4, 1960, after**Hawaii**became the fiftieth state on August 21, 1959. *Library of Congress, On This Day in History**1822**Charles Babbage read a paper to the Astronomical Society of London entitled “Note on the application of machinery to the computation of astronomical and mathematical tables.” He announced the successful completion of a “Diﬀerence engine,” the forerunner of our modern computers. See Dubbey, The Mathematical Work of Charles Babbage, p. 175. *VFR

**1951**UNIVAC I, the ﬁrst commercial electronic computer, was demonstrated and dedicated at the Bureau of the Census at Philadelphia. It could accept information from magnetic tape at the rate of 10,000 characters per second, yet could retain a maximum of 1000 numbers. *VFR

**BIRTHS**

**1736 Charles-Augustin de Coulomb**was a French physicist best known for the formulation of Coulomb's law, which states that the force between two electrical charges is proportional to the product of the charges and inversely proportional to the square of the distance between them. Coulombic force is one of the principal forces involved in atomic reactions. The inverse-square relationship is also seen in the relationship of the gravitation force between masses. In 1777, he invented a torsion balance which he subsequently modified for electrical measurements. He also did research on friction of machinery, on windmills, and on the elasticity of metal and silk fibres.*TIS

1832 Nikolaus August Otto (14 June 1832, Holzhausen an der Haide, Nassau - 26 January 1891, Cologne)born. German engineer who developed the four-stroke internal-combustion engine, which offered the first practical alternative to the steam engine as a power source. A French engineer, Alphonse Beau de Rochas, formulated the basic design for the four-stroke internal combustion engine and patented it in 1862, but never built a working model. In 1876, Otto used principles from Beau de Rochas and others to construct the prototype of today's automobile engines, often called the Otto-cycle engine. He sold thousands of copies before Beau de Rochas sued him and invalidated Otto's patent. But light, efficient Otto-cycle engines largely enabled the creation of automobiles, powerboats, motorcycles and even airplanes. *TIS

**1856**

**Andrey Andreyevich Markov**Russian mathematician who helped to develop the theory of stochastic processes, especially those called Markov chains, sequences of random variables in which the future variable is determined by the present variable but is independent of the way in which the present state arose from its predecessors. (For example, the probability of winning at the game of

*Monopoly*can be determined using Markov chains.) His work based on the study of the probability of mutually dependent events has been developed and widely applied to the biological and social sciences. *TIS

**1868 Karl Petr born.**He worked in analytic number theory, algebraic equations, and invariant theory. *VFR

**1903**

**Alonzo Church**made important contributions to mathematical logic and theoretical computer science. *SAU

**1917 Alte Selberg**born in Langesund, Norway. Norwegian-born mathematician who is one of the foremost analytic number theorists. After working in isolation during WW II, due to the occupation of Norway by the Nazis, his accomplishments in the theory of the Riemann zeta function became known. During the 1950's he developed the Selberg trace formula, his most famous accomplishment. It establishes a duality between the length spectrum of a Riemann surface and the eigenvalues of the Laplacian which is analogous to the duality between the prime numbers and the zeros of the zeta function. He was awarded the Fields Medal in 1950 for his work in number theory on generalisations of the sieve methods of Viggo Brun. In 1986 he won the Wolf Prize. *TIS

**DEATHS**

**1746 Colin MacLaurin**organized the defence of Edinburgh, Scotland, during the Jacobite rebellion. Due to the exertion and exposure he ruined his health and died on this date of edema. For the previous twenty years his main work was on ﬂuxions, although he was a popular lecturer on many subjects at the University of Edinburgh. *VFR His major work on the fluxions was in response to the attack on the calculus by Bishop Berkeley

**1768 James Short,**British optician and astronomer who produced the first truly parabolic and elliptic (hence nearly distortionless) mirrors for reflecting telescopes. During his working life of over 35 years, Short made about 1,360 instruments - not only for customers in Britain but also for export: one is still preserved in Leningrad, another at Uppsala and several in America. Short was principal British collator and computer of the Transit of Venus observations made throughout the world on 6th June 1761. His instruments travelled on

*Endeavour*with Captain Cook to observe the next Transit of Venus on 3rd June 1769, but Short died before this event took place.*TIS

*Died within one week of his birth date (10 June)*

**1946 Federigo Enriques**died in Rome. He was an Italian mathematician, now known principally as the first to give a classification of algebraic surfaces in birational geometry, and other contributions in algebraic geometry. *SAU

Credits:

*VFR = V Frederick Rickey, USMA

*TIS= Today in Science History

*Wik = Wikipedia

*SAU=St Andrews Univ. Math History

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