Saturday, 3 June 2017

On This Day in Math - June 3

1908 article discussing the return of the comet in 1910
Whenever two unknown magnitudes appear
in a final equation, we have a locus,
the extremity of one of the unknown magnitudes
describing a straight line or a curve.
~Fermat Introduction to Plane and Solid Loci

The 154th day of the year; 154 is the smallest number which is a palindrome in base 6, [444]6 ; base 8 ,[242]8; and base 9 ,[181]9 all three.  Student's might search for a number that is a palindrome in other simple bases.

154 also has an interesting property with appropriate powers, 1+56+42= 15642. What other day numbers can you find with similar properties?



1636  In a letter to Fr. Marin Mersenne, Fermat describes the spiral with polar equation r2=a2 x. 

1696 Halley finds "his" comet; Entered in the Journal of the Royal Society on this day:
"Halley produced the Elements of the Calculation of the Motion of the two Comets that Appear'd in the years 1607 and 1682, which are in all respects alike, as to the place of their Nodes and Perihelia, their Inclinations to the sun.."
; *Lisa Jardine, Ingenious Pursuits pg37-38

1769 Capt. James Cook pauses on his ﬁrst circumnavigation of the globe to observe the transit of Venus in Tahiti. Cook and his ninety-eight foot bark, Endeavour, carried the Venus transit observation crew mounted by the Royal Society, led by a future Royal Soc. President, Joseph Banks. They would erect an observation station at Point Venus in Tahiti to observe the June 3, 1769 observation under clear blue skys. *Timothy Ferris, Coming of Age in the Milky Way
Banks himself never observed the transit. His journal records, "I then wishd success to the observers Msrs Gore and Monkhouse and repaird to the Island, where I could do the double service of examining the natural produce and buying provisions for my companions who were engagd in so usefull a work." *Captain Cook's Endeavour Journal website
For those who could not make such trips for the viewing, a fold-out view was in Benjamin Martin's 1773s "Institutions of Astronomical Calculations"

1796 The first observatory in the U S was built by David Rittenhouse at his family farm in Norriton, Pa. in order to observe the transit of Venus across the sun on this date. He made the telescope and quadrant used for the observation. Rittenhouse was the first American astronomer to acquire international fame. He invented the first light diffraction grating, and discovered a comet. *Kane, Famous First Facts, pg 535

1856 Lewis Carroll took his ﬁrst photo of Alice Liddel.

1880   Alexander Graham Bell transmitted the first wireless telephone message on his newly invented photophone from the top of the Franklin School in Washington, D.C. Bell believed that the photophone was his most important invention. The device allowed the transmission of sound on a beam of light. Of the eighteen patents granted in Bell's name alone, and the twelve that he shared with his collaborators, four were for the photophone.
Bell's photophone worked by projecting the voice through an instrument toward a mirror. Vibrations in the voice caused similar vibrations in the mirror. Bell directed sunlight into the mirror, which captured and projected the mirror's vibrations. The vibrations were transformed back into sound at the receiving end of the projection. The photophone functioned similarly to the telephone, except that the photophone used light as a means of projecting the information and the telephone relied on electricity. (Library of Congress)

In 1965, the first American astronaut to make a spacewalk was Major Edward White II,  when he spent 20 minutes outside the Gemini 4 capsule during Earth orbit at an altitude of 120 miles. A tether and 25 foot airline were wrapped in gold tape to form a single, thick cord. He used a hand-held 7.5 pound oxygen jet propulsion gun to maneuver. The launch had taken place a few hours earlier on the same day. During the remainder of the flight, pilot White and his crewmate commander McDivitt completed 12 scientific and medical experiments. The total time in orbit was almost 98 hours, making 62 orbits. Soviet cosmonaut Aleksei A. Leonov, had made the first ever spacewalk for 10 minutes about three months earlier. *TIS

1983 The Movie Wargames was released. It had the first use of the term "firewall" to appear in the movies.


1659 David Gregory (3 June 1659 – 10 October 1708) Scottish mathematician and astronomer. In 1702 he published a book Astronomiae physicae et geometricae elementa, an effort in the popularization of Newtonian science. However, in the matter of chromatic aberration, Gregory noted something that Newton had missed. Different kinds of glass spread the colours of the spectrum by different amounts. He suggested a suitable combination of two different kinds of glass might eliminate chromatic aberration. (A half century later, Dollond accomplished this result. (see below)) Telescopes were a special interest of his, and Gregory also experimented with making an achromatic telescope. *TIS  He was the nephew of astronomer and mathematician James Gregory.  (Thanks to ThonyC for calling my attention to an error of omission in the note above. Here, I hope, is the corrected history of the development of the achromatic lense[Credit for the invention of the first achromatic doublet is often given to an English barrister and amateur optician named Chester Moore Hall. Hall wished to keep his work on the achromatic lenses a secret and contracted the manufacture of the crown and flint lenses to two different opticians, Edward Scarlett and James Mann. They in turn sub-contracted the work to the same person, George Bass. He realized the two components were for the same client and, after fitting the two parts together, noted the achromatic properties. Hall failed to appreciate the importance of his invention, and it remained known to only a few opticians.
In the late 1750s, Bass mentioned Hall's lenses to John Dollond, who understood their potential and was able to reproduce their design. Dollond applied for and was granted a patent on the technology in 1758, which led to bitter fights with other opticians over the right to make and sell achromatic doublets.]



1657 William Harvey (1 April 1578 – 3 June 1657) English physician and discoverer of the true nature of the circulation of the blood and of the function of the heart as a pump. Functional knowledge of the heart and the circulation had remained almost at a standstill ever since the time of the Greco-Roman physician Galen - 1,400 years earlier. Harvey's courage, penetrating intelligence, and precise methods were to set the pattern for research in biology and other sciences for succeeding generations, so that he shares with William Gilbert, investigator of the magnet, the credit for initiating accurate experimental research throughout the world.*TIS

1903 Leopold Bernhard Gegenbauer (2 Feb 1849 - 3 June 1903) was an Austrian mathematician who gave his name to a sequence of orthogonal polynomials. He gave the well-known asymptotic estimate 6n/π2 for the number of square-free integers not exceeding n.*SAU


1971 Heinz Hopf  (19 November 1894 – 3 June 1971)  topologist   He studied under Ludwig Bieberbach, receiving his doctorate in 1925. In his dissertation, Connections between topology and metric of manifolds (German Über Zusammenhänge zwischen Topologie und Metrik von Mannigfaltigkeiten), he proved that any simply connected complete Riemannian 3-manifold of constant sectional curvature is globally isometric to Euclidean, spherical, or hyperbolic space. He also studied the indices of zeros of vector fields on hypersurfaces, and connected their sum to curvature. Some six months later he gave a new proof that the sum of the indices of the zeros of a vector field on a manifold is independent of the choice of vector field and equal to the Euler characteristic of the manifold. This theorem is now called the Poincaré-Hopf theorem.*Wik

1980 Naum Ilyich Akhiezer (6 March 1901 – 3 June 1980) was a Soviet mathematician of Jewish origin, known for his works in approximation theory and the theory of differential and integral operators. He is also known as the author of classical books on various subjects in analysis, and for his work on the history of mathematics. He is the brother of the theoretical physicist Aleksander Akhiezer.*Wik

1990  Robert (Norton) Noyce was a U.S. engineer and coinventor (1959), with Jack Kilby, of the integrated circuit, a system of interconnected transistors on a single silicon microchip. He held sixteen patents for semiconductor devices, methods, and structures. In 1968, he and colleague Gordon E. Moore cofounded N.M. Electronics, which later was renamed Intel Corporation. Noyce served as Intel's president and chairman (1968-75), then as vice chairman until 1979. *TIS
1995  J(ohn) Presper Eckert, Jr. was an American engineer and coinventor of the first general-purpose electronic computer, a digital machine that was the prototype for most computers in use today.  In 1946, Eckert with John W. Mauchly fulfilled a government contract to build a digital computer to be used by the U.S. Army for military calculations. They named it ENIAC for Electronic Numerical Integrator and Computer. By 1949, they had started a manufacturing company for their BINAC computer. This was followed by a business oriented computer, UNIVAC (1951), which was put to many uses and spurred the growth of the computer industry. By 1966 Eckert held 85 patents, mostly for electronic inventions. *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
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