**The shortest path between two truths in the real domain passes through the complex domain.**

**The 308th day of the year**; 308 is the sum of two consecutive primes.

If 18 circles are drawn in the plane, they can separate the plane into 308 regions. Student's might try to find the maximum number of regions for smaller numbers of circles, find a pattern, write f(n).

308

^{3}+ 308

^{0}+ 308

^{8}is prime

**EVENTS**

**1647**The earliest citation of Quadratic in English in the OED was a Nov 4, 1647 was by John Pell in a letter to C. Cavendish, "Not so high as a quadratic equation.".

QUADRATIC is derived from the Latin quadratus, meaning "square." In English, quadratic was used in 1668 by John Wilkins (1614-1672) in An essay towards a real character, and a philosophical language [London: Printed for Sa. Gellibrand, and for John Martyn, 1668]. He wrote: "Those Algebraical notions of Absolute, Lineary, Quadratic, Cubic" *SAU

**1833**On this day in 1833, William Hamilton read a paper to the Royal Irish Academy

expressing complex numbers as algebraic couples, or ordered pairs of real numbers. a + bi, (a,b) *SAU

(The following makes me think Hamilton did not use the term "Complex number" at this time, but worked with a + bi form.)

Most of the 17th and 18th century writers spoke of a + bi as an imaginary quantity. Carl Friedrich Gauss (1777-1855) saw the desirability of having different names for ai and a + bi, so he gave to the latter the Latin expression numeros integros complexos. Gauss wrote:

...quando campus arithmeticae ad quantitates *imaginarias*extenditur, ita ut absque restrictione ipsius obiectum constituant numeri formae

*a*+

*bi,*denotantibus

*i*pro more quantitatem imaginariam $\sqrt{-1}$, atque

*a, b*indefinite omnes numeros reales integros inter $\mathrm{\infty}$

$∞$. Tales numeros vocabimus numeros integros complexos, ita quidem, ut reales complexis non opponantur, sed tamquam species sub his contineri censeatur.The citation above is from Gauss's paper "Theoria Residuorum Biquadraticorum, Commentatio secunda," Societati Regiae Tradita, Apr. 15, 1831, published for the first time in Commentationes societatis regiae scientiarum Gottingensis recentiones, vol. VII, Gottingae, MDCCCXXXII (1832)]. [Julio González Cabillón]

The term complex number was used in English in 1856 by William Rowan Hamilton. The OED2 provides this citation: Notebook in Halberstam & Ingram Math. Papers Sir W. R. Hamilton (1967) III. 657: "a + ib is said to be a complex number, when a and b are integers, and i = [sqrt] -1; its norm is a2 + b2; and therefore the norm of a product is equal to the product of the norms of its factors."

**1845**, Michael Faraday, working in his laboratory at the Royal Institution, hung a piece of heavy glass between the poles of an electro-magnet and observed that the glass aligned itself across the lines of force of the magnet. He further experimented on many other substances, with similar results, a phenomena that he named diamagnetism. These investigations showed Faraday that magnetism was inherent within matter. This led to his lecture "Thoughts on Ray-vibrations" in April 1846, which he expanded in the following years into his field theory of electro-magnetism. This was the progenitor for mathematical descriptions formed by Thomson, and especially for the seminal work of James Clerk Maxwell. *TIS

**In 1869**, the first issue was published of the journal Nature, editted by astronomer Sir Norman Lockyer. The first issue included articles on astronomy, plants, moths, science teaching in schools, an obituary for Thomas Graham, paleontology and meeting notices. Nature remains one of the most popular and well respected science journals in the world, printing research articles from across a wide range of scientific fields. *TIS

You can read the first issue here (HT Ben Gross@BHGross144)

**In 1879,**James Jacob Ritty (1837-1918) with help from his brother John invented the first cash register, intended to combat stealing by bartenders in the Pony House Restaurant, his Dayton, Ohio saloon. His idea came on a cruise, when he saw a device that counted the revolutions of the ship's propeller. Their first model looked like a clock, but instead of the hands indicating hours and minutes, they indicated dollars and cents. Behind the dial two adding discs accumulated the total of the amounts recorded. Known as "the incorruptible cashier," with no cash drawer, it would show anyone within sight how much had been recorded. However, the Ritty brothers failed to sell their cash registers in large quantities - largely because shop staff distrusted this "thief trap"*TIS

**1943**Robert Oppenheimer, working on the Manhatten Project, is so impressed by Richard Feynman that he writes his Physics dept chair at Berkeley to recommend that they hire him after the war. He includes in the recommendation, two comments by others of note; Hans Bethe stated that he would rather lose any two other men than Feynman from the project, and Wigner stated, "He is a second Dirac, only this time human." *Shaun Usher, Letters of Note web site

**1952**Television makes its first foray into predicting a presidential election based on computer analysis of early returns. The Univac computer makes an incredibly accurate projection that the network doesn't think credible. Pre-election polls had predicted anything from a Democratic landslide to a tight race with the Demo candidate, Illinois Gov. Adlai Stevenson, slightly ahead of the Republican, five-star Gen. Dwight D. Eisenhower, Supreme Commander of Allied Forces in Europe in World War II. So it was a surprise at 8:30 p.m. Eastern time when Univac predicted Eisenhower would pile up 438 electoral votes to Stevenson's 93.

In New York, news boss Mickelson scoffed at putting the improbable prediction on air. In Philadelphia, Woodbury added new data to the mix. At 9 p.m. correspondent Charles Collingwood announced to the audience that Univac was predicting 8-7 odds for an Eisenhower win.

But wait! Back in Philly, Woodbury discovered that he'd mistakenly added a zero to Stevenson's totals from New York state. When he entered the correct data and ran it through Univac, he got the same prediction as before: Ike 438, Adlai 93,

As the evening wore on, an Eisenhower landslide gathered momentum. The final vote was 442 to 89. Univac was less than 1 percent off. *Wired.com

*J. Presper Eckert and Walter Cronkite discuss the UNIVAC prediction, CHM |

**1969**Pakistan issued a stamp honoring Alhazen (ab¯u-‘Al¯ıal-Hasan ibn al-Hasan ibn al-Haytham) (965–c. 1040), astronomer and optician. Pictured is a diagram showing the reﬂection of light. [Scott #281]. *VFR

**BIRTHS**

**1744 Johann(III) Bernoulli**(4 Nov 1744 in Basel, Switzerland

- 13 July 1807 in Berlin, Germany) wrote a number of works on astronomy and probability theory. Bernoulli wrote a number of works on astronomy, reporting on astronomical observations and calculations, but these are of little importance. Strangely his most important contributions were the accounts of his travels in Germany which were to have a historical impact.

In the field of mathematics he worked on probability, recurring decimals and the theory of equations. As in his astronomical work there was little of lasting importance. He did, however, publish the Leipzig Journal for Pure and Applied Mathematics between 1776 and 1789.

He was well aware of the famous mathematical line from which he was descended and he looked after the wealth of mathematical writings that had passed between members of the family. He sold the letters to the Stockholm Academy where they remained forgotten about until 1877. At that time when these treasures were examined, 2800 letters written by Johann(III) Bernoulli himself were found in the collection. *SAU (See "A Confusion of Bernoulli's" by the Renaissance Mathematicus.)

**1765 Pierre-Simon Girard**(Caen, 4 November 1765 – Paris, 30 November 1836) was a French mathematician and engineer, who worked on fluids. A prodigy who invented a water turbine at age 10, Girard worked as an engineer at the École Nationale des Ponts et Chaussées. He was in charge of planning and construction of the Amiens canal and the Ourcq canal. He collaborated with Gaspard de Prony on the Dictionnaire des Ponts et Chaussées (Dictionary of Bridges and Highways). He wrote works on fluids and on the strength of materials.*Wik

**1908 Viktor Vladimirovich Wagner**, also Vagner (4 November 1908 – 15 August 1981) was a Russian mathematician, best known for his work in differential geometry and on semigroups. *Wik

**1921 Andrew Mattei Gleason**(November 4, 1921 – October 17, 2008) was an American mathematician and the eponym of Gleason's theorem and the Greenwood–Gleason graph. After briefly attending Berkeley High School (Berkeley, California)[1] he graduated from Roosevelt High School in Yonkers, then Yale University in 1942, where he became a Putnam Fellow. He subsequently joined the United States Navy, where he was part of a team responsible for breaking Japanese codes during World War II. He was appointed a Junior Fellow at Harvard in 1946, and later joined the faculty there where he was the Hollis Professor of Mathematicks and Natural Philosophy. He had the rare distinction among Harvard professors of having never obtained a doctorate. He retired in 1992. He is well-known for his work on Hilbert's fifth problem.*Wik

**1933 The Honorable Sir Charles Kuen Kao**,(4 November 1933) is a Chinese-born American and British physicist who pioneered in the development and use of fiber optics in telecommunications. Kao, known as the "Godfather of Broadband", "Father of Fiber Optics" or "Father of Fiber Optic Communications", was awarded half of the 2009 Nobel Prize in Physics for "groundbreaking achievements concerning the transmission of light in fibers for optical communication". Kao holds dual citizenship in Great Britain and the United States. *Wik

**DEATHS**

**1652 Jan-Karel della Faille**or Jean Charles de La Faille (1 March 1597 in Antwerp, Belgium - 4 Nov 1652 in Barcelona, Spain) was a Flemish Jesuit who was the first to determine the center of gravity of the sector of a circle. He proved that the centers of gravity of a sector of a circle, of a regular figure inscribed in it, of a segment of a circle, or of an ellipse lie on the diameter of the figure. These theorems are founded on a postulate from Luca Valerio's De centro gravitatis solidorum (1604). ... La Faille ended his work with four corollaries which revealed his ultimate goal: an examination of the quadrature of the circle. *SAU

**1698 Erasmus Bartholin**(13 Aug 1625, 4 Nov 1698) Danish physician, mathematician , physicist, died in Copenhagen. He discovered the optical phenomenon of double refraction. In 1669, Bartholin observed that images seen through Icelandic feldspar (calcite) were doubled and that, when the crystal was rotated, one image remained stationary while the other rotated with the crystal. Such behaviour of light could not be explained using Isaac Newton's optical theories of the time. Subsequently, this was explained as the effect of the polarisation of the light. Bartholin wrote a large number of mathematical works, and made astronomical observations, including the comets of 1665. He is also famed for his medical work, in particular his introduction of quinine in the fight against malaria.*TIS

**1912 John Monroe Van Vleck**(March 4, 1833–November 4, 1912) was an American mathematician and astronomer. He taught astronomy and mathematics at Wesleyan University in Middletown, Connecticut for more than 50 years (1853-1912), and served as acting university president twice. The Van Vleck Observatory (at Wesleyan University) and the crater Van Vleck on the Moon are named after him. *Wik

**1917 William Du Bois Duddell**(1872- 4 Nov 1917) English electrical engineer who invented the sensitive moving coil oscillograph able to photographically record a light spot tracing the oscillations of an electrical voltage, and other electrical instruments. He devised what may be regarded as the first electric musical instrument, the Singing Arc (1899), based on the sounds emitted by an electric carbon arc lamp when its supply voltage was varied. It was an outcome of his investigation to solve the problem of the undesirable humming or whining noises generated by carbon arc street lighting. This research discovered an associated principle of negative resistance. The audio frequencies were generated by switching suitable resonant circuits to the arc. Duddell died aged only 45 years old. *TIS

**1954 Archibald Read Richardson**(21 Aug 1881 in London, England - 4 Nov 1954 in Cape Town, South Africa) graduated from Imperial College London and then taught at the college. He was badly wounded in World War I. He became Professor of Mathematics at Swansea. His main interests were in algebra. *SAU

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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