Wednesday, 30 November 2016

On This Day in Math - November 30

Gilbert shall live, till Load-stones cease to draw,
Or British Fleets the boundless Ocean awe.
— John Dryden

The 335th day of the year; 2335 is the smallest power of two which equals the sum of four consecutive primes. *Prime Curios This seems astounding to me, that such a huge number would be the first.

There are 67 primes smaller than 335, and so 335 is divisible by the number of primes less than itself..  How common is that for integers.  

Lagrange's theorem tells us that each positive integer can be written as a sum of four squares, but many can be written as the sum of only one or two squares. 335 is one of the numbers that can not be written with less than four non-zero squares. The smallest examples are 7, 15, and 23. If you take any number in this sequence, and raise it to an odd positive power, you get another number in the sequence, so now you know that 73 = 343 is also not expressible as the sum of less than four non-zero squares.

3340 BC Our ancient Irish ancestors were expert astronomers, who carved images of an eclipse on ancient stone megaliths over 5000 years ago. November 30th 3340 BC: The world's oldest known solar eclipse was recorded in stone.
Substantially older than the recordings made in 2800 BC by the Chinese astronomers, it is situated at Loughcrew in Co Meath. The Irish Neolithic astronomer priests at this site recorded events on 3 stones relating to the eclipse, as seen from that location.
This is the only eclipse that fits these petroglyphs out of 92 solar eclipses tracked by the discoverer, Irish archaeoastronomer Paul Griffin. With none of the technology available to modern mankind, the Neolithic Irish constructed complex structures in stone which not only endured for five millennia, but were built so accurately that they still perform their astronomical functions today. Many historians believe the Celts created a “festival of light” to welcome an eclipse, which they were capable of predicting. *

1536 Lodovico Ferrari arrived at Cardan's house on 30 November, a fourteen year old boy ready to take over his cousin Luke's position and become a servant. Cardan, upon the discovery that the lad could read and write, exempted him from menial tasks and appointed the youngster as his secretary. *SAU (Cardano gives this date as 14 November, and writes that Ludovico ("Luigi") and his brother (Luke?)arrived together. He noted that a magpie chirped in the courtyard so long they knew someone must be arriving. *Tales of Mathematicians and Physicists By Simon Gindikin)

In 1609, the modern face of the moon first emerged when Galileo Galilei in Padua turned his telescope toward the moon, noted the irregularities of the crescent face, and made a drawing to record his discoveries. He made at least five more drawings of the moon over the next eighteen days, prepared careful watercolor sketches from these drawings, and then selected four of these to be engraved for his revolutionary Starry Messenger, which appeared the following March. Galileo's treatise announced to an astonished public that the moon was a cratered chunk of elements - a world - and not some globe of quintessential perfection. It was a new land, to be explored, charted, and named. *TIS

1703 Newton made president of the Royal Society, an office he held until his death.*VFR

1710 John Machin was elected a Fellow of the Royal Society. *SAU

1712 William Jones elected fellow of the Royal Society. In 1706 he introduced the Greek letter π for the ratio of the circumfrence of a circle to a diameter in his book Synopsis palmariarum matheseos (1706). This title is hard to translate. Literally it means a synopsis of the palm leaves of mathematics. Thus it is a compendium of the most praisworthy parts of mathematics. Earlier William Oughtred (1647) and Isaac Barrow (1669) used the same symbol for twice the number. The symbol was not generally used in our sense until Euler, who adopted it in 1737, popularixed π in his Introductio in analysin infinitorum of 1748. See DSB 7, 163, and “The ubiquitous π ” by Dario Castellanos, Mathematics Magazine 61(1988), 67–98, especially p. 91. A nice post by Thony Christie, at The Renaissance Mathematicus discusses Jones part in preserving John Collins Library.

1753 Benjamin Franklin received the Copley Medal, the highest honor of the Royal Society of London, for his “curious experiments and observations on electricity.” He was the first American to receive the Copley Medal. Three years later he was elected a member of the Royal Society. *VFR

In 1784, American physician and scientist John Jeffries recorded the first scientific data for free air, to a height of 9,309-ft, during a balloon flight in London, England, including twelve observations of temperature, pressure, and humidity. Jeffries' values agree closely with modern determinations. Jeffries had provided himself with thermometer, barometer, electrometer, hygrometer and timepiece. He also took air samples at different elevations for Cavendish, who subsequently made a chemical analysis of the air. This was the first of two balloon flights Jeffries financed. He flew with Frenchman Jean Pierre Blanchard, who had experience in balloon flight. On 7 Jan 1785, they made the first balloon crossing of the English Channel.*TIS

1877 Luigi Bianchi received his degree in mathematics. His work on metric differential geometry found application in Einstein’s studies on relativity.*VFR

In 1904, the first electron tube, a diode thermionic valve, was invented by John Ambrose Fleming. The valve consists of a carbon or tungsten filament lamp, to which is added a metal plate (insulated from the filament), and a connecting wire brought through the glass wall of the bulb to a third terminal outside. When battery current is applied to the filament making it incandescent, the space between the filament and the insulated plate will be found to conduct elecrons in only one direction. That means if the valve is connected in a circuit in with an oscillating current, its one-way conductivity will convert the oscillating current into a unidirectional current capable of actuating a telephone receiver. He notified Marconi in a 30 Nov 1904 letter.*TIS

1917 Bose Institute founded. Bose Institute is a research institute in the fields of Physics, Chemistry, Plant biology, Microbiology, Biochemistry, Biophysics, Animal physiology, Immunotechnology and Environmental science. The institute was established in 1917 by Acharya Jagdish Chandra Bose, who was the founder of modern scientific research in India. Bose Institute pioneered the concept of inter-disciplinary research in India in synch with global trends. Its alumni have achieved renown in India and the world.
Acharya Jagadish Chandra Bose founded the Institute on 30'th November 1917 with the following opening speech:
“I dedicate today this Institute as not merely a laboratory but a temple .... In the pursuit of my investigations I was unconsciously led into the border region of physics and physiology. To my amazement, I found boundary lines vanishing, and points of contact emerging, between the realms of the living and the non-living .... The lectures given here will not be mere repetitions of second-hand knowledge. They will announce new discoveries, demonstrated for the first time in these halls. Through regular publication of the work of the Institute, these Indian contributions will reach the whole world. They will become public property. No patents will ever be taken. The spirit of our national culture demands that we should forever be free from the desecration of utilizing knowledge only for personal gain."

In 1954, in Sylacauga, Alabama, USA, Ann Hodges, 32, was bruised on the arm and hip by a meteorite that fell through the roof of her house into her living room. It smashed the case of her wooden radio and struck her as she lay resting on her sofa. The 9-lb (4-kg), 6 in (15 cm) diameter fragment came from a larger, likely more than 150-lb, chondrite meteorite that exploded over central Alabama about 2 pm, according to reports from people in several states that saw a bright flash across the sky. This remains (2006) the only recorded instance of a person being hit by a meteorite. She donated it in 1956 to the Alabama Museum of Natural History, and it is known by her name as the Hodges Meteorite.*TIS
I imagine Ms Hodges never heard "Stars Fell on Alabama" in quite the same way again. 

1959 The first two IBM 7090 computers are delivered. Along with the faster version, which IBM released three years later, the series was a popular family of transistorized mainframes. Designed for scientific research and large-scale technological application, the computers were used in such projects as the Mercury and Gemini space flights and the Ballistic Missile Early Warning System. *CHM

1967 Ireland issued two stamps to commemorate the tercentenary of the birth of Jonathan Swift, author of Gulliver’s Travels. If you have read this book, then you know why this entry is included here; if you haven’t, then you should, and then you would. [Scott #240-241]. *VFR (For one example, see Bob M's comment below, Thanks Bob)


1549 Sir Henry Savile (30 Nov 1549 in Bradley (near Halifax), Yorkshire, England - 19 Feb 1622 in Eton, Berkshire, England) Savile was an English mathematician who founded professorships of geometry and astronomy at Oxford. It is interesting to read Savile's comments in these lectures on why he felt that mathematics at that time was not flourishing. Students did not understand the importance of the subject, Savile wrote, there were no teachers to explain the difficult points, the texts written by the leading mathematicians of the day were not studied, and no overall approach to the teaching of mathematics had been formulated. Of course, as we shall see below, fifty years later Savile tried to rectify these shortcomings by setting up two chairs at the University of Oxford. *SAU

1602 Otto von Guericke (originally spelled Gericke) (November 20, 1602 – May 11, 1686 (Julian calendar); November 30, 1602 – May 21, 1686 (Gregorian calendar)) was a German scientist, inventor, and politician. He is best remembered for his invention of the Magdeburg hemispheres, popularized in the writings of Caspar Schott. His major scientific achievements were the establishment of the physics of vacuums, the discovery of an experimental method for clearly demonstrating electrostatic repulsion, and his advocacy of the reality of "action at a distance" and of "absolute space". *Wik

1711 Ebenezer Kinnersley (30 Nov 1711; 4 Jul 1778) English-born American experimenter and inventor who investigated electricity. In 1748 Kinnersley demonstrated that the electric fluid actually passed through water, using a 10-ft long trough of water. In 1751, as one of the earliest popularizers of science, he began delivering lectures on "The Newly Discovered Electrical Fire." His experiments discovered the difference between the electricity that was produced by the glass and sulphur globes, which he communicated to Benjamin Franklin at Philadelphia, since they showed beyond a doubt that the positive and negative theory was correct. He also sought ways to protect buildings from lightning, invented an electric thermometer (c. 1755), and demonstrated that electricity can produce heat.*TIS

1756 Ernst Florens Friedrich Chladni (30 Nov 1756; 3 Apr 1827) German physicist, known as the "father of acoustics" for his mathematical investigations of sound waves. Chladni figures, seen when thin plates covered in sand at set in vibration, are complex patterns of vibration with nodal lines that remain stationary and retain sand. He demonstrated these to an audience of scientists in 1809. He measured the speed of sound in various gases by determining the pitch of the note of an organ pipe filled with different gases. To determine the speed of sound in solids, Chladni, used analysis of the nodal pattern in standing-wave vibrations in long rods. He performed on the euphonium, an instrument he invented, made of glass and steel bars vibrated by rubbing with a moistened finger. He also investigated meteorites.*TIS

1869 Nils Dalén (30 Nov 1869; 9 Dec 1837)Swedish engineer who won the Nobel Prize for Physics in 1912 for his invention of the automatic sun valve, or Solventil, which regulates a gaslight source by the action of sunlight, turning it off at dawn and on at dusk or at other periods of darkness. It rapidly came into worldwide use for buoys and unmanned lighthouses. While recovering from an accident, convalescing at home, he noticed how much time his wife spent caring for their wood-burning stove. He decided to invent a more efficient and cost-effective stove. In 1922, Dalen's Amalgamated Gas Accumulator Co. patented his design and put the first AGA stoves into production. These stoves produced a radiant heat that kept the kitchen warm. The AGA remains popular today.*TIS (My wife's favorite entry. Her first experience with an AGA was to turn materials for a pie into pure carbonized dust.)

1891 Edward Lindsay Ince (30 Nov 1891 in Amblecote, Staffordshire, England
- 16 March 1941 in Edinburgh, Scotland) Ince graduated from Edinburgh and researched at Edinburgh and Cambridge. He worked at universities in Leeds, Liverpool, Cairo, Edinburgh and Imperial College London before moving back to Edinburgh as Head of Technical Mathematics. He worked on Special Functions. *SAU

1910 Franz Leopold Alt (November 30, 1910 – July 21, 2011) was an Austrian-born American mathematician who made major contributions to computer science in its early days. He was best known as one of the founders of the Association for Computing Machinery, and served as its president from 1950 to 1952. *Wik

1936 Dmitri Victorovich Anosov (November 30, 1936 in Moscow, ) is a Soviet and Russian mathematician, known for his contributions to dynamical systems theory.
He is a full member of the Russian Academy of Sciences and a laureate of the USSR State Prize (1976). He was a student of Lev Pontryagin.*Wik


1603 William Gilbert (24 May 1544, 30 Nov 1603) English scientist, the "father of electrical studies" and a pioneer researcher into magnetism, who spent years investigating magnetic and electrical attractions. Gilbert coined the names of electric attraction, electric force, and magnetic pole. He became the most distinguished man of science in England during the reign of Queen Elizabeth I. Noting that a compass needle not only points north and south, but also dips downward, he thought the Earth acts like a bar magnet. Like Copernicus, he believed the Earth rotates on its axis, and that the fixed stars were not all at the same distance from the earth. Gilbert thought it was a form of magnetism that held planets in their orbits. *TIS

1647 (Francesco) Bonaventura Cavalieri (1598, 30 Nov 1647) Italian mathematician who made developments in geometry that were precursors to integral calculus. Cavalieri's theory of indivisibles, presented in his Geometria indivisibilis continuorum nova (1635) was a development of Archimedes' method of exhaustion incorporating Kepler's theory of infinitesimally small geometric quantities. The area and volume of various geometric figures can easily be found with this method. He was largely responsible for introducing logarithms as a computational tool in Italy through his book Directorium Generale Uranometricum, including logarithms of trigonometric functions for astronomers. He also wrote on optics and astronomy. Galileo thought highly of his writing, and corresponded with him. *TIS

1720 Pierre Jartoux (c1670; Embrun, France.- 30 Nov, 1720, Manchuria) known in China as Du Demei, Jartoux was a Jesuit Priest who went to live and work in China. His knowledge came to the attention of the Emperor and he was called to Peking (Beijing) to work in the calendar bureau. The emperor took notice of his skills in theoretical mathematics as well as with clocks and other mechanical devices. When not occupied at court, Jartoux ministered to Christians in the capital. In 1708 he assisted two Jesuit confreres, Joachim Bouvet and Jean-Baptiste Regis, in the first stages of making a map of the Chinese empire. His travels took him to the Great Wall north of the capital and throughout Manchuria, where he also ministered to the Christians. Illness forced him to return to Peking, where he began to collate the maps of the provinces in preparation for a general atlas. The final version was presented to the emperor one year after Jartoux died in Manchuria.
He is remembered here for his influence on the introduction of some Western mathematical ideas into the mathematical culture of China and Japan. In China his influence on shows in the 1759 work of Mei Juecheng, the Chishui yizhen (Pearls recovered from the Red River). This contained the infinite series expansion for sin(x) which was discovered by James Gregory and Isaac Newton. In fact it was Jartoux who introduced the infinite series for the sine into China in 1701 and it was known there by the name 'formula of Master Du'. In fact Pearls recovered from the Red River was one of two chapters that Mei Juecheng appended to the works of Mei Wending that he was editing and republishing. Mei Juecheng's study of the motion of the moon to provide improved predictions of eclipses of the moon used the best of European and Chinese astronomical data, and surpassed both cultures work.
In Japan, he was probably the source of the critical equation in the "yenri" (Circle Principle) presented by Takebe. His use of a "Wallis-like" infinite series was accompanied by a very unsatisfactory explanation of his development of the series. D. E. Smith and Mikami believe that he acquired the formula from Jartoux, who had passed on the same series (along with five others) to Mei Juecheng who added three to it in the above mentioned Chinese work. * SAU, Smith/Mikami "A History of Japanese Mathematics"

1761 John Dollond (10 Jun 1706, 30 Nov 1761) British maker of optical and astronomical instruments who developed (1758) and patented an achromatic (non- colour- distorting) refracting telescope and a practical heliometer, a telescope used to measure the Sun's diameter and the angles between celestial bodies. In the 1730's, Chester More Hall, an attorney with an interest in telescopes, first discovered that flint glass appeared to have a greater color dispersion than crown glass did at the same magnifications. Hall reasoned that if he cemented the concave face of a flint glass lens to the convex face of a crown glass lens, he could remove the dispersion properties (and thus, chromatic aberration) from both lenses simultaneously. Dollond learned of the technique in the 1750's and developed it.*TIS

1836 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

1850 Germain Henri Hess (7 Aug 1802, 30 Nov 1850) Swiss-born Russian chemist whose studies of heat in chemical reactions formed the foundation of thermochemistry. He formulated an empirical law, Hess's law of constant heat summation (1840), which states that the heat evolved or absorbed in a chemical process is the same whether the process takes place in one or in several steps. It is explained by thermodynamic theory, which holds that enthalpy is a state function. Chemists have made great use of the law of Hess in establishing the heats of formation of compounds which are not easily formed from their constituent elements. His early investigations concerned minerals and the natural gas found near Baku, and he also discovered the oxidation of sugars to yield saccharic acid.*TIS

1921 Hermann Amandus Schwarz (25 Jan 1843 in Hermsdorf, Silesia (now Poland)
- 30 Nov 1921 in Berlin, Germany) Schwarz worked on the conformal mapping of polyhedral surfaces onto the spherical surface and on a problem of the calculus of variation, namely surfaces of least area. In 1870 he produced work related to the Riemann mapping theorem. Although Riemann had given a proof of the theorem that any simply connected region of the plane can be mapped conformally onto a disc, his proof involved using the Dirichlet problem. Weierstrass had shown that Dirichlet's solution to this was not rigorous, see for details. Schwarz's gave a method to conformally map polygonal regions to the circle. Then, by approximating an arbitrary simply connected region by polygons he was able to give a rigorous proof of the Riemann mapping theorem. Schwarz also gave the alternating method for solving the Dirichlet problem which soon became a standard technique.
His most important work is a Festschrift for Weierstrass's 70th birthday. Schwarz answered the question of whether a given minimal surface really yields a minimal area. An idea from this work, in which he constructed a function using successive approximations, led Émile Picard to his existence proof for solutions of differential equations. It also contains the inequality for integrals now known as the 'Schwarz inequality', *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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