Tuesday, 14 July 2020

On This Day in Math - July 14

Antoine Caron: Astronomers Studying an Eclipse *TIA

Nature is not embarrassed by difficulties of analysis.
~Augustin Fresnel

The 196th day of the year, A Lychrel number is a natural number which cannot form a palindromic number through the iterative process of repeatedly reversing its base 10 digits and adding the resulting numbers. 196 is the lowest number conjectured to be a Lychrel number; the process has been carried out for one billion iterations without finding a palindrome, but no one has ever proven that it will never produce one. The number produced on the one billionth iteration had 413,930,770 digits. The name "Lychrel" was coined by Wade VanLandingham—a rough anagram of his girlfriend's name Cheryl. No Lychrel numbers are known, though many numbers are suspected Lychrels, the smallest being 196. (Students might try finding the number of iterations of the process to find a palindrome for various n. 195, for example, takes four iterations :
195 + 591 = 786
786 + 687 = 1473
1473 + 3741 = 5214
5214 + 4125 = 9339)
DO not try the numbers 89 or 98. Harry J Saal used a computer to repeatedly iterate this process and finally did come up with a palindrome, the number 8,813,200,023,188 on the 24th iteration.

Jim Wilder noticed that 142 =196 and 132=169... are there other squares of consecutive numbers that share the same digits?

A number is said to be square-full if for every prime, p, that divides it, p2 also divides it. 196 is such a number. Are there cube-full numbers? (of course there are, but what are they?) Stay tuned, one is coming soon. 


1686 On June 20th Halley Wrote to Newton that Hooke has protested his "discovery" of the inverse square law should be noted in Principia. Newton responded On July 14, 1686, with a peace offering; "And now having sincerely told you the case between Mr Hooke and me, I hope I shall be free for the future from the prejudice of his letters. I have considered how best to compose the present dispute, and I think it may be done by the inclosed scholium to the fourth proposition." This scholium was "The inverse law of gravity holds in all the celestial motions, as was discovered also independently by my countrymen Wren, Hooke and Halley."

1696  Construction of the Eddystone lighthouse began today by Henry Winstanley.  Winstanley ...investing some of the money he had made from his work and commercial enterprises in five ships. Two of them were wrecked on the Eddystone Rocks near Plymouth, and he demanded to know why nothing was done to protect vessels from this hazard. Told that the reef was too treacherous to mark, he declared that he would build a lighthouse there himself, and the Admiralty agreed to support him with ships and men.
In the 1690s he opened a Mathematical Water Theatre known as "Winstanley's Water-works" in London's Piccadilly. This was a commercial visitor attraction which combined fireworks, perpetual fountains, automata and ingenious mechanisms of all kinds, including "The Wonderful Barrel" of 1696 which served visitors with hot and cold drinks from the same piece of equipment. It was a successful and profitable venture and continued to operate for some years after its creator’s death.(*Today in History)

1776 The beginning of Cook's third and last voyage made with the Resolution and the Discovery, which cleared the channel on 14 July 1776. This voyage, in which Cook was killed, came to an end in 1780.*Wik

1791 A mob in Birmingham, England, rioted during festivities marking the anniversary of the fall of the Bastille on this date in 1789. The mob, which ran wild for three days, destroyed the house, laboratory and library of Joseph Priestley, discoverer of oxygen, because of his anti religious views and espousal of revolutionary causes.*VFR Within a few years, on 7 Apr 1794, he forever left England and traveled to the United States. Priestley discovered oxygen nearly 20 years earlier, on 1 Aug 1774.*TIS

1831 Evariste Galois again arrested, as a precautionary measure. He received a six months sentence. *VFR

In 1867, Alfred Nobel demonstrated dynamite for the first time at a quarry in Redhill, Surrey. In 1866 Nobel produced what he believed was a safe and manageable form of nitroglycerin called dynamite. He established his own factory to produce it but in 1864 an explosion at the plant killed Nobel's younger brother and four other workers. Deeply shocked by this event, he now worked on a safer explosive and in 1875 came up with gelignite. Other inventions followed including ballistite, a form of smokeless power, artificial gutta-percha and a mild steel for armour-plating.*TIS

1868 Alvin J. Fellows of New Haven, Connecticut, received patent #79,965 for the first tape measure. It was enclosed in a circular case with a spring lock to hold the tape at any desired point. *VFR (for my son Robin, who seems to collect them as icons of his trade) Earlier, a machine to print ribbon for the supple sewing tape measures had already been patented on 3 Sep 1847, after four years of research by the French fashion designer, Lavigne. Further, however, Sheffield, England claims to be not just the home of stainless steel, but also where the spring tape measure was invented. *TIS  (This was for the spring type tapes common today. Earlier tapes were produced with a brass fold-out clip to rewind them... One my grand-daughter just found for her dad at a boot-sale for 50 pence was an old Chesterman that was marked in links (.01 chains) and rods (1/4 of a chain) on one side. .... "James Chesterman moved to Sheffield from London in 1820. Nine years later he patented the spring tape measure. He also invented the self-winding window blind, produced the first long steel Measuring tape and the first Woven metallic tape. His business adopted the bow as its trademark, and he named his factory the bow works which moved to this site in 1864.  James Chesterman & Co became synonymous with high quality measuring instruments, especially tapes, callipers and squares. In 1963 amalgamation with John Rabone & Sons created Rabone Chesterman, who were subsequently bought by Stanley Tools and transferred to Stanley's Woodside Plant.  Bow Works was refurbished and extended for its new occupants, Norwich Union in 1993."

1887 The first textbook about the international language, Esperanto, was published by its inventor, Dr. Ludwig Zamenhof, a Pole. Esperanto means “one who hopes.” The Italian mathemati¬cian, Giuseppi Peano, created an international language of his own, Latina sina flexione (Latin without inflections), but it was even less successful than Esperanto. *VFR

1897 The Dorabella Cipher is an enciphered letter written by composer Edward Elgar to Dora Penny, which was included with a "thank you" note from his wife dated July 14, 1897. Penny never deciphered it and its meaning remains unknown.
Elgar also named Variation 10 of his 1899 Variations on an Original Theme (Enigma) Dorabella as a dedication to Dora Penny. *Wik

1943 George Washington Carver was honored by U.S. President Franklin Delano Roosevelt dedicating $30,000 for a National Monument to his accomplishments. The area of Carver's childhood near Diamond Grove, in southwest Missouri has been preserved as a park, with a bust of the agricultural researcher, instructor, and chemical investigator. This park was the first designated national monument to an African American in the United States. In 1850-65, Diamond was a typical "crossroads village" near a diamond-shaped grove of trees not far from the Carver farm in Newton County. Also called Diamond Grove, it consisted of a general store, a combination blacksmith shop and post office, and a church that served as a schoolhouse during the week.*TIS

1954 At a Conference for California Teachers of Mathematics, a Los Angeles dentist named Leon Bankoff presented a talk proving that the 2000 year old proof of Archimedes that there were a pair of congruent "Archimedean Twin Circles" in the Arbelos was in fact false. He produced a third identical circle, now usually called the "Bankoff triplet circle".
Later (1979) Thomas Schoch discovered a dozen new Archimedean circles; and then in 1998, Peter Y. Woo of Biola University, generalized two of Schoch's circles, to discover an infinite family of Archimedean circles named the Woo circles in 1999 *Wik *Mathematics Magazine For more on the Archimedean Circles, see my blog on  The Shoemaker's Knife Cuts Beautiful Math Across the Centuries

1965 In the Evening of July 14, the Mariner space craft sent back 22 minutes of imaging from a close pass of Mars. These first images came in in strips of 200 numbers, each representing a shade of black to white for one of 200 rows of such pixels to make an image of the surface of the Red Planet. Knowing that at their stage of image creation, it would be many hours before the images were prepared by the computer printers, the telecommunications engineers at JPL began to attach the numbered strips on a bulletin board, and hand color the pixels in red, brown, and yellow pastels. Too impatient to await the computer drawn images, the first press released photos were images of the hand drawn, paint by number image. *NASA

1977 Minor planet (2509) Chukotka 1977 NG. Discovered by N. S. Chernykh at Nauchnyj. Named for a National Area of the R.S.F.S.R., situated in the northeastern part of the U.S.S.R. The discoverer participated in an expedition there to observe the 1972 total solar eclipse. *NSEC

2004 A patent application by John St. Clair was filed for a training program to teach people to walk through walls:Publication number US20060014125 A1   (Ok, just think about it a minute.  Someone had to say,  "Yeah, we'll give them a patent for that.")


2015 The New Horizons probe, launched on Jan. 19, 2006, with Clyde Tombaugh's ashes on board,  arrived at Pluto on July 14, 2015. *The Las Cruces Sun-New
Also on board was a 1991 US postage stamp which was a motivator for people in the project.


1610 Ferdinand II (9 July 1578 – 15 February 1637) Fifth grand duke (granduca) of Tuscany, a patron of sciences, whose rule was subservient to Rome. Ferdinand II de' Medici was Grand Duke from 1621. He encouraged scientific studies, and he protected Galileo and the Accademia del Cimento (1657 - 1667). He also devised a sealed thermometer which, unlike Galileo's open one, was not affected by changes in air pressure. It was to him that Galileo dedicated the lens with which he had discovered the satellites of Jupiter and he also made him a gift of the armed lodestone. J. W. Blaeu dedicated to him one of his globes of the fifth type. Ferdinand II was also a patron of Robert Dudley.*TIS

1671 Jacques Eugène d'Allonville, Chevalier de Louville par Fontenelle (July 14, 1671 – September, 1732) French astronomer and mathematician.
He was born in the Château de Louville, and studied mathematics before joining the navy. He achieved the rank of colonel before retiring from military service in 1713, following the peace of Utrecht. He thereafter took up the study of astronomy.
He is noted for determining a method for precisely calculating the occurrence of solar eclipses.
The crater Louville on the Moon is named in his honor. *TIA

1793 George Green baptized in Nottingham, England. The date of his birth is unknown. His most famous work, An Essay on the Application of Mathematical Analysis to the Theory of Electricity and Magnetism was published, by subscription, in March 1828. Most of the fifty-two subscribers were friends and patrons. The work lay unnoticed until William Thomson rediscovered it and showed it to Liouville and Sturm in Paris in 1845. The Theory of Potential it developed led to the modern mathematical theory of electicity. *VFR
George Green was an English mathematician, born near Nottingham, who was first to attempt to formulate a mathematical theory of electricity and magnetism. He was a baker while, remarkably, he became a self-taught mathematician. In March 1828 he published An Essay on the Application of Mathematical Analysis to the Theories of Electricity and Magnetism. He became an undergraduate at Cambridge in October 1833 at the age of 40. Lord Kelvin (William Thomson) subsequently saw, was excited by the Essay. Through Thomson, Maxwell, and others, the general mathematical theory of potential developed by an obscure, self-taught miller's son heralded the beginning of modern mathematical theories of electricity.*TIS

1905 Laurence Chisholm Young (14 July 1905 – 24 December 2000) was a mathematician known for his contributions to measure theory, the calculus of variations, optimal control theory, and potential theory. He is the son of William Henry Young and Grace Chisholm Young, both prominent mathematicians. The concept of Young measure is named after him. *Wik

1918 Jay W(right) Forrester (born July 14, 1918- ) is a U.S. electrical engineer and management expert. In 1944-51 he supervised the building of the Whirlwind computer at the Massachusetts Institute of Technology, for which he invented the random-access magnetic core memory, the information-storage device employed in most digital computers. He also studied the application of computers to management problems, developing methods for computer simulation.*TIS


1800 Lorenzo Mascheroni (May 13, 1750 – July 14, 1800) was a geometer who proved in 1797 that all Euclidean constructions can be made with compasses alone, so a straight edge in not needed. In fact this had been (unknown to Mascheroni) proved in 1672 by a little known Danish mathematician Georg Mohr. *SAU In his Adnotationes ad calculum integrale Euleri (1790) he published a calculation of what is now known as the Euler–Mascheroni constant, usually denoted as γ (gamma).*Wik

1827 Augustin Jean Fresnel (10 May 1788, Broglie (Eure)- 14 July 1827 (aged 39)
Ville-d'Avray (Hauts-de-Seine)) French physicist who first investigated the effect of interference of light, with results known as Fresnel fringes. This decisively work, together with further experiments with polarized light supported Thomas Young's wave theory of light Fresnel advanced the wave theory by identifying light as transverse waves rather than the longitudinal waves previously assumed by Young and Huygens. His pioneering work in optics included showing that white light is composed of a spectrum of innumerable wavelengths ranging from red to shorter violet wavelenths. In 1819, he improved the optical system of lighthouses by replacing metal reflectors with revolutionary stepped lenses of his design.*TIS

1865 Benjamin Gompertz (March 5, 1779 – July 14, 1865), was a self educated mathematician, denied admission to university because he was Jewish.[citation needed] Nevertheless he was made Fellow of the Royal Society in 1819. Gompertz is today mostly known for his Gompertz law (of mortality), a demographic model published in 1825. The model can be written in this way:

N(t) = N(0) e^{-c (e^{at}-1)},

where N(t) represents the number of individuals at time t, and c and a are constants.

This model is a refinement of the demographic model of Malthus. It was used by insurance companies to calculate the cost of life insurance. The equation, known as a Gompertz curve, is now used in many areas to model a time series where growth is slowest at the start and end of a period. The model has been extended to the Gompertz–Makeham law of mortality.

1899 Sir Arthur Thomas Cotton (15 May 1803 – 24 July 1899) British engineer whose life-work was constructing irrigation, navigation canals and dams for water storage in Southern India, saving thousands from famine and promoting local economy. He joined the Madras engineers in 1819, fought in the first Burmese war (1824-26) and began his ambitious irrigation project (1826-62). He built dams on several rivers, transforming the drought-stricken Tanjore district into the richest part of the state of Madras. His ambitious masterplan was not completed in his lifetime, but his ideas anticipated projects that were subsequently taken up. In the present time, India's goal of a National Water Grid confronts the problem of increasingly scarce water. Cotton founded the Indian school of hydraulic engineering.*TIS

1953 Richard von Mises (19 April 1883, Lviv – 14 July 1953, Boston, Massachusetts) Austrian-American mathematician and aerodynamicist who notably advanced statistics and the theory of probability. Von Mises' contributions range widely, also including fluid mechanics, aerodynamics, and aeronautics. His early work centred on aerodynamics. He investigated turbulence, making fundamental advances in boundary-layer-flow theory and airfoil design. Much of his work involved numerical methods and this led him to develop new techniques in numerical analysis. He introduced a stress tensor which was used in the study of the strength of materials.Von Mises' primary work in statistics concerned the theory of measure and applied mathematics. His most famous, yet controversial, work was in probability theory. *TIS He is often credited with the creation of the "Birthday Problem", but in this blog I suggest otherwise.

1956 John Miller studied at Glasgow and Göttingen. He returned to Glasgow to the Royal College of Science and Technology (the precursor to Strathclyde University). He became President of the EMS in 1913. *SAU

1960 Maurice de Broglie (27 April 1875–14 July 1960)(6th duke) (Louis-César-Victor-) Maurice de Broglie was a French physicist who made many contributions to the study of X rays. While in the navy (1895-1908), he first distinguished himself by installing the first French shipboard wireless. From 1912, his chief interest was X-ray spectroscopy. His "method of the rotating crystal" was an application of Bragg's "focussing effect" to eliminate spurious spectral lines. De Broglie discovered the third L absorption edge (1916), which led to the exploration of "corpuscular spectra." During 1921-22, he worked with his brother Louis to refine Bohr's specification of the substructure of the various atomic shells. He also did pioneer work in nuclear physics and cosmic radiation. *TIS

2016  Maryam Mirzakhani, the first woman and first Iranian to win the Fields Medal,died of metastatic breast cancer  at the age of 40. She had been a professor at Stanford University since 2008. *Sci Am

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

Monday, 13 July 2020

On This Day in Math - July 13

There is (gentle reader) nothing (the works of God only set apart) which so much beautifies and adorns the soul and mind of man as does knowledge of the good arts and sciences. ... Many ... arts there are which beautify the mind of man; but of all none do more garnish and beautify it than those arts which are called mathematical, unto the knowledge of which no man can attain, without perfect knowledge and instruction of the principles, grounds, and Elements of Geometry.

~John Dee, The Mathematical Preface

The 195th day of the year..195 is the sum of eleven consecutive primes: 3 + 5 + 7 + 11 + 13 + 17 + 19 + 23 + 29 + 31 + 37 Students might wonder which numbers can (and cannot) be expressed as the sum of one or more consecutive Primes.

195 is also the third integer that is the sum of the squares of three consecutive primes.*Prime Curios

also, 1*95 = 19*5 Derek Orr tells me there are only four non-trivial 3-digit numbers with this property *@Derektionary

a Heronian triangle is a triangle that has side lengths and area that are all integers. There is an almost-equilateral, scalene triangle with one side of 195. The other sides are 194, and 193. Students can find the area using Heron's formula.


Newton writes to John Collins, "...about the infinite series I am not yet resolved, not knowing when I shall proceed to finish it."   *Correspondence of Scientific Men of the Seventeenth Century ..., Volume 2

1773 Gerolamo Saccheri, a Jesuit priest, received the imprimatur of the Inquisition for his Euclides ab Omni Naevo Vindicatus (Euclid Cleansed of Every Blemish), an important forerunner of non-Euclidean geometry. [George E. Martin, The Foundations of Geometry and the Non-Euclidean Plane, p. 304]*VFR

1783 Astronomer William Bayly is paid 200 pounds by the Board of Longitude for "as a recompense for his troubles in reducing, compiling, and printing the astronomical observations of Captain Cooks last voyage, intended to be published with the historical account thereof."  *Derek Howse, Britain's Board of Longitude, The Finances
In 1772 Bayly accompanied William Wales as an astronomer on Cook's second voyage of discovery to the southern hemisphere. The two ships employed in the expedition, the Resolution and the Adventure sailed on 13 June. He also sailed in Cook's third and last voyage made with the Resolution and the Discovery, which cleared the channel on 14 July 1776. This voyage, in which Cook was killed, came to an end in 1780.

2012 the third Friday-the-thirteenth of the year. Each Gregorian 400-year cycle contains 146,097 days (365 × 400 = 146,000 normal days, plus 97 leap days) and they equal 146,097 days, total. 146,097 ÷ 7 = 20,871 weeks. Thus, each cycle contains the same pattern of days of the week (and thus the same pattern of Fridays that are on the 13th).
The 13th day of the month is slightly more likely to be a Friday than any other day of the week. On average, there is a Friday the 13th once every 212.35 days (compared to Thursday the 13th, which occurs only once every 213.59 days).
2012 has had Friday-the-13ths in January, April and July . pointed out that these three Fri-13ths occur in intervals of 13 weeks.
According to the Stress Management Center and Phobia Institute in Asheville, North Carolina, an estimated 17 to 21 million people in the United States are affected by a fear of this day. Some people are so paralyzed by fear that they avoid their normal routines in doing business, taking flights or even getting out of bed. "It's been estimated that \([US]$800 or $900\) million is lost in business on this day". Despite this, representatives for both Delta and Continental Airlines say that their airlines do not suffer from any noticeable drop in travel on those Fridays.
According to folklorists, there is no written evidence for a "Friday the 13th" superstition before the 19th century. The earliest known documented reference in English occurs in Henry Sutherland Edwards' 1869 biography of Gioachino Rossini. *Wik

2016 Jaime Escalante commemorative stamp was officially unveiled at the 87th conference of the League of United Latin American Citizens (LULAC) today in Washington, D.C. Escalante, a teacher in his native Bolivia who arrived in the states in 1963, became known for using innovative methods to teach inner-city students in East Los Angeles that some considered "unteachable," and many of whom went on to master calculus under his tutelage.
His story was the subject of the seminal 1988 movie "Stand and Deliver," which is one of the most viewed movies in U.S. film history. *NBC

2018 Next solar eclipse on a Friday the 13th. The last solar eclipse on a Friday 13th was in December 1974. Both are partial solar eclipses. There are 24 solar eclipses on a Friday the 13th between the years 0 and 3000; Of which 13 partial, 9 annular and 2
total solar eclipses. *NSEC


1527 John Dee born in London, England (13 July 1527–1608 or 1609). In 1570 he wrote a “fruitfull Praeface” to the Billingsley translation of Euclid, which he edited. This was the first English Euclid.
Dee was a noted English mathematician, astronomer, astrologer, occultist, navigator, imperialist and consultant to Queen Elizabeth I. He devoted much of his life to the study of alchemy, divination and Hermetic philosophy.
Dee straddled the worlds of science and magic just as they were becoming distinguishable. One of the most learned men of his age, he had been invited to lecture on advanced algebra at the University of Paris while still in his early twenties. Dee was an ardent promoter of mathematics and a respected astronomer, as well as a leading expert in navigation, having trained many of those who would conduct England's voyages of discovery.*Wik Aubrey's Brief Lives gives Dee credit for inventing the phrase, "The British Empire."

Thony Christie, The Renaissance Mathematicus has written a really interesting blog post on Dee.

1741 Carl Friedrich Hindenburg (13 July 1741– 17 March 1808) published a series of works on combinatorial mathematics.*SAU
Hindenburg co-founded the first German mathematical journals. He also influenced Christian Kramp's work in combinatorics. In 1796, he edited Sammlung combinatorisch-analytischer Abhandlungen, which contained a claim that de Moivre's multinomial theorem was "the most important proposition in all of mathematical analysis"*Wik

1822 Heinrich Louis d'Arrest13 July 1822 – 14 June 1875) German astronomer who, while a student at the Berlin Observatory, hastened the discovery of Neptune by suggesting comparison of the sky, in the region indicated by Urbain Le Verrier's calculations, with a recently prepared star chart. The planet was found the same night. His father-in-law was A. F. Moebius (1790 - 1868). d'Arrest found several comets, the one of 1851 with a period of 6.6 years bears his name. One work he published was on the Asteroids between Mars and Jupiter, another work titled Siderum nebulosorum observationes Hafniensis contained 1942 nebula, 340 described for the first time.*TIS The crater D'Arrest on the Moon is named after him, as well as a crater on the Martian satellite Phobos and the asteroid 9133 d'Arrest.

1924 Donald Edward Osterbrock (July 13, 1924 - January 11, 2007) was an American astronomer who was a leading authority on the history of astronomy, and director of the University of California's Lick Observatory. He applied physics to produce accurate models of stars. For example, treating the outer part of the sun as turbulent and convective, he explained the seemingly anomalous fact that the sun's corona is hotter than its surface. He investigated the nature of ionized gas around hot stars, and was a pioneer in the use of spectroscopic methods for the study of gaseous nebulae. He discovered new types of active galactic nuclei, which are powered by black holes in the centers of galaxies. He fostered the construction of the 10-meter Keck Telescopes in Hawaii. *TIS

1932 Hubert Reeves, CC OQ (born July 13, 1932) is a Canadian astrophysicist and popularizer of science. He attended Collège Jean-de-Brébeuf, a prestigious French-language college in Montreal. He has been a Director of Research at the Centre national de la recherche scientifique since 1965 and currently lives in Paris, France where he often speaks on television promoting science. *Wik

1944 Erno Rubik (July 13, 1944, ) Hungarian mathematician, educator and inventor of Rubik's Cube (1974), which became a popular toy of the 1980s. Rubik's Cube consists of 26 small cubes that rotate on a central axis; nine coloured cube faces, in three rows of three each, form each side of the cube. When the cube arrangement is randomized, the player must then return it to the original condition of faces with matching colours, which is one among 43 quintillion possible configurations.*TIS


1762 James Bradley (March 1693 – 13 July 1762) English astronomer, the third Astronomer Royal, who in 1728 announced his discovery of the aberration of starlight, an apparent slight change in the positions of stars caused by the the motion of the person looking at them with the yearly motion of the Earth. That finding provided the first direct evidence for the revolution of the Earth around the Sun. Bradley was one of the first post-Newtonian observational astronomers who led the quest for precision. From the aberration of starlight, Bradley was also able to make calculations giving the speed of light to be about 283,000 km/s. Further, Bradley discovered that the earth nods a little on its axis, which he named as nutation.*TIS

1794 James Lind FRSE FRCPE (4 October 1716 – 13 July 1794) was a Scottish physician. He was a pioneer of naval hygiene in the Royal Navy. He is of matheamtical interest because he conducted the first modern clinical trial. He developed the theory that citrus fruits cured scurvy. He argued for the health benefits of better ventilation aboard naval ships, the improved cleanliness of sailors' bodies, clothing and bedding, and below-deck fumigation with sulphur and arsenic. He also proposed that fresh water could be obtained by distilling sea water. His work advanced the practice of preventive medicine and improved nutrition.
The concepts behind clinical trials are ancient. The Book of Daniel chapter 1, verses 12 through 15, for instance, describes a planned experiment with both baseline and follow-up observations of two groups who either partook of, or did not partake of, "the King's meat" over a trial period of ten days. Persian physician Avicenna, in The Canon of Medicine (1025) gave similar advice for determining the efficacy of medical drugs and substances. In spite of this history, there seems to have been no clinical trials actually practiced in Western Europe. He blocked a group of twelve men suffering form the effects of scurvy after two months at sea into six different treatment groups of two each. He applied six different treatments, one group getting an issue of cider, one getting citrus, and four other possible alternatives. (The word placebo would not be used until 1772.) Both men in the citrus group showed considerable improvement, and one of the Cider subjects showed mild improvement after the study was stopped in six days. *Wik

1807 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.)

1896 Friedrich August Kekulé von Stradonitz (7 September 1829–13 July 1896) Kekulé was a German theoretical chemist who figured out how carbon atoms could have a valence of four and join together to make long isomers or even rings. He was the first to discover the ring structure of benzene and greatly advanced the understanding of organic chemistry and aromatic compounds of the time.
Kekulé wrote about the method of his discovery where he was sitting by the fireplace and started to nod off. He dreamed of atoms arranging themselves in groups of ever increasing size until they became long chains. The chains started to wind and turn like snakes until one snake grabbed its own tail. He woke up suddenly and spent the rest of the nightworking out the structure.*This Day in Science History

1921 Gabriel Lippmann (16 August 1845 – 13 July 1921) French physicist, born Hollerich, Luxembourg, who received the Nobel Prize for Physics in 1908 for producing the first colour photographic plate. Lippmann was a giant of his day in classical physics research, especially in optics and electricity. He worked in Berlin with the famed Hermann von Helmholtz before settling in Paris to head (in 1886) the Sorbonne's Laboratories of Physical Research until his death. His inventions include an instrument for precisely measuring minute differences in electrical power and the "coleostat" for steady, long-exposure sky photography.*TIS

1941 Ivan Ivanovich Privalov (13 Feb 1891 in Nizhny Lomov, Penza guberniya (now oblast), Russia - 13 July 1941 in Moscow, USSR) Privalov, often in collaboration with Luzin, studied analytic functions in the vicinity of singular points by means of measure theory and Lebesgue integrals. He also obtained important results on conformal mappings showing that angles were preserved on the boundary almost everywhere. In 1934 he studied subharmonic functions, building on the work of Riesz. He published the monograph Subharmonic Functions in 1937 which gave the general theory of these functions and contained many results from his papers published between 1934 and 1937. *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

Sunday, 12 July 2020

On This Day In Math - July 12

Technical skill is mastery of complexity while creativity is mastery of simplicity.
Sir Christopher Zeeman

This is the 194th day of the year, 1944+1 = 1,416,468,497 is prime *Prime Curios

194 is also the smallest number that can be written as the sum of 3 squares (not all unique) in five ways. (There is a slightly larger number that is expressible as the sum of 3 unique squares in five ways. )

194 is the product of the largest and smallest prime less than 100.

194 is the sum of three consecutive squares, \( 194 = 7^2 + 8^2 + 9^2 \)

194 is the even base of the Largest Heronian triangle with consecutive integer sides that can be year dates.  Heronian triangles are triangles that have all three sides and the area as integers.  The three sides are 193, 194, 195, and the Area is 16,296 sq units.  I have seen these called Super Heronian triangles, but I call them Sang-Heronian triangles after the earliest study I know about them by Edward Sang of Edinburgh, Scotland in1864  Because these bases are always equal, the altitude from that base must also be an integer. And one more biggie... If you construct the altitude to the even base, one side or the other of it will always form a primitive Pythagorean triangle.  For each new bigger triangle, it switches sides.  In the triangle for this date, the PPT is 95, 193, 195.  I won't to write a little more about this than space here allows, so I will link it here then.


1389 King Richard II appoints Geoffrey Chaucer to the position of chief clerk of the king's works in Westminster. Although remembered today for his unfinished "Canterbury Tales" (he had intended 200 stories but only finished 22), he achieved fame during his lifetime as a philosopher, alchemist and astronomer, composing a scientific treatise on the astrolabe for his ten year-old son Lewis.

1831 Gauss to Schumacher: “I protest against the use of an infinite quantity as an actual entity; this is never allowed in mathematics. The infinite is only a manner of speaking, in which one properly speaks of limits to which certain ratios can come as near as desired, while others are permitted to increase without bound.” *VFR

1844 Captain J.N. Taylor of the Royal Navy first demonstrated the fog horn. At the time, it was called a telephone - to mean far-signalling, thus an instrument like a fog-horn, used on ships, railway trains, etc., for signalling by loud sounds or notes. The 19 July 1844 Times (London) reported, "Yesterday week was a levee day at the Admiralty, and amongst the numerous models..was Captain J. N. Tayler's telephone instrument... The chief object of this powerful wind instrument is to convey signals during foggy weather. Also the Illustrated London News on 24 Aug. 1844 referred to "The Telephone; a Telegraphic Alarum. Amongst the many valuable inventions..that of the 'Telephone, or Marine Alarum and Signal Trumpet', by Captain J. N. Taylor."*TIS

1925 Heisenberg announced the basic principles of quantum mechanics. *VFR

1969 What is believed to be the first photo of a laser appeared on the cover of Electronics,on this date .

1979 The Gossamer Albatross completed the first wholly man-powered flight across the English Channel. See August 23, 1971. *VFR

2011  Google announces winners of Google Science Fair . The top three winners by age category are:
  • Lauren Hodge in the 13-14 age group. Lauren studied the effect of different marinades on the level of potentially harmful carcinogens in grilled chicken.
  • Naomi Shah in the 15-16 age group. Naomi endeavored to prove that making changes to indoor environments that improve indoor air quality can reduce people’s reliance on asthma medications.
  • Shree Bose in the 17-18 age group. Shree discovered a way to improve ovarian cancer treatment for patients when they have built up a resistance to certain chemotherapy drugs.


1808 Reverend Robert Main (July 12, 1808 – May 9, 1878) English astronomer.
Born in Kent, the eldest son of Thomas Main, Robert Main attended school in Portsea before studying mathematics at Queens' College, Cambridge, where he graduated in 1834. He served for twenty-five years (1835-60) as First Assistant at the Royal Greenwich Observatory, and published numerous articles, particularly on stellar and planetary motion, stellar parallax, and the dimensions and shapes of the planets. From 1841 to 1861 he was successively an honorary secretary, a vice-president, and President of the Royal Astronomical Society, and in 1858 was awarded the Society's Gold Medal. In 1860 he became director of Radcliffe Observatory at Oxford University after the death of Manuel Johnson, and was elected as a Fellow of the Royal Society. *Today in Astronomy

1854 George Eastman's birthday (July 12, 1854 – March 14, 1932). Eastman was the American inventor of rolled photographic film. He formed the Eastman Kodak Company to bring photography to the average person. For \($25\), a person could buy a camera with 100 exposures. Eastman promised, "You push the button, we do the rest." Once all 100 pictures were taken, the camera and a \($10\) processing fee was returned to Kodak where they reloaded the camera with film and developed and printed the pictures. *This Day in Science History

1861 George Washington Carver African-American educator, scientist, chemist, inventor, botanist. After the Civil War, Southern farmers planted cotton year after year, and the soil lost its fertility. Yields dropped. Between 1890 and 1910, the cotton crop was devastated by the bolweevil. George Washington Carver was appointed head of the agriculture department at The Tuskegee Institute in Alabama by Booker T. Washington (1896). Carver discovered and taught how to maintain the fertility of the soil. Further, his discovered two new crops that would grow well there: peanuts and sweet potatoes. Further, Carver created a market by inventing hundreds of new uses for for these crops, from milk to printer's ink .*TIS

1875 Ernst Fischer (12 July 1875 – 14 November 1954) is best known for the Riesz-Fischer theorem in the theory of Lebesgue integration.*SAU His main area of research was mathematical analysis, specifically orthonormal sequences of functions which laid groundwork for the emergence of the concept of a Hilbert space. *Wik

1895 R(ichard) Buckminster Fuller (July 12, 1895 – July 1, 1983) was an American inventor, educator, author, philosopher, engineer and architect who developed the geodesic dome, the only large dome that can be set directly on the ground as a complete structure, and the only practical kind of building that has no limiting dimensions (i.e., beyond which the structural strength must be insufficient). He held over 2000 patents.*TIS

1913 Willis Eugene Lamb, Jr (July 12, 1913 – May 15, 2008) was an American physicist and joint winner, with Polykarp Kusch, of the Nobel Prize for Physics in 1955 "for his discoveries concerning the fine structure of the hydrogen spectrum." His experimental work spurred refinements in the quantum theories of electromagnetic phenomena.*TIS The Lamb shift was an energy difference between the 2S½ and 2P½ energy levels of the hydrogen atom. According to the current theory, these two levels should have the same amount of energy, but when the electrons were exposed to a magnetic field, the energy level of 2S½ was slightly different. This discovery led to the renormalization theory of quantum electrodynamics. *This Day in Science History

1922 Michael Ventris (12 July 1922 – 6 September 1956) English architect and cryptographer who in 1952 deciphered the Minoan Linear B script. These were the inscriptions on ancient clay tablets found in Crete and a few other locations; writings which had baffled archaeologists since their discovery in 1900. He showed the script to be Greek in its oldest known form, dating from about 1400 to 1200 BC, roughly the period of the events narrated in the Homeric epics. One of the most tantalizing riddles of classical archaeology was solved, but not without creating some puzzling situations. The reading of these tablets in the Greek language raised the question: How could a literate people in the fourteenth century BC become illiterate for almost five centuries, to regain literacy in the eighth century? Ventris died young, in an auto accident, soon after his triumph.*TIS


1682 Jean Picard (July 21, 1620 – July 12, 1682) French Jesuit, active astronomer, cartographer, hydraulics engineer, Jean Picard devised a movable-wire micrometer to measure the diameters of celestial objects such as the Sun, Moon and planets. For land surveying and leveling, he designed instruments that incorporated the astronomical telescope. He greatly increased the accuracy of measurements of the Earth, using Snell's method of triangulation (Mesure de la Terre, 1671). This data was used by Newton in his gravitational theory. Picard was one of the first to apply scientific methods to the making of maps. Among his other skills were hydraulics; he solved the problem of supplying the fountains at Versailles with water.*TIS

1834 David Douglas (25 June 1799 – 12 July 1834) Scottish botanist who was one of the most successful of the great 19th century plant collectors. He established about 240 species of plants in Britain. His first foreign plant-hunting expedition (1824) was made throughout the Pacific Northwest of the U.S. The Douglas fir, which he cultivated from 1827, is named after him. He introduced other conifers including the Sitka spruce, now commercially important to the timber industry, and numerous garden plants and shrubs, including the lupin, California poppy and the flowering currant. At age 35, he died in by accident in Hawaii, when he fell into a pit dug by the islanders to trap wild cattle where he was trapped with a bull that also fell into the pit. He was gored to death by the bull.*TIS (add to candidate for most unusual death. see also Eduord Lucas, and Francis Bacon, send your nominees)

1983 Ernst Gabor Straus (February 25, 1922 – July 12, 1983) was a German-American mathematician who helped found the theories of Euclidean Ramsey theory and of the arithmetic properties of analytic functions. His extensive list of co-authors includes Albert Einstein and Paul Erdős as well as other notable researchers including Richard Bellman, Béla Bollobás, Sarvadaman Chowla, Ronald Graham, László Lovász, Carl Pomerance, and George Szekeres. It is due to his collaboration with Straus that Einstein has Erdős number 2. *Wik

*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
Posted by Pat Ballew at 00:30

Saturday, 11 July 2020

On This Day in Math - July 11

Ten decimal places of π are sufficient to give the circumference
of the earth to a fraction of an inch, 
and thirty decimal places would give the circumference of the visible universe
to a quantity imperceptible to the most powerful microscope.
~Simon Newcomb  

Today is the 193rd day of the year; 193 is one of a twin prime pair and is the sum of products of the first three twin primes pairs: 3*5 + 5*7 + 11*13 = 193. *Prime Curios

The square of 193 (37249) concatenated with its reverse (which is a prime) results in a palindrome that is the product of 2 palindromes, one non-prime (1001) and one prime (3721273).

193 is the smallest prime whose fifth power contains all digits from 1 to 9.

(I also like 193/71 is the closest ratio of two primes less than 2000 to the number e.)


1663 John Wallis, Savilian Professor of Geometry at Oxford, gave a specious proof of Euclid’s parallel postulate. See W. W. Rouse Ball, Mathematical Recreations and Essays, 6th edition, pp. 314– 315.*VFR

1686 Leibniz published his first paper on the integral calculus in Acta eruditorum.*VFR  This paper contains the first appearance in print of the elongated s integral notation used today. He had used the symbol earlier in a manuscript on Oct 29, 1675.

1699 Halley's final log entry for his first voyage of discovery commanding the Paramore, “The Gunns and Gunners Stores were delivered to the Tower Officers and that Same Evening we moord our Shipp at Deptford” *halleyslog.wordpress.com

1700 Royal Prussian Academy of Sciences at Berlin founded. Leibniz was primarily responsible for the founding and directed it for sixteen years. [HM 2, p. 310; American Journal of Physics, 34(1966), p. 22]*VFR

1731 Alexis-Claude Clairaut elected to the French academy. He was only eighteen. *VFR

1738 Isaac Greenwood, the first Hollis Professor at Harvard, was “ejected” from his chair for drunk­enness. [I. B. Cohen, Some Early Tools of American Science, p. 36.]  *VFR

1747 Benjamin Franklin writes to Peter Collinson, London Businessman and member of the Royal Society, to describe the, "wonderful effects of pointed bodies, both in drawing off and throwing off the electrical fire."* A history of physics in its elementary branches By Florian Cajori

1811 Italian scientist Amedeo Avogadro published his memoire about the molecular content of gases. *TIS

1814 Amp`ere submitted a paper on general solutions of differential equations. It contains thought-provoking remarks and interesting examples which had to wait several decades for proper under­standing and recognition. [Ivor Grattan-Guiness, Convolutions in French Mathematics, 1800– 1840, pp. 700ff, 1389]*VFR

1859 The Current Big Ben (the bell) is first heard ringing in the Westminster clock tower. Why Big Ben? After Benjamin Hall (1802-67). In Aug 1856 the bell, with Hall's name inscribed on it, was cast, but cracked after tests in October 1857. The substitute was also defective but worked sufficiently well to be hung in Oct 1858. Named Big Ben, it was first heard on 11 July 1859. Two months later it too cracked & fell silent for 4 years; it was repaired with help of Sir George Airy, astronomer royal, & rings to this day. *Oxford DNB@ODNB

1976 K&E produced its last slide rule, which it presented to the Smithsonian Institution. A common method of performing mathematical calculations for many years, the slide rule became obsolete with the invention of the computer and its smaller, hand-held sibling, the calculator. (*This Day in History-Computer History Museum)

1979  U.S. space station, Skylab, re-entered the Earth's atmosphere. It disintegrated, spreading fragments across the southeastern Indian Ocean and over a sparsely populated section of western Australia, where a cow died after being struck by a piece of falling debris. *TIS (Proving the potential effectiveness of weapons in space?)

In 1991, a solar eclipse cast a blanket of darkness stretching 9,000 miles from Hawaii to South America, lasting nearly seven minutes in some places. It was the so-called eclipse of the century. A total solar eclipse - the moon passing between the sun and the earth - is the moon's shadow cast on the casting its shadow on the earth's surface. Total eclipses occur almost once per year, but are often over an ocean or remote countries. The solar eclipse on July 11, 1991, was a thrill for scientists. It traveled over the several astronomical observatories on the top of Mauna Kea. Their 14,000 feet elevation was actually above the cloud level, which obstructed the view for those below. *TIS

On this day about "one year" ago German astronomer Johanne Galle discovered Neptune ... One Neptunian year that is! *rmathematicus, Thony Christie;
On July 11, 2011, Neptune completed its first full barycentric orbit since its discovery on September 23, 1846, *Wik


1732  Joseph Jérôme Le Français de Lalande, (11 July 1732 – 4 April 1807) was a an astronomer, born in Bourg-en-Bresse, France. He determined the Moon's parallax from Berlin for the French Academy (1751). He was appointed professor of Astronomy, Collège de France (1762), and subsequently, director of the Paris Observatory. He published his Traité d'astronomie in 1764 - tables of the planetary positions that were considered the best available for the rest of the century. In 1801 he also published a comprehensive star catalogue. He died in 1807, apparently of tuberculosis. *TIS

1811 Sir William Robert Grove, (11 July 1811 – 1 August 1896) British physicist and a justice of Britain's high court (from 1880), who first offered proof of the thermal dissociation of atoms within a molecule. He showed that steam in contact with a strongly heated platinum wire is decomposed into hydrogen and oxygen in a reversible reaction. In 1839, Grove mixed hydrogen and oxygen in the presence of an electrolyte, and produced electricity and water. This Grove Cell was the invention of the fuel cell. The technology was not seriously revisited until the1960s. Through the electrochemical process, the energy stored in a fuel is converted - without combusting fuel - directly into DC electricity.*TIS

1857 Sir Joseph Larmor (11 July 1857 Magheragall, County Antrim, Ireland – 19 May 1942 Holywood, County Down, Northern Ireland), Irish physicist, the first to calculate the rate at which energy is radiated by an accelerated electron, and the first to explain the splitting of spectrum lines by a magnetic field. His theories were based on the belief that matter consists entirely of electric particles moving in the ether. His elaborate mathematical electrical theory of the late 1890s included the "electron" as a rotational strain (a sort of twist) in the ether. But Larmor's theory did not describe the electron as a part of the atom. Many physicists envisioned both material particles and electromagnetic forces as structures and strains in that hypothetical fluid. *TIS

1857 Alfred Binet (July 11, 1857 – October 18, 1911) who introduced his famous IQ test in 1905. *VFR French experimental psychologist, the director of the psychological laboratory of the Sorbonne, Paris (1894). He made fundamental contributions to the measurement of intelligence.With Theodore Simon, Binet produced a series of graded tasks typical of the intellectual development of children of different ages (1905). This scale was extended (1908-11), and the tasks were assigned to the age level at which average children could manage them. Thus children could be scored for the level, or mental age, they reached. This test formed the basis for the Stanford-Binet Tests.*TIS (today in Science also gives Binet's birthdate on July 11th, with a different description:  French psychologist who was a pioneer in the field of intelligence testing of the normal mind. He took a different approach than most psychologists of his day: he was interested in the workings of the normal mind rather than the pathology of mental illness. He wanted to find a way to measure the ability to think and reason, apart from education in any particular field. In 1905 he developed a test in which he had children do tasks such as follow commands, copy patterns, name objects, and put things in order or arrange them properly. He gave the test to Paris schoolchildren and created a standard based on his data. From Binet's work, "IQ" (intelligence quotient), entered the vocabulary. The IQ is the ratio of "mental age" to chronological age, with 100 being average.)

1890 Giacomo Albanese (11 July 1890 – 8 June 1947) was an Italian mathematician known for his work in algebraic geometry. He took a permanent position in São Paulo, Brazil, in 1936. *Wik

1902 Samuel Abraham Goudsmit (The Hague, July 11, 1902 — Reno, December 4, 1978) Dutch-born U.S. physicist who, with George E. Uhlenbeck, a fellow graduate student at the University of Leiden, Neth., formulated (1925) the concept of electron spin. It led to recognition that spin was a property of protons, neutrons, and most elementary particles and to a fundamental change in the mathematical structure of quantum mechanics. Goudsmit also made the first measurement of nuclear spin and its Zeeman effect with Ernst Back (1926-27), developed a theory of hyperfine structure of spectral lines, made the first spectroscopic determination of nuclear magnetic moments (1931-33), contributed to the theory of complex atoms and the theory of multiple scattering of electrons, and invented the magnetic time-of-flight mass spectrometer (1948).*TIS

1922 John William Scott Cassels  (11 July 1922 in Durham - ) initially worked on elliptic curves. After a period when he worked on geometry of numbers and diophantine approximation, he returned in the later 1950s to the arithmetic of elliptic curves, writing a series of papers connecting the Selmer group with Galois cohomology and laying some of the foundations of the modern theory of infinite descent. His best-known single result may be the proof that the Tate-Shafarevich group, if it is finite, must have order that is a square; the proof being by construction of an alternating form. Cassels has often studied individual Diophantine equations by algebraic number theory and p-adic methods. 
His publications include 200 papers. His advanced textbooks have influenced generations of mathematicians; some of Cassels's books have remained in print for decades. *Wik

1382 Nicole Oresme (c. 1320–5 – July 11, 1382), was a French mathematician who invented coordinate geometry long before Descartes. He was the first to use a fractional exponent and also worked on infinite series. *SAU
Oresme was Bishop of Liseux and died there, but I was recently (2011) at the Cathedral and cold find no mark of his life there.
"His most important contributions to mathematics are contained in "Tractatus de figuratione potentiarum et mensurarum difformitatum", still in manuscript. An abridgment of this work printed as "Tractatus de latitudinibus formarum" (1482, 1486, 1505, 1515), has heretofore been the only source for the study of his mathematical ideas. In a quality, or accidental form, such as heat, the Scholastics distinguished the intensio (the degree of heat at each point) and the extensio (e.g., the length of the heated rod): these two terms were often replaced by latitudo and longitudo, and from the time of St. Thomas until far on in the fourteenth century, there was lively debate on the latitudo formæ. For the sake of lucidity, Oresme conceived the idea of employing what we should now call rectangular co-ordinates: in modern terminology, a length proportionate to the longitudo was the abscissa at a given point, and a perpendicular at that point, proportional to the latitudo, was the ordinate. He shows that a geometrical property of such a figure could be regarded as corresponding to a property of the form itself only when this property remains constant while the units measuring the longitudo and latitudo vary. Hence he defines latitudo uniformis as that which is represented by a line parallel to the longitude, and any other latitudo is difformis; the latitudo uniformiter difformis is represented by a right line inclined to the axis of the longitude. He proves that this definition is equivalent to an algebraical relation in which the longitudes and latitudes of any three points would figure: i.e., he gives the equation of the right line, and thus forestalls Descartes in the invention of analytical geometry. This doctrine he extends to figures of three dimensions.
Besides the longitude and latitude of a form, he considers the mensura, or quantitas, of the form, proportional to the area of the figure representing it. He proves this theorem: A form uniformiter difformis has the same quantity as a form uniformis of the same longitude and having as latitude the mean between the two extreme limits of the first. He then shows that his method of figuring the latitude of forms is applicable to the movement of a point, on condition that the time is taken as longitude and the speed as latitude; quantity is, then, the space covered in a given time. In virtue of this transposition, the theorem of the latitude uniformiter difformis became the law of the space traversed in case of uniformly varied motion: Oresme's demonstration is exactly the same as that which Galileo was to render celebrated in the seventeenth century. Moreover, this law was never forgotten during the interval between Oresme and Galileo: it was taught at Oxford by William Heytesbury and his followers, then, at Paris and in Italy, by all the followers of this school. In the middle of the sixteenth century, long before Galileo, the Dominican Dominic Soto applied the law to the uniformly accelerated falling of heavy bodies and to the uniformly decreasing ascension of projectiles." 
*Catholic Encyclopedia online

1733 Jakob Hermann (16 July 1678, Basel – 11 July 1733, Basel) was a Swiss mathematician who made contributions to dynamics. *SAU

1807 George Atwood was an English mathematician best known for his invention of a low-friction pulley system.*SAU He is the author of Phoronomia, an early treatise on Mechanics. 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 Euler. *Wik

1778 Joseph Stepling, (29 June 1716 in Regensburg; 11 July 1778 in Prague) His fields included astronomy, physics and mathematics. At the age of 17 he documented with great accuracy the 1733 lunar eclipse. Later Euler was among his long list of correspondents. He transposed Aristotelian logic into formulas, thus becoming an early precursor of modern logic. already adopted the atomistic conception of matter he radically refused to accept Aristotelian metaphysics and natural philosophy. In 1748, at the request of the Berlin Academy, he carried out an exact observation of a solar and lunar eclipse in order to determine the precise location of Prague. During Stepling's long tenure at Prague, he set up a laboratory for experimental physics and in 1751 built an observatory, the instruments and fittings of which he brought up to the latest scientific standard.
v Even though he passed up a professorship in philosophy in favor of a chair in mathematics, Empress Maria Theresa appointed him director of the faculty of philosophy at Prague as part of the reform of higher education. He was very interested in cultivating the exact sciences and founded a society for the study of science modeled on the Royal Society of London. In their monthly sessions. over which he presided until his death, the group carried out research work and investigations in the field of pure mathematics and its appiication to physics and astronomy. A great number of treatises of this academy were published.
Stepling corresponded with the outstanding contemporary mathematicians and astronomers: Christian Wolf. Leonhard Euler. Christopher Maire, Nicolas-Louis de Lacaille, Maximilian Heli, Joseph Franz, Rudjer Boskovic, Heinrich Hiss, and others. Also, Stepling was particularly successful in educating many outstanding scientists, including Johann Wendlingen, Jakob Heinisch, Johannes von Herberstein, Kaspar Sagner, Stephan Schmidt, Johann Korber, and Joseph Bergmann. After his death, Maria Theresia ordered a monument erected in the library of the University of Prague *Joseph MacDonnell, Fairfield Univ web page

1745 George Atwood (Baptized October 15, 1745, Westminster,London – 11 July 1807, London) was an English mathematician who invented a machine for illustrating the effects of Newton's first law of motion. He was the first winner of the Smith's Prize in 1769. He was also a renowned chess player whose skill for recording many games of his own and of other players, including François-André Danican Philidor, the leading master of his time, left a valuable historical record for future generations.

He attended Westminster School and in 1765 was admitted to Trinity College, Cambridge. He graduated in 1769 with the rank of third wrangler and was awarded the inaugural first Smith's Prize. Subsequently he became a fellow and a tutor of the college and in 1776 was elected a fellow of the Royal Society of London.

In 1784 he left Cambridge and soon afterwards received from William Pitt the Younger the office of patent searcher of the customs, which required but little attendance, enabling him to devote a considerable portion of his time to mathematics and physics.

He died unmarried in Westminster at the age of 61, and was buried there at St. Margaret's Church. Over a century later, a lunar crater was renamed Atwood in his honour. *Wik

1871 Germain Sommeiller (February 15, 1815 - July 11, 1871) French-Italian engineer who built the Mount Cenis (Fréjus) Tunnel (1857-70) through the Alps, the world's first important mountain tunnel. The two track railway tunnel unites Italian Savoy (north of the mountains) through Switzerland with the rest of Italy to the south. At 8 miles long and it was more than double the length of any previous tunnel. In 1861, after three years of tedious hand-boring a mere eight inches a day into the rock face, Sommeiller introduced the first industrial-scale pneumatics for tunnel digging. He built a special reservoir, high above the tunnel entrance, to produce a head of water that compressed air (to 6 atm.) for pneumatic drills, able to dig up to 20 times faster. Authorised on 15 Aug 1857, the tunnel opened on 17 Sep 1871, as a major triumph of engineering.*TIS Note his death was only a few months before the opening of his great project.

1909 Astronomer and mathematician Simon Newcomb (March 12, 1835 – July 11, 1909) died in Washington D.C. He was such a revered scientist that President Taft attended his funeral.*VFR  Canadian-American astronomer and and mathematician who prepared ephemerides (tables of computed places of celestial bodies over a period of time) and tables of astronomical constants. He was an astronomer (1861-77) before becoming Superintendent of the U.S. Nautical Almanac Office (1877-97). During this time he undertook numerous studies in celestial mechanics. His central goal was to place planetary and satellite motions on a completely uniform system, thereby raising solar system studies and the theory of gravitation to a new level. He largely accomplished this goal with the adoption of his new system of astronomical constants at the end of the century. *TIS
Newcomb is buried in Arlington National Cemetery 
Newcomb is often quoted as saying that heavier than air flight was impossible from a statement he made only two months before the Wright Brothers flight at Kitty Hawk, N.C.
"The mathematician of to-day admits that he can neither square the circle, duplicate the cube or trisect the angle. May not our mechanicians, in like manner, be ultimately forced to admit that aerial flight is one of that great class of problems with which men can never cope… I do not claim that this is a necessary conclusion from any past experience. But I do think that success must await progress of a different kind from that of invention."   He also is famously quoted for saying, "We are probably nearing the limit of all we can know about astronomy." 

1995 Andrzej Alexiewicz (11 February 1917, Lwów, Poland – 11 July 1995) was a Polish mathematician, a disciple of the Lwow School of Mathematics. Alexiewicz was an expert at functional analysis and continued and edited the work of Stefan Banach. *Wik

*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

Friday, 10 July 2020

Memories of the UK, Signs of the Times (or of the Thames)

Repost of an old blog about British vernacular"

 In 1887 Oscar Wilde wrote: `We have really everything in common with America nowadays except, of course, language'. Some say he may have been paraphrasing something by George B. Shaw. Whichever said it first, they were wrong; the British are different. I've been over here for a while, and I don't giggle anymore when I hear a seven-year-old ask his mom to buy him some new rubbers (erasers). I even know I'm not looking for footweae when I go to a boot sale (flea-market). But sometimes the British road signs just take me back to square one.

The sign above is an example. It is located in Greenwich near the loaction where they are restoring the Cutty Sark. You have to figure out what it means. It is not just that they use the same words to mean different stuff. They just have a different mind set. North of my home here in Stoke Ferry as I drove towards Kings Lynn there was a sign that read, "Cats Eyes removed ahead" Yikes!!!

A common road sign that I have yet to figure out has the warning, "Beware of oncoming traffic in center of road"???? If there is a problem with oncoming traffic in the center of the road, shouldn't this sign be turned the other way and say something like, "Get your Butt back in your own lane!" You see? The British just think differently.

Ok, one more example. I was in London to see the "Tut" exhibit last weekend (a bit disappointing, actually) and in King's Cross station I noticed this sign.

The sign is located on an electronic schedule that tells you the track on which trains depart. When the station is busiest, they apparently turn them off so people won't crowd around them.... YES, READ IT AGAIN... In the peak periods they remove information. People blindly wandering from track to track apparently are less likely to congregate in one place and create congestion... Ok, I don't really know why they have such a sign, or why they would do it.... My only explanation... The British ARE different.

On This Day in Math - July 10

That which is not good for the bee-hive cannot be good for the bees. 

~ Marcus Aurelius

The 192nd day of the year; 192 is the smallest number that together with its double and triple contain every digit from 1-9 exactly once. There are three other values of n so that n, 2n, and 3n contain each non-zero digit exactly once. Can you find them?

192 is the sum of ten consecutive primes (5 + 7 + 11 + 13 + 17 + 19 + 23 + 29 + 31 + 37)

192 is the number of edges on a 6th dimension hypercube, it is the last day of the year which is the number of edges of a hypercube.

Diophantus probably knew, and Lagrange proved, that every positive integer can be written as a sum of four perfect squares. Jacobi] proved the stronger result that the number of ways in which a positive integer can be so written equals 8 times the sum of its divisors that are not multiples of 4. Use this theorem to prove that there are 192 ways to express 14 as a sum of four squares.

See More Math Facts for every year date here


1600 Kepler’s interest in optics arose as a direct result of his observations of the partial solar eclipse of 10 July 1600. Following instructions from Tycho Brahe, he constructed a pinhole camera; his measurements, made in the Graz marketplace, closely duplicated Brahe’ and seemed to show that the moon’s apparent diameter was considerably less than the sun’s. Kepler soon realized that the phenomenon resulted from the finite aperture of the instrument (see Fig. 5); his analysis, assisted by actual threads, led to a clearly defined concept of the light ray, the foundation of modern geometrical optics.
Kepler’s subsequent work applied the idea of the light ray to the optics of the eye, showing for the first time that the image is formed on the retina. He introduced the expression “pencil of light,” with the connotation that the light rays draw the image upon the retina; he was unperturbed by the fact that the image is upside down. *Encyclopedia.com

1610 Galileo receives a letter from Cosimo II agreeing to his salary requests, and confirming him as "First Mathematician of our Stadium in Pisa" but with no requirements that he live or lecture in Pisa, "except when it may please you as an honor." *The Copernican Question: Prognostication, Skepticism, and Celestial Order By Robert S. Westman

1637 First meeting of the Acad´emie Fran¸caise. *VFR

1676 Flamsteed began living at the Observatory with his two servants. On 19  July,  his long series of Greenwich  observations began?  *Rebekah Higgitt, Teleskopos

1794  Star in a crescent moon?  Astronomer Royal Investigates. The results are read to the Royal Society..."An Account of an Appearance of Light, like a Star, Seen Lately in the Dark Part of the Moon, by Thomas Stretton, in St. John's Square, Clerkenwell, London; with Remarks upon This Observation, and Mr. Wilkins's. Drawn up, and Communicated by the Rev. Nevil Maskelyne, D. D. F. R. S. and Astronomer Royal"  *Phil. Trans. R. Soc. Lond. January 1, 1794 84:435-440;

1796 Date of the entry EγPHKA! num=Δ+Δ+Δ in Gauss’s scientific diary, recording his discovery that every positive integer is the sum of three triangular numbers. [Thanks to Howard Eves] *VFR

1826 Cauchy presented a proof to the Acad´emie dealing with existence theorems for first-order dif-ferential equations. [Ivor Grattan-Guiness, Convolutions in French Mathematics, 1800–1840, pp. 758 and 1401] *VFR

1843 Jacques Philippe Marie Binet, age 57, elected to the Acad´emie des Sciences to succeed Lacroix. He is an example of a mathematician who published much late in life. He worked in mechanics, elasticity, perturbation theory, determinants, and the calculus. [Ivor Grattan-Guiness, Convo¬lutions in French Mathematics, 1800–1840, pp. 191 and 1410] *VFR

1908 at 5:45 in the morning, Kammerlingh Onnes, of Leiden, wins the race to produce liquified helium.   75 liters of liquid air is used to condense 20 liters of liquid oxygen, from which 20 milli-liters of liquid helium under reduced pressure. *Quantum Generations: A History of Physics in the Twentieth Century  By Helge Kragh

1925 The “Monkey Trial” of John T. Scopes began in Dayton, Tennessee. Clarence Darrow defended him. The prosecution, conducted by William Jennings Bryan, presented a strong case, and he was convicted of violating a state law prohibiting the teaching of evolution. Although the law was later overturned, this case provided a strong blow to science education. Scopes was not a biologist and never taught evolution. Rather he was a mathematics and physics teacher who volunteered to stand trial to furnish a test case. *VFR
The trial ran for 12 days. A local school teacher, John Scopes, was prosecuted under the state's Butler Act, but was supported by the American Civil Liberties Union. This law, passed a few months earlier (21 Mar 1925) prohibited the teaching of evolution in public schools. The trial was a platform to challenge the legality of the statute. Local town leaders,(wishing for the town to benefit from the publicity of the trial) had recruited Scope to stand trial. He was convicted (25 Jul) and fined $100. On appeal, the state supreme court upheld the constitutionality of the law but acquitted Scopes on the technicality that he had been fined excessively. The law was repealed on 17 May 1967. *TIS

1950 France honors Lazar Carnot (1753–1823) with a postage stamp. [Scott #B251]. *VFR

1950 The German Democratic Republic, to celebrate the 250th anniversary of the founding of the Academy of Sciences, Berlin, issued postage stamps picturing Leonhard Euler and Gottfried von Leibniz. [Scott #58, 66]. *VFR 

Leibniz was also honored with stamp issues in 1980 and 1996 it seems.

1993 MASH fans will remember that there was always a sign telling how many miles to Toledo and frequently they talked of the hotdogs at Tony Pacos (they are good). On this date the Cake Walk and Jazz Band (I believe the band is called "The Cakewalken Jass Band") celebrated their twenty-fifth anniversary with a live broadcast at Tony Pacos that was broadcast on public radio in Toledo. So what does this have to do with mathematics? Well, Ray Heitger, their clarinetist, leader, and one of the founding members happens to be a math teacher. If you can’t get to Toledo to hear them play, perhaps you can find one of their six LPs.*VFR
Tony Packo's Cafe is restaurant that started in the Hungarian neighborhood of Birmingham, on the east side of Toledo, Ohio at 1902 Front Street. The restaurant gained notoriety by its mention in several M*A*S*H episodes and is famous for its signature sandwich and large collection of hot dog buns signed by celebrities.     In 2011 it listed five restaurants in the Toledo area. *Wik


1682 Roger Cotes born (10 July 1682 — 5 June 1716). In January 1706 he was named the first Plumian professor of astronomy and natural philosophy at Cambridge. It was Cotes who first showed that e was the natural base to choose for the logarithm. *VFR He did not realize his full potential because he died at age 33, leaving anunfinished series of imposing researches on optics and a large number of other unpublished manuscripts. Newton, who seldom spoke well of anyone else, said of Cotes, "If Cotes had lived, we might have known something."
Thony Christie at the Renaissance Mathematicus has a nice post about Cotes.

1832  Alvan Graham Clark  (July 10, 1832 – June 9, 1897)  U.S. astronomer, one of an American family of telescope makers and astronomers who supplied unexcelled lenses to many observatories in the U.S. and Europe during the heyday of the refracting telescope. He began a deep interest in astronomy while still at school, then joined the family firm of Alvan Clark & Sons, makers of astronomical lenses. In 1861, testing a new lens, he looked through it at Sirius and observed faintly beside it, Sirius B, the twin star predicted by Friedrich Bessel in 1844. Carrying on the family business, after the deaths of his father and brother, Clark made the 40" lenses of the Yerkes telescope (still the largest refractor in the world). Their safe delivery was a source of anxiety. He died shortly after their first use. *TIS

1856 Nikola Tesla (10 July 1856 – 7 January 1943)Serbian-American inventor and researcher who designed and built the first alternating current induction motor in 1883. [This statement seems to be in error,according to Wikipedia which states," In 1824, the French physicist François Arago formulated the existence of rotating magnetic fields, termed Arago's rotations, which, by manually turning switches on and off, Walter Baily demonstrated in 1879 as in effect the first primitive induction motor. Practical alternating current induction motors seem to have been independently invented by Galileo Ferraris(1885) and then Tesla (1887).]He emigrated to the United States in 1884. Having discovered the benefits of a rotating magnetic field, the basis of most alternating-current machinery, he expanded its use in dynamos, transformers, and motors. Because alternating current could be transmitted over much greater distances than direct current, George Westinghouse bought patents from Tesla the system when he built the power station at Niagara Falls to provide electricity power the city of Buffalo, NY. [Born in Croatia of Serbian parents. Some sources give birthdate as 9 Jul; he is said to have been born on the stroke of midnight.]

1878  Oliver Dimon Kellogg (10 July 1878 in Linwood, Pennsylvania, USA - 26 July 1932 in Greenville, Maine, USA) was appointed to the University of Missouri in 1905 where,  despite a heavy teaching and administrative load he was able to publish  impressive papers on potential theory. In 1908 he published three papers, namely Potential functions on the boundary of their regions of definition  and Double distributions and the Dirichlet problem, both in the Transactions of the American Mathematical Society, and A necessary condition that all the roots of an algebraic equation be real  in the Annals of Mathematics.  In 1912 he published the important work Harmonic functions and Green's integral  in the Transactions of the American Mathematical Society. This paper includes what today is called 'Kellogg's theorem' on harmonic and Green's functions. *SAU

1883 Frank Albert Benford, Jr., ((see note below about date of birth)1883 Johnstown, Pennsylvania – December 4, 1948) was an American electrical engineer and physicist best known for rediscovering and generalizing Benford's Law, a statistical statement about the occurrence of digits in lists of data.
Benford is also known for having devised, in 1937, an instrument for measuring the refractive index of glass. An expert in optical measurements, he published 109 papers in the fields of optics and mathematics and was granted 20 patents on optical devices.
His date of birth is given variously as May 29 or July 10, 1883. After graduating from the University of Michigan in 1910, Benford worked for General Electric, first in the Illuminating Engineering Laboratory for 18 years, then the Research Laboratory for 20 years until retiring in July 1948. He died suddenly at his home on December 4, 1948. *Wik

1928  Errett Albert Bishop (July 10, 1928 – April 14, 1983) (His) work is so wide ranging that it is difficult to give an overview in a biography such as this. Let us look at the book Selected papers which was published in 1986 and reprints some of Bishop's most significant contributions. The book divided Bishop's papers into five categories:
(1) Polynomial and rational approximation. Examples are extensions of Mergelyan's approximation theorem and the theorem of Frigyes Riesz and Marcel Riesz concerning measures on the unit circle orthogonal to polynomials. Bishop found new methods in dealing with these problems;
(2) The general theory of function algebras. Here Bishop worked on uniform algebras (commutative Banach algebras with unit whose norms are the spectral norms) proving results such as antisymmetric decomposition of a uniform algebra, the Bishop-DeLeeuw theorem, and the proof of existence of Jensen measures. In 1965 Bishop wrote an excellent survey Uniform algebras examining the interaction between the theory of uniform algebras and that of several complex variables.
(3) Banach spaces and operator theory. An examples of a paper by Bishop on this topic is Spectral theory for operators on a Banach space (1957). He introduced the condition now called the Bishop condition which turned out to be very useful in the theory of decomposable operators.
(4) Several complex variables. Examples of Bishop's papers in this area are Analyticity in certain Banach spaces (1962). He proved important results in this area such as the biholomorphic embedding theorem for a Stein manifold as a closed submanifold in Cn, and a new proof of Remmert's proper mapping theorem.
(5) Constructive mathematics. Bishop become interested in foundational issues around 1964, about the time he was at the Miller Institute. He wrote a famous text Foundations of constructive analysis (1967) which aimed to show that a constructive treatment of analysis is feasible.*SAU


1851 Louis-Jacques-Mandé Daguerre  (18 November 1787 – 10 July 1851) French painter and physicist who invented the daguerreotype, the first practical process of photography. Though the first permanent photograph from nature was made in 1826/27 by Joseph-Nicéphore Niepce of France, it was of poor quality and required about eight hours' exposure time. The process that Daguerre developed required only 20 to 30 minutes. The two became partners in the development of Niepce's heliographic process from 1829 until the death of Niepce in 1833. Daguerre continued his experiments, and he discovered that exposing an iodized silver plate in a camera would result in a lasting image after a chemical fixing process.*TIS

1910  Johann Gottfried Galle (9 June 1812 – 10 July 1910) German astronomer who on 23 Sep 1846, was the first to observe the planet Neptune, whose existence had been predicted in the calculations of Leverrier. Leverrier had written to Galle asking him to search for the new planet at a predicted location. Galle was then a member of the staff of the Berlin Observatory and had discovered three comets. In 1838, while assistant to Johann Franz Encke, Galle discovered the dark, inner C ring of Saturn at the time of the maxium ring opening. In 1851, he became professor of astronomy at Breslau and director of the observatory there. In 1872, he proposed the use of asteroids rather than regular planets for determinations of the solar parallax, a suggestion which was successful in an international campaign (1888-89). *TIS

1916 John Emory McClintock (19 Sept 1840 in Carlisle, Pennsylvania , USA - 10 July 1916 in Bay Head, New Jersey, USA) was for many years the leading actuary in America. He  published 30 papers between 1868 and 1877 on actuarial questions. His  publications were not confined to questions relating tolife insurance policies however. He published about 22 papers on mathematical topics. One paper treats difference equations as differential equations of infinite order and others look at quintic equations which are soluble algebraically. He published A simplified solution of the cubic  in 1900 in the Annals of Mathematics. Another work, On the nature and use of the functions employed in the recognition of quadratic residues  (1902), published in the Transactions of the American Mathematical Society, is on quadratic residues.*SAU

1936 Salvatore Pincherle (March 11, 1853 — July 10, 1936) worked on functional equations and functional analysis. Together with Volterra, he can claim to be one of the founders of functional analysis.*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