Antoine Caron: Astronomers Studying an Eclipse *TIA |

**Nature is not embarrassed by difficulties of analysis.**

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 14

^{2}=196 and 13

^{2}=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, p

^{2}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 20

^{th}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

*http://connecticuthistory.org |

**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.")

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