## Wednesday 13 July 2022

### 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

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 in 1864  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.

EVENTS

1672
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.

1836
Central High School is the second oldest continuously public high school in the United States. The school was chartered by an Act of Assembly and approved on June 13, 1836.  The city set aside money for building the new high school including an astronomical observatory.  By 1840, after donations from Sears Cook Walker, A wealthy Actuary of the city, it was surely the finest Observatory in America, eclipsing both the new Naval Observatory, and the Yale Observatory.
Sears Cook Walker was a regular user of the observatory, who later went bankrupt, worked for the Naval Observatory, and by 1947 computed an orbit for newly discovered Neptune.

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

BIRTHS

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.
*VFR
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

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1779  William Hedley, a British mine superintendent and engineer, was born July 13, 1779. In 1813, Hedley, working with Timothy Hackworth and Jonathan Forster, designed and had constructed a steam locomotive to haul coal on a five-mile track from the mines in Newcastle to the river Tyne. This locomotive, called Puffing Billy, was the first to use friction coupling between the drive wheels and the track; all previous engines employed some kind of cog wheel operating on a geared track. Puffing Billy worked quite reliably, although it didn't move too fast (5 mph top speed). The original locomotive had to be altered to run on 8 wheels in order to spread the weight, since the cast-iron rails were liable to fracture, but with the introduction of rolled iron rails, it was able to revert to its original 4-wheel design.

Puffing Billy was finally retired in 1862 and ended up in the Science Museum in London, where you may see it today .  It is the oldest surviving steam locomotive in the world.  There is a working replica of Puffing Billy at the Beamish Museum in County Durham in northern England; you may view a video of the replica locomotive coming at you down the track, or you may ride along with the engineer. Notice the wonderful topside grasshopper beams that connect the cylinders to the drive wheels.

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

DEATHS

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