## Saturday 13 July 2024

### 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.

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

I think this refers to his work De Methodis .  Newton had written the manuscript De Analysi per Aequationes Numero Terminorum Infinitas (1669; “On Analysis by Equations with an Infinite Number of Terms”) , which he was stung into writing after his logarithmic series was rediscovered and published by Nicolaus Mercator.

Newton never finished the De Methodis, and, despite the enthusiasm of the few whom he allowed to read De Analysi, he withheld it from publication until 1711. This, of course, only hurt him in his priority dispute with Gottfried Wilhelm Leibniz. *Britannica

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.

On October 5th 2001, there was a ceremony at Portsmouth dockyard for the unveiling of a plaque to William Bayly. The plaque is located in the lobby of the old Royal Naval Academy where Bayly was Master for 21 years.

The placing of the plaque in this heritage building required the approval of both the Admiralty and English Heritage.

The new plaque reads as follows: William Bayly 1737-1810, Astronomer and Circumnavigator, was born in Bishop's Cannings Wiltshire. He sailed twice around the world with Captain James Cook and was later Master at the Royal Naval Academy located in this building from 1785 to 1806.

Ms Floss Bayly with her niece in front of the memorial plaque

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.

1977 a power failure blacked out New York. Starting at about 9 pm, four lightning strikes on high-voltage transmission lines within the course of about half-an-hour knocked out electricity and plunged millions of residents of New York City into darkness. Unlike the calm during a similar blackout in 1965, the 1977 blackout erupted in chaos. The city was already in the midst of a financial crisis and high unemployment. Responding to the tension of the times, mobs set fires, smashed windows and hauled away food, clothing and appliances. It took 25 hours to restore power to the entire city. About 4,500 people were arrested during the riots, which resulted in damage estimated at \$61 million.

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 Last solar eclipse on a Friday the 13th. The previous  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

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.

1904 Alfred Leon Foster (July 13,1904- December 24, 1994) was an American mathematician.[1] He was a professor at the University of California, Berkeley, from 1934 until 1971. In 1932, he was an Invited Speaker at the ICM in Zürich.

In 1934, he accepted a regular position at Berkeley. At that time, Griffith Evans was Head of the Mathematics Department and was charged by President Sproul with building a first-class mathematics center, which he did. Alfred Foster and Charles Morrey (the first department chairman after Evans' retirement) were Evans' first two appointments. Except for subsequent sabbatical leaves, spent most notably in Freiburg and Tübingen, Foster served continuously at Berkeley until his retirement at the then-mandatory age of 67 in 1971.

Foster's Ph.D. dissertation and his first few papers were in mathematical logic. From this point, he soon focused on the related theory of Boolean algebras and Boolean rings and was thus led from logic to algebra. He extensively studied the role of duality in Boolean theory. Subsequently, he developed a theory of n-ality for certain rings, which played for n-valued logics the role of Boolean rings vis-a-vis Boolean algebras. The late Benjamin Bernstein of the Berkeley mathematics faculty was his collaborator in some of this research. This work culminated in his seminal paper "The Theory of Boolean-like Rings", appearing in 1946.

Foster was married to Else Wagner; their marriage produced four children and eight grandchildren

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

1321 Ibn al‐Bannāʾ al‐Marrākushī (29 December 1256 – 31 July 1321), was a Maghrebi Muslim polymath who was active as a mathematician, astronomer, Islamic scholar, Sufi and astrologer.

Ibn al-Banna' wrote over 100 works encompassing such varied topics as Astronomy, Astrology, the division of inheritances, Linguistics, Logic, Mathematics, Meteorology, Rhetoric, Tafsir, Usūl al-Dīn and Usul al-Fiqh. One of his works, called Talkhīṣ ʿamal al-ḥisāb (Arabic: تلخيص أعمال الحساب) (Summary of arithmetical operations), includes topics such as fractions and sums of squares and cubes. Another, called Tanbīh al-Albāb, covers topics related to:

calculations regarding the drop in irrigation canal levels,

arithmetical explanation of the Muslim laws of inheritance

determination of the hour of the Asr prayer,

explanation of frauds linked to instruments of measurement,

enumeration of delayed prayers which have to be said in a precise order, and

calculation of legal tax in the case of a delayed payment

He also wrote an introduction to Euclid's Elements.[10]

He also wrote Rafʿ al-Ḥijāb 'an Wujuh A'mal al-Hisab (Lifting the Veil from Faces of the Workings of Calculations) which covered topics such as computing square roots of a number and the theory of continued fractions. *Wik

 *SAU

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 night working 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 color 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

1934 Mary Emma Byrd (November 15, 1849 – July 13, 1934) was an American educator and is considered a pioneer astronomy teacher at college level. She was also an astronomer in her own right, determining cometary positions by photography. Mary E. Byrd was born November 15, 1849, in Le Roy, Michigan, to the reverend John Huntington Byrd and Elizabeth Adelaide Lowe as the second of six children. [A point of clarification since I have lived in Michigan for 50+ years, there are three small communities I Michigan named Le Roy or Leroy.  Another mathematician/astronomer , Forrest Ray Molten, was also born in LeRoy, but not the same one as Mary.  She was born in the LeRoy a few miles south of Battle Creek along Mi 66.]

In the late 19th century it was very difficult for a young woman to get higher education. Mary Byrd was a teacher, on and off, while trying to get an education. Byrd graduated from Leavenworth High School. She attended Oberlin College from 1871 to 1874, when John Millott Ellis was the college president. She left Oberlin before graduating and graduated from the University of Michigan with a B.A. in 1878. In 1879 Byrd worked as the principal of Wabash High School in Indiana until 1882, when she left to study astronomy at Harvard College Observatory under Dr. E.C. Pickering. She received the degree of Doctor of Philosophy from Carleton College in 1904.

n 1883 she became the First Assistant at the Godsell Observatory at Carleton College, and in 1887 she was appointed Director of the Smith College Observatory and professor of astronomy.

Byrd had a particular research interest in "fixing positions of comets by micrometer measures of their distance from known stars."

In 1906, Byrd, at the height of her career, resigned from her positions at Smith because the college accepted money from Andrew Carnegie and John D. Rockefeller, which she found reprehensible. Upon her resignation, she returned to Lawrence, Kansas. She continued writing, and contributed many articles to Popular Astronomy magazine.

During her life Byrd was a member of the Astronomical and Astrophysical Society of America (now the American Astronomical Society or simply AAS), the Astronomical Society of the Pacific, the British Astronomical Association, the Anti-Imperialist League of Northampton, the American Mathematical Society (Ref. New York Mathematical Society list of members June 1892, page 6. *Wik

 *SAU

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

1974 Patrick Maynard Stuart Blackett, Baron Blackett, OM, CH, FRS (18 November 1897 – 13 July 1974), was a British experimental physicist known for his work on cloud chambers, cosmic rays, and paleomagnetism, awarded the Nobel Prize in Physics in 1948.[6] In 1925 he became the first person to prove that radioactivity could cause the nuclear transmutation of one chemical element to another. He also made a major contribution in World War II advising on military strategy and developing operational research. His views saw an outlet in third world development and in influencing policy in the Labour government of the 1960s. *Wik

2016 Elliott Ward Cheney Jr. (June 28, 1929 – July 13, 2016) was an American mathematician and an emeritus professor at the University of Texas at Austin. Known to his friends and colleagues as Ward Cheney, he was one of the pioneers in the fields of approximation theory and numerical analysis. His 1966 book, An Introduction to Approximation Theory, remains in print and is "highly respected and well known", "a small book almost encyclopedic in character", and "is a classic with few competitors".Following the launch of Sputnik 1 by the Soviet Union in 1957, the United States intensified its focus on its aerospace program. Cheney became a research scientist at Convair Astronautics in San Diego, California, where his mathematical team worked on calculations for the Atlas rocket—which would take John Glenn into space.

Cheney also worked for Space Technology, near Los Angeles, and taught at UCLA, with visiting positions at Michigan State University and Iowa State University. In addition, Ward was a consultant and/or a guest worker at Boeing Scientific Research Laboratories, The Aerospace Corporation, and IBM Research Laboratory. In the summers of 1961–63, he was director of the NSF Summer Institute in Numerical Analysis at the University of California, Los Angeles.

In 1964, Ward joined the mathematics faculty of The University of Texas at Austin, where he taught for the next 41 years, until his retirement at age 76

Cheney served continuously on the editorial board of the Journal of Approximation Theory from its inception in 1968 until sometime after the start of 2015, and published 14 papers there. *Wik

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