## Saturday 24 June 2023

### On This Day in Math - June 24

"For example" is not a proof.

Jewish proverb

The 175th day of the year;
175 is the smallest number n greater than 1 such that n^6 $\pm 6$ are both prime. *Prime Curios & Derek Orr

175 - 25 = 150 and 150 /10 = 15 so 20^2-15^2 = 175

175 is the number of partitions of 35 into prime parts.

From Jim Wilder ‏@wilderlab : $175 = 1^1 + 7^2 + 5^3$ There is one more three digit year date which has this same relation.  Find it.

A normal Magic square of order 7 has a "magic constant" of 175 for the sum of each row, column or diagonal.  The one below comes from the "Geeks For Geeks" web site, but this particular Geek wishes they had rotated it one-quarter turn clockwise so that the smallest number is in the center of the bottom row.

And if you want a unique way to create any normal magic square (and with a little imagination, lots of other odd order magic squares) for a nice way to create the one above , but rotated  https://pballew.blogspot.com/2018/06/suprise-unique-approach-for-odd-order.html

EVENTS

1497 A claim for the name America being first used for the newly discovered continent, or at least part of it. Supposedly named by John Cabot in honor of his Bristol sponsor, Welshman Robert Ameryk, a prosperous merchant. According to accounts from the period, a record for that year in the Bristol calendar stated, "... on Saint Johns Day, the land of America was found by merchants of Bristowe, in a ship of Bristowe called the Mathew."
Thony Christie has pointed out that the above was written in a 1565 chronicle about the city of Bristol (Bristow). By that time the name America was common in Europe and does not suggest that, in fact, Cabot had used any such name. The lack of any other substantiation for this claim, and the strength of the naming for Vespucci, make this seem like local boasting.
The first use of the name on a map was on the Waldseemuller map of 1507. As was common at the time, the map was accompanied by a cosmographia explaining the basics of cartography and how to use the map. In his  Cosmographiae Introductio  Waldseemuller makes clear that it is named for Vespucci.  Its full title translates to, "Introduction to Cosmography With Certain Necessary Principles of Geometry and Astronomy To which are added The Four Voyages of Amerigo Vespucci A Representation of the Entire World, both in the Solid and Projected on the Plane, Including also lands which were Unknown to Ptolemy, and have been Recently Discovered".
While Cabot certainly discovered the mainland of the Americas before Vespucci, it seems that the weight of evidence for why we use the name America is weighted heavily toward the Amerigo Vespucci theory.  An excellent analysis of the evidence on that side, and the lack of evidence in support of Ameryk, is given by The Renaissance Mathematicus here.  *PB combined notes from many sources.

 Detail sowing America printed *Wik

1634 Gilles Personne de Roberval was proclaimed the winner of the triennial competition for the Ramus chair at the Coll`ege Royal in Paris. Thereafter, he kept his mathematical discoveries secret so that he could continue to win the competition and keep the chair. As a consequence he lost credit for many of his discoveries. *VFR
He worked on the quadrature of surfaces and the cubature of solids, which he accomplished, in some of the simpler cases, by an original method which he called the "Method of Indivisibles"; but he lost much of the credit of the discovery as he kept his method for his own use, while Bonaventura Cavalieri published a similar method which he independently invented.
Another of Roberval’s discoveries was a very general method of drawing tangents, by considering a curve as described by a moving point whose motion is the resultant of several simpler motions. He also discovered a method of deriving one curve from another, by means of which finite areas can be obtained equal to the areas between certain curves and their asymptotes. To these curves, which were also applied to effect some quadratures, Evangelista Torricelli gave the name "Robervallian lines."
Portrait of Gilles Personne de Roberval (1602-1675) at the inauguration of the French Academy of Sciences, 1666, where he was a founding member.

 *Wik

1644 In a letter to Torricelli, Fr. Marin Mersenne gives a method to find a number with any number of factors. He explained; since 60 = 2*2*3*5 subtract one from each factor (1,1,2, 4) and make them the exponents of any primes.. he used 24*32*5*7= 5040.. Of course Plato knew much earlier that 5040 had sixty factors.In Laws, Plato suggests that 5040 is the optimal number of citizens in a state because a) It is the product of 12, 20, and 21;  b) the 12th part of it can still be divided by 12; and c) it has 59 proper divisors, including all numbers for 1 to 12 except 11, and 5038--which is very close to 5040--is divisible by 11.

1687 In a letter to Huygens, Fatio de Dullier used an integrating factor to solve the differential equation 3x dy − 2y dx = 0. No earlier instance of an integrating factor is known. The fundamental conception of integrating factors was due to Euler (1734) and further developed by Clairaut (1739). *VFR

In 1778, David Rittenhouse observed a total solar eclipse in Philadelphia. In a letter to him, dated 17 Jul 1778, Thomas Jefferson wrote that "We were much disappointed in Virginia generally on the day of the great eclipse, which proved to be cloudy." Rittenhouse (1732-1796) was not only an American astronomer, but also a mathematician and public official. He is reputed to have built the first American-made telescope and was the first director of the U.S. Mint (1792-1795).*TIS  Jefferson was an excellent applied mathematician and had contacted Rittenhouse on another occasion.  Travelling through France ten years later, " in 1788, he noticed peasants near Nancy plowing, and fell to wondering about the design of the moldboard, that is, the surface which turns the earth: he spent the next ten years working on this, on and off, wondering how to achieve the most efficient design, both offering least frictional resistance, and which also would be easy for farmers out in the frontiers to construct, far from technical help. He consulted the Pennsylvania mathematician Robert Patterson (born in Ireland in 1743), and consulted also another Philadelphia luminary, the self-taught astronomer and mathematical instrument-maker David Rittenhouse (1732-1796)."   Jefferson also communicated with Thomas Paine about bridge design, suggesting the use of catenary arches.  Jefferson is believed to be the first person ever to use the term "catenary" in English.

re-creation of Jefferson's improved design for the moldboard of an agricultural plow, the large, wooden part at the bottom.

1847 The first observation with the Great Refractor at Harvard was of the Moon on the afternoon of June 24, 1847. A number of significant achievements quickly followed. The eighth satellite of Saturn was discovered in 1848 by W.C. Bond and his son, George P. Bond, who was to succeed his father as Director in 1859. In 1850, Saturn's crape, or inner, ring was first observed, again by the Bonds. That same year, the first daguerreotype ever made of a star, the bright Vega, was taken by J.A. Whipple working under W.C. Bond, following several years of experiments using smaller telescopes. One of the earliest photographs of a double star, Mizar and Alcor in the handle of the Big Dipper, was achieved in 1857, using the wet-plate collodion process. *Observatory web page...  The 15 inch Great Refractor was "once the biggest and best telescope in the United States, perhaps the world."  *Frederik Pohl, Chasing Science, pg 42.

In 1898, a U.S. commemorative stamp was first used that carried the design of a major engineering construction project, the Mississippi River Bridge, a triple-arch steel bridge between East St. Louis, Illinois and St. Louis,

Missouri. Each span was roughly 500 feet and rested on piers resting on bedrock some 100 feet beneath the river bottom. Opened on 4 Jul 1874, the bridge was named after its designer, the self-trained engineer, James Eads. The upper level road also carried streetcars, which are seen in the stamp design along with steam ships on the river below. The trains that ran on its lower level are hidden from view at this angle. (Although still in use, the bridge no longer carries rail traffic.) The design was reissued in 1998.*TIS

In 1975, a moon tremor, caused by a strike of Taurid meteors, was detected by the seismometer network left on the Moon's surface by American astronauts. The major series of lunar impacts between 22 - 26 Jun 1975 represented 5% of the total number of impacts detected during the eight years of the network's operation, and included numerous 1-ton meteorites. The impacts were detected only when the nearside of the Moon (where the astronauts landed) was facing the Beta Taurid radiant. At the same time, there was a lot of activity detected in Earth's ionosphere, which has been linked with meteor activity. The Taurid meteor storm crosses the Earth orbit twice a year, during the period 24 Jun to 6 Jul and the period 3 Nov to 15 Nov.*TIS

1978 Charon first suggested for the name of Pluto's moon. Charon was originally known by the temporary designation S/1978 P 1, according to the then recently instituted convention. On June 24, 1978, U.S. Naval Observatory astronomer James Christy who had discovered the moon, first suggested the name Charon as a scientific-sounding version of his wife Charlene's nickname, "Char."
Although colleagues at the Naval Observatory proposed Persephone, Christy stuck with Charon after discovering it coincidentally refers to a Greek mythological figure: Charon is the ferryman of the dead, closely associated in myth with the god Hades, whom the Romans identified with their god Pluto. Official adoption of the name by the IAU waited until late 1985 and was announced on January 3, 1986.
There is minor debate over the preferred pronunciation of the name. The practice of following the classical pronunciation established for the mythological ferryman Charon is used by major English-language dictionaries such as the Merriam-Webster and Oxford English Dictionary.[19][20] These indicate only one pronunciation of "Charon" when referring specifically to Pluto's moon: with an initial "k" sound. Speakers of languages other than English, and many English-speaking astronomers as well, follow this pronunciation.
However, Christy himself pronounced the ch in the moon's name as sh, after his wife Charlene. *Wik

2012 Lonesome George, the last Pinta Island tortoise dies. Also known as the Pinta giant tortoise, Abingdon Island tortoise, or Abingdon Island giant tortoise, was a subspecies of Galápagos tortoise native to Ecuador's Pinta Island.
The subspecies was described by Albert Günther in 1877 after specimens arrived in London. By the end of the 19th century, most of the Pinta Island tortoises had been wiped out due to hunting. By the mid-20th century, it was assumed that the species was extinct until a single male was discovered on the island in 1971. Efforts were made to mate the male, named Lonesome George, with other subspecies, but no viable eggs were produced. Lonesome George died on June 24, 2012. The subspecies is believed to have become extinct; however, there has been at least one first-generation hybrid individual found outside Pinta Island *Wik

BIRTHS

1880 Oswald Veblen(June 24, 1880 – August 10, 1960) American mathematician, born in Decorah, Iowa, who made important contributions to differential geometry and early topology. Many of his contributions found application to atomic physics and relativity. Along with his interest in the foundations of geometry he developed an interest in algebraic topology, or analysis situs as it was then called and by 1912 was writing papers on this subject. Gradually he became more interested in differential geometry. From l922 onward most of his papers were in this area and in its connections with relativity. His work on axioms for differentiable manifolds and differential geometry contributed directly to the field.*TIS

1909 William Penney (24 Jun 1909, 3 Mar 1991 at age 81)(Baron Penney of East Hendred) British nuclear physicist who led Britain's development of the atomic bomb. Penney was to Britain as Robert Oppenheimer was to the U.S. He was a prominent part of the British Mission at Los Alamos during WW II, where his principal assignment was studying the damage effects from the blast wave of the atomic bomb, but he became involved in implosion studies as well. Penney's combination of expertise, analytical skill, effective communication, and the ability to translate them into practical application soon made him one of the five members of the Los Alamos “brain trust” that made key decisions. He was the only Briton to be part of the ten man Target Committee that drew up the list of targets for the atomic bombing of Japan. *TIS

1912 Wilhelm Cauer (June 24, 1900 – April 22, 1945) was a German mathematician and scientist. He is most noted for his work on the analysis and synthesis of electrical filters and his work marked the beginning of the field of network synthesis. Prior to his work, electronic filter design used techniques which accurately predicted filter behaviour only under unrealistic conditions. This required a certain amount of experience on the part of the designer to choose suitable sections to include in the design. Cauer placed the field on a firm mathematical footing, providing tools that could produce exact solutions to a given specification for the design of an electronic filter. *Wik
By the end of World War II, he was, like millions of less-distinguished countrymen and -women, merely a person in the way of a terrible conflagration.
Cauer succeeded in evacuating his family west, where the American and not the Soviet army would overtake it — but for reasons unclear he then returned himself to Berlin. His son Emil remembered the sad result.

The last time I saw my father was two days before the American Forces occupied the small town of Witzenhausen in Hesse, about 30 km from Gottingen. We children were staying there with relatives in order to protect us from air raids. Because rail travel was already impossible, my father was using a bicycle. Military Police was patrolling the streets stopping people and checking their documents. By that time, all men over 16 were forbidden to leave towns without a permit, and on the mere suspicion of being deserters, many were hung summarily in the market places. Given this atmosphere of terror and the terrible outrages which Germans had inflicted on the peoples of the Soviet Union, I passionately tried to persuade my father to hide rather than return to Berlin, since it was understandable that the Red Army would take its revenge. But he decided to go back, perhaps out of solidarity with his colleagues still in Berlin, or just due to his sense of duty, or out of sheer determination to carry out what he had decided to do.
Seven months after the ending of that war, my mother succeeded in reaching Berlin and found the ruins of our house in a southern suburb of the city. None of the neighbors knew about my father’s fate. But someone gave identification papers to my mother which were found in a garden of the neighborhood. The track led to a mass grave with eight bodies where my mother could identify her husband and another man who used to live in our house. By April 22, 1945, the Red Army had crossed the city limits of Berlin at several points. Although he was a civilian and not a member of the Nazi Party, my father and other civilians were executed by soldiers of the Red Army. The people who witnessed the executions were taken into Soviet captivity, and it was not possible to obtain details of the exact circumstances of my father’s death.

*ExecutedToday.com

1915 Sir Fred Hoyle (24 June 1915 – 20 August 2001) English mathematician and astronomer, best known as the foremost proponent and defender of the steady-state theory of the universe. This theory holds both that the universe is expanding and that matter is being continuously created to keep the mean density of matter in space constant. He became Britain's best-known astronomer in 1950 with his broadcast lectures on The Nature of the Universe, and he recalled coining the term "Big Bang" in the last of those talks. Although over time, belief in a "steady state" universe as Hoyle had proposed was shared by fewer and fewer scientists because of new discoveries, Hoyle never accepted the now most popular "Big Bang" theory for the origin of the universe.

1927 Martin Lewis Perl (June 24, 1927 – September 30, 2014) was an American physicist who won the Nobel Prize in Physics in 1995 for his discovery of the tau lepton.
He received his Ph.D. from Columbia University in 1955, where his thesis advisor was I.I. Rabi. Perl's thesis described measurements of the nuclear quadrupole moment of sodium, using the atomic beam resonance method that Rabi had won the Nobel Prize in Phyics for in 1944.
Following his Ph.D., Perl spent 8 years at the University of Michigan, where he worked on the physics of strong interactions, using bubble chambers and spark chambers to study the scattering of pions and later neutrons on protons.[1] While at Michigan, Perl and Lawrence W. Jones served as co-advisors to Samuel C. C. Ting, who earned the Nobel Prize in Physics in 1976.
Seeking a simpler interaction mechanism to study, Perl started to consider electron and muon interactions. He had the opportunity to start planning experimental work in this area when he moved in 1963 to the Stanford Linear Accelerator Center (SLAC), then being built in California. He was particularly interested in understanding the muon: why it should interact almost exactly like the electron but be 206.8 times heavier, and why it should decay through the route that it does. Perl chose to look for answers to these questions in experiments on high-energy charged leptons. In addition, he considered the possibility of finding a third generation of lepton through electron-positron collisions. He died after a heart attack at Stanford University Hospital on September 30, 2014 at the age of 87. *Wik

DEATHS

1832 Timofei Fedorovic Osipovsky (February 2, 1766–June 24, 1832) was a Russian mathematician, physicist, astronomer, and philosopher. Timofei Osipovsky graduated from the St Petersburg Teachers Seminary.
He was to became a teacher at Kharkov University. Kharkov University was founded in 1805. The city of Kharkov, thanks to its educational establishments, became one of the most important cultural and educational centers of Ukraine. Osipovsky was appointed to Kharkov University in 1805, the year of the foundation of the University. In 1813 he became rector of the University. However in 1820 Osipovsky was suspended from his post on religious grounds.
His most famous work was the three volume book A Course of Mathematics (1801–1823). This soon became a standard university text and was used in universities for many years. *Wik

1880 Jules Lissajous (March 4, 1822, Versailles – June 24, 1880, Plombières-les-Bains) was a French mathematician best known for the Lissajous figures produced from a pair of sine waves. *SAU  The curves are also called Bowditch curves for the early American mathematician, Nathanial Bowditch,  who worked with them earlier.  In general, a parametric curve with equations x= A sin(k t ); y= B sin(m t), the curves can describe things as simple as a circle or ellipse to more complex open and closed curves.  If the ratio of k/m is rational, the curve will eventually close.

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