## Wednesday 26 June 2024

### On This Day in Math - June 26

When you measure what you are speaking about and express it in numbers,
but when you cannot express it in numbers
.

William Thomson, Lord Kelvin

The 177th day of the year; there are 177 graphs with seven edges.  *What's So Special About This Number.  (only 79 of these are connected graphs)

• 177 is the smallest magic constant for a 3 x 3 prime magic square

$\begin{bmatrix} 17 & 89 & 71 \\ 113 & 59 & 5 \\ 47 & 29 & 101 \end{bmatrix}.$

An old idea that was new to me, from John Golden@mathhombre and here.  Use two Simple Squares to make a  third, and I just did one with magic sum of 177.
2   3   1
1   2   3
3   1   2

And
53  61  57
61  57  53
57  53  61

Now add the numbers in same location

55  64  58
62  59  56
60  54  63

77 is also a Leyland number,  expressible as a^b + b^a. both greater than one . using 2 and 7 in this case.  . The numbers are named for British mathematician Paul Layland from Oxford University.  There are only nine year days that are Leyland numbers.  Only one of those nine is prime.

EVENTS

1424 Of the 20 total eclipses to visit the Orkneys and Shetland Islands in the period 1 - 3000AD it was the 13th longest in the whole of the UK at 3 minutes 56 seconds it was surpassed in Orkney by those of 364, 885, 1185, 1433, 2681. The eclipse track traveled across Denmark, Germany, Poland, Ukraine, Moldavia, and the Black Sea. (ref. SW-UK eclipses) *NSEC

1614   The first lottery of significance in the new world was held on this date by the Virginia Company.  The first Great Prize was 4,500 Crowns. *JN Kane, Famous First Facts (I have seen the date of this lottery also given as 1612)

Lotteries held a prominent place in the early history of America, including an important role in financing the establishment of the first English colonies. The first such lottery, in 1612, raised 29,000 pounds for the Virginia Company. Lotteries were frequently used in colonial-era America to finance public works projects such as paving streets, constructing wharves, even building churches. In the 18th century, lotteries were used to finance construction of buildings at Harvard and Yale. George Washington sponsored a lottery in 1768 to build a road across the Blue Ridge Mountains, but it was unsuccessful.  (*NATIONAL GAMBLING IMPACT STUDY COMMISSION)

The article mentioned above included this statement, "A more far-reaching development was the advent of on-line computerized vending. The first major innovation from this was a daily numbers game, modeled on the illegal numbers games historically present in all major American cities. The advantages to the player of this new, legal game included the ability to choose his own "lucky" number, thereby giving him a greater sense of participation (even if his actual odds of winning remained unaffected by his choices) "  I wonder how many statisticians would disagree with the comment in parentheses?

1765 Benjamin Franklin writes to Peter Collinson about numerous topics including Accounts of Spouts and Whirlwinds, and a comment on his earlier kite experiments; but includes, "I am endeavouring to answer Dr. Parsons’s Request relating to the Indian Names of the Cardinal Numbers." *franklinpapers

1794,The Battle of Fleuruswas the most significant battle of the Flanders Campaign in the Low Countries during the French Revolutionary Wars. It was the first battle in history that incorporated aerial reconnaissance and observation of an enemy force. This was provided by a French helium balloon, l'Entreprenant, operated by a small crew.  Almost all comments about the balloons effectiveness by both sides dismissed its influence as non-existent.

Jourdan at Fleurus with the balloon l'Entreprenant in the background. Painted by Mauzaisse in 1837; on display in the Galerie des Batailles, Versailles.

1819, The first US patent for a velocipede, a predecessor of the bicycle, was issued to William K. Clarkson Jr. of New York. Little information remains available, however, because a fire at the Patent Office in 1836 destroyed the patent record, and it was not restored.
The first known bicycle was shown by the Comte de Sivrac, who in 1791 was seen riding a two-wheel "wooden horse" in the gardens of the Palais Royal in Paris. Called a celerifere, the machine had two rigidly mounted wheels, so that it was incapable of being steered. To change direction, it was necessary to lift, drag, or jump the front wheel to one side.
In 1817, Charles, Baron von Drais, of Sauerbrun, devised a front wheel capable of being steered. He also gave it a padded saddle, and an armrest in front of his body, which assisted him in exerting force against the ground. Granted a patent in 1818, he took his Draisienne to Paris, where it was again patented and acquired the name vélocipède, a term that was to continue in use until about 1869 when the word “bicycle” came into use.
 1818 Draisienne

1881 The great comet of 1881. Observed on the night of June 25-26 at 1h. 30m. A.M. from a print by Étienne Léopold Trouvelot, a French artist, astronomer and amateur entomologist. He is noted for the unfortunate introduction of the Gypsy Moth into North America. *The New York Public Library Digital Collections

1896 An early x-ray photograph of Sir William Crookes’s hand, taken with a cathode tube that bears his name, the Crookes Tube. The man taking these pioneering radiographs was the engineer Alan Archibald Campbell Swinton, later a Fellow of the Royal Society. He took the first x-ray images in Britain in January 1896 and by a year later the medical professions were bringing him surgical cases for analysis. *Keith Moore, Royal Society Blog

In 1974, at 8:01 a.m., a package of Wrigley's chewing gum with a bar code printed on it passed over a scanner at the Marsh Supermarket, Troy, Ohio, and became the first product ever logged under the new Universal Product Code (UPC) computerized recognition system. Invented by IBM, and approved for use in 1973, the UPC is a 12-number bar code representing the manufacturer's identity and an assigned product number. Within nanoseconds, this information is read with a laser beam moving at around 10,000 inches per second and transfers it to the store's database computer for price lookup and inventory management*TIS

In 1984, the National Maritime Museum, of which the Royal Observatory, Greenwich is a part, encouraged people up and down the Line to organise events in order to mark the so-called ‘centenary’ of the Prime Meridian. Although the International Meridian conference took place in October 1884, the Museum designated Tuesday 26 June as ‘Meridian Day’, on the grounds that any outdoor events would be less likely to be affected by the weather.
Commemorative six-inch diameter plastic plaques were offered to any individual who could show that the Meridian passed through the curtilage of their property. Potential claimants were required to write to their regional office of the Ordnance Survey to verify their claim and send this as proof of authenticity to the English Tourist Board who were distributing them. No records of how many were issued can be traced. The locations of just four are known, along with the existence of a fifth.
The National Maritime Museum also arranged for the Enfield Foundry to cast a bronze plaque as a more enduring alternative. At the time, it was stated that they would only be produced if 20 or more orders were received. How many were made is unknown, the Foundry’s records having been destroyed. Only three have been located to date. (If you are aware of one of these locations, please informe me, thanks PB)

In 2000, the completion of a working draft reference DNA sequence of the human genome was announced at the White House by President Bill Clinton, and representatives from the Human Genome Project (HGP) and the private company Celera Genomics. Clinton stated that even greater discoveries would follow from the working draft. As a draft, it contained some gaps and errors, but represented about 95% of all genes. HGP expected to use it as a scaffold for generating the high-quality reference genome sequence within three years. This provides knowledge to link genes with particular diseases, of the influence of genetics and to help discover new treatments.
*TIS

BIRTHS

1730 Charles Messier
(26 June 1730 – 12 April 1817) French astronomer who discovered 15 comets. He was the first to compile a systematic catalog of "M objects." The Messier Catalogue (1784), containing 103 star clusters, nebulae, and galaxies. (In Messier's time a nebula was a term used to denote any blurry celestial light source.) He established alphanumeric names for the objects (M1, M2, etc.), which notation continues to be used in astronomy today.

The Orion Nebula as drawn by Messier, and which he gave the designation M 42 in his catalog

1824 Lord Kelvin (26 June 1824 – 17 December 1907) Born as William Thomson, he became an influential physicist, mathematician and engineer who has been described as a Newton of his era. At Glasgow University, Scotland, he was a professor for over half a century. The name he made for himself was more than just a temperature scale. His activities ranged from being the brains behind the laying of a transatlantic telephone cable, to attempting to calculate the age of the earth from its rate of cooling. In 1892, when raised to the peerage as Baron Kelvin of Largs, he had chosen the name from the Kelvin River, near Glasgow.*TIS

1878 Leopold Löwenheim (26 June 1878 in Krefeld, Germany (also the birthplace of Max Zorn) – 5 May 1957 in Berlin) was a German mathematician who worked on mathematical logic and is best-known for the Löwenheim-Skolem paradox.*SAU
The Nazi regime forced him to retire because under the Nuremberg Laws he was considered only three quarters Aryan. In 1943 much of his work was destroyed during a bombing raid on Berlin. Nevertheless, he survived the Second World War, after which he resumed teaching mathematics.

Löwenheim (1915) gave the first proof of what is now known as the Löwenheim–Skolem theorem, often considered the starting point for model theory.

1915 Paul Joseph Kelly (June 26, 1915 – July 15, 1995) was an American mathematician who worked in geometry and graph theory. Kelly was born in Riverside, California. He earned bachelor's and master's degrees from the University of California, Los Angeles before moving to the University of Wisconsin–Madison for doctoral studies; he earned his Ph.D. in 1942 with a dissertation concerning geometric transformations under the supervision of Stanislaw Ulam.
Kelly is known for posing the reconstruction conjecture with his advisor Ulam, which states that every graph is uniquely determined by the ensemble of subgraphs formed by deleting one vertex in each possible way. He also proved a special case of this conjecture, for trees.

He is the coauthor of three textbooks: Projective geometry and projective metrics (1953, with Herbert Busemann), Geometry and convexity: A study in mathematical methods (1979, with Max L. Weiss), and The non-Euclidean, hyperbolic plane: Its structure and consistency (1981, with Gordon Matthews).

1918 Yudell Leo Luke (26 June 1918 – 6 May 1983) was an American mathematician who made significant contributions to the Midwest Research Institute, was awarded the N. T. Veatch award for Distinguished Research and Creative Activity in 1975, and appointed as Curator's Professor at the University of Missouri in 1978, a post he held until his death. Luke published eight books and nearly 100 papers in a wide variety of mathematical areas, ranging from aeronautics to approximation theory. By his own estimation, Luke reviewed over 1800 papers and books throughout his career.*SAU

1936 Gonzalo Pérez Iribarren (b. June 26, 1936, Carmelo – August 27, 1998, Montevideo ) was a Uruguayan mathematician and statistician .
In addition to cultivating literature, painting, and being a great fan of photography, Gonzalo Pérez had a strong vocation for the application of mathematics in the natural sciences. Thus, among his contributions is his pioneering activity in the study of the flows of the great Uruguayan rivers (the Uruguay River and the Negro River ), which gave rise to the discovery of the incidence of the El Niño phenomenon on the climate. of Uruguay.*Wik
He was forced to spend ten years in exile during the right-wing dictatorship beginning in 1973. He returned to Uruguay in 1983 and was the main force in rebuilding the Institute of Mathematics and Statistics and setting up the Basic Sciences Development Programme.*SAU

1937 Robert Coleman Richardson (June 26, 1937 – February 19, 2013) was an American physicist who (with Douglas Osheroff and David Lee) was awarded the 1996 Nobel Prize for Physics for their discovery of superfluidity in the isotope helium-3. As helium is reduced in temperature toward almost absolute zero, a strange phase transition occurs, and the helium takes on the form of a superfluid. The atoms had until that point had moved with random speeds and directions. But as a superfluid, the atoms then move in a co-ordinated manner!

1969 Andrei Yuryevich Okounkov (June 26, 1969 - ) is a Russian mathematician who works on representation theory and its applications to algebraic geometry, mathematical physics, probability theory and special functions. He is currently a professor at Columbia University. In 2006, he received the Fields Medal "for his contributions to bridging probability, representation theory and algebraic geometry." *Wik

DEATHS

1274 Nasir al-Tusi (born 18 February 1201 in Ṭūs, Khorasan – died on 26 June 1274 in al-Kāżimiyyah district of metropolitan Baghdad), was an Islamic astronomer and mathematician who joined the Mongols who conquered Baghdad. He made important contributions to astronomy and wrote many commentaries on Greek texts.*SAU Among the many wonderful antiquities at the Bodleian Library is a 16th century printing of the 13th century Arabic translation by Nasir al-Din al-Tusi of Euclid's Elements. It was part of the collection donated by Thomas Allen.

Manuscript diagram of a Tusi couple, in ink with annotations, inserted at the page with a printed Tusi couple, in the Library’s copy of Nicholas Copernicus, De revolutionibus, 1543 (Linda Hall Library, photo by Karl Galle)

1796 David Rittenhouse (April 8, 1732 – June 26, 1796) American astronomer, instrument maker and inventor who was an early observer of the atmosphere of Venus. For observations for the transit of Venus on 3 Jun 1769, he constructed a high precision pendulum clock, an astronomical quadrant, an equal altitude instrument, and an astronomical transit. He was the first one in America to put spider web as cross-hairs in the focus of his telescope. He is generally credited with inventing the vernier compass and possibly the automatic needle lifter. He was professor of astronomy at the University of Pennsylvania. Benjamin Franklin consulted him on various occasions. For Thomas Jefferson he standardized the foot by pendulum measurements in a project to establish a decimal system of weights and measures.*TIS
 Diagram from David Rittenhouse'sobservations of the 1769 transit of Venus *WIK

1810 Joseph Montgolfier (26 August 1740 – 26 June 1810) French ballooning pioneer, with his younger brother, Étienne. An initial experiment with a balloon of taffeta filled with hot smoke was given a public demonstration on 5 Jun 1783. This was followed by a flight carrying three animals as passengers on 19 Sep1783, shown in Paris and witnessed by King Louis XVI. On 21 Nov 1783, their balloon carried the first two men on an untethered flight. In the span of one year after releasing their test balloon, the Montgolfier brothers had enabled the first manned balloon flight in the world. *TIS
 irst public demonstration inAnnonay, 5 June 1783 *Wik

1914 Lyman Spitzer Jr. (June 26, 1914 – March 31, 1997) was American astrophysicist who advanced knowledge of physical processes in interstellar space and pioneered efforts to harness nuclear fusion as a clean energy source. He made major contributions in stellar dynamics and plasma physics. He founded study of the interstellar medium (gas and dust between stars from which new stars are formed). Spitzer studied in detail interstellar dust grains and magnetic fields as well as the motions of star clusters and their evolution. He studied regions of star formation and was among the first to suggest that bright stars in spiral galaxies formed recently. Spitzer was the first person to propose the idea of placing a large telescope in space and was the driving force behind the development of the Hubble Space Telescope. *Tis

1951 George Udny Yule (18 February 1871 – 26 June 1951) graduated in Engineering from University College London and then studied in Bonn. He worked with Karl Pearson on the statistics of regression and correlation. He took a post with an examinations board before being appointed to a Cambridge fellowship. He is best known for his book: Introduction to the Theory of Statistics.*SAU

1967 Henry Thomas Herbert Piaggio (2 June 1884–26 June 1967) graduated from Cambridge and then worked at the University of Nottingham. He is best known for his text-book on Differential Equations.("An Elementary Treatise on Differential Equations and their Applications".) *SAU

1990 Joseph Carl Robnett Licklider (March 11, 1915 – June 26, 1990), known simply as J.C.R. or "Lick" was an American computer scientist, considered one of the most important figures in computer science and general computing history. He is particularly remembered for being one of the first to forsee modern-style interactive computing, and its application to all manner of activities; and also as an Internet pioneer, with an early vision of a world-wide computer network long before it was built. He did much to actually initiate all that through his funding of research which led to a great deal of it, including today's canonical graphical user interface, and the ARPANET, the direct predecessor to the Internet.*Wik

1997 Robert Wertheimer Frucht (later known as Roberto Frucht) (9 August 1906 – 26 June 1997)] was a German-Chilean mathematician; his research specialty was graph theory and the symmetries of graphs.
Frucht is known for Frucht's theorem, the result that every group can be realized as the group of symmetries of an undirected graph, and for the Frucht graph, one of the five smallest cubic graphs without any nontrivial symmetries. LCF notation, a method for describing cubic Hamiltonian graphs, was named for the initials of Joshua Lederberg, H. S. M. Coxeter, and Frucht, its key developers.

With Coxeter and David L. Powers, Frucht was coauthor of a book on zero-symmetric graphs, the cubic graphs that have exactly one symmetry taking each vertex to each other vertex.

Frucht was elected to the Chilean Academy of Sciences as a corresponding member in 1979. A special issue of the Journal of Graph Theory was published in Frucht's honor in 1982, and another special issue of the journal Scientia, Series A (the journal of the mathematics department of Federico Santa María Technical University) was published in honor of his 80th birthday in 1986.  *Wik
The Frucht graph.

2011 Jack Warga ( Warsaw , September 20 , 1922 - Boynton Beach, June 26, 2011 ) was an American mathematician , born in Poland .
Warga was born in Warsaw , the son of a Jewish furrier. After suffering an anti-Semitic racist attack, his father decided enough was enough and in 1938 sent him to study in Brussels where he had family. When he finished secondary studies, he entered the École Polytechnique de Bruxelles , where he could not even finish the first year because in 1940 the Nazis invaded Belgium . The young Warga escaped from Belgium via Paris and Vichy , but since France did not seem like a very safe place for a Jew either, he continued his escape through Spain and Cuba , until he arrived in New York in 1943. The older part of his family died in the holocaust .

Since arriving in the United States he served in the United States Army as an officer, until the war ended in 1945, when he continued his studies at New York University . In 1950 he obtained his doctorate with a dissertation on number theory supervised by Harold N. Shapiro. In the following years he worked as a mathematician in different naval research organizations, until in 1957 he became the chief mathematician of the research and development division of the aerospace company AVCO in Wilmington (Massachusetts) , a position he maintain until 1966 when he was appointed professor at Northeastern University in Boston .  Warga retired in 1993.

Warga's research work was in the field of applied mathematics . More specifically, his contributions were pioneering in control and optimization theory, in which he introduced the concept of relaxed control .  His book Optimal Control of Differential and Functional Equations (1972) was for many years the standard text on the subject

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