**As long as algebra and geometry have been separated, their progress have been slow and their uses limited; but when these two sciences have been united, they have lent each mutual forces, and have marched together towards perfection.**

~Joseph Louis Lagrange

The 240th day of the year; 240 has more divisors (20 of them) than any previous number. What would be the next number that has more?

240 is the product of the first 6 Fibonacci numbers 240 = 1*1*2*3*5*8 *Derek Orr

These are often called Fibonacci factorials or fibonorials. 240 would be \(6!_F\), also called the Fibonacci factorial

The Kissing Number, the number of spheres that can be placed around a central sphere so that they all are touching it, for the eighth dimension is 240. Beyond the fourth dimension, only the eighth and twenty-fourth are known exactly. The 24th dimension is the highest dimension for which the exact "kissing number", is known. For the 24th dimension, the "kissing number is 196,560.

240 is the smallest number expressible as the sum of consecutive primes in three ways, *Prime Curios (113+127, 53+59+61+67, 17 + 19 + 23 + 29 + 31 + 37 + 41 + 43.)

240 is the product of the first 6 Fibonacci numbers, 240 = 1*1*2*3*5*8 *Derek Orr

These are often called Fibonacci factorials or fibonorials. 240 would be \(6!_F\), also called the Fibonacci factorial

**412 BC** The ancient city of Syracuse suffered heavily under siege by the Athenians during the Peloponnesian War. A turn of events occurred during the Second Battle of Syracuse: on Aug. 28, 41.C. a lunar eclipse occurred, causing the superstitious Athenians to delay departure. The Syracuseans took advantage of Athenian indecision and decisively defeated the unprotected Athenian expedition as it sat exposed in the harbor. *listosaur.com

Monument to Archimedes in Piazza Archimedes

**1314 **On this day in 1314, the University of St Andrews was founded. It is the third oldest university in the English-speaking world and was established by a papal bull from Pope Benedict XIII.

**1666** John Evelyn Records in his diary: "to the Royal Society, where one Mercator, an excellent mathematician, produced his rare clock and new motion to perform the equations, and Mr. Rooke, his new pendulum." The Mercator is Nicholas Mercator who taught mathematics in London (1658–1682). He designed a marine chronometer for Charles II, and designed and constructed the fountains at the Palace of Versailles. Mathematically, he is most well known for his treatise Logarithmo-technica on logarithms, published in 1668 in which he described the Mercator series, also independently discovered by Gregory Saint-Vincent \( \ln(1 + x) = x - \frac{1}{2}x^2 + \frac{1}{3}x^3 - \frac{1}{4}x^4 + \cdots. \)

I suspect the "Mr Rooke" should have been Hooke who is mentioned at the meeting in Pepys' Diary. *Wik, *John Evelyn Diary

*Wik |

**1730** Murder by Unicorn Horn on a Holborn skittle-ground : On the 28th of August 1730, Joseph Hastings died after receiving “several mortal Bruises with an Unicorn’s Horn”, wielded by John Williams of St. Andrew’s Holborn eleven days earlier. The assault occurred on a Holborn skittle-ground, witnessed by several local men.

Williams was angered by Hastings response to his offer to purchase the (probably Narwhal) horn and an argument ensued which led to the beating. More detail at Sloan Letters

Image: Five foot long tusk from Nicholson Whaling Collection, Providence Public Library

Footnote: Skittles is a bowling game, usually with nine pens, or quills. The winner was the one who got them all down with the smallest number of rolls. The rules for what seems a simple game could be very complex.

**1742** a letter from Euler to Goldbach in 1742, Euler proves no number of the form 4n^{4} +1 can be a prime. In the letter he showed that 1 + 4x^{4} =(2x^{2} + 2x + 1)(2x^{2} − 2x + 1) *Euler Correspondence

I think he must have been making an obvious exception of 5. Almost all of them end in five except numbers where n=5, 15, etc. 1+4(5^4) = 2501 = [2 (5^2) + 2(5) + 1 ][2 (5^2) - 2(5) + 1}= 61 * 41

**In 1789**, Enceladus, the sixth-largest moon of Saturn, was discovered by Fredrick William Herschel on August 28, 1789, during the first use of his new 1.2 m (47 in) telescope, then the largest in the world. Little was known about Enceladus until the two Voyager spacecraft passed near it in the early 1980s.

Enceladus is named after the giant Enceladus of Greek mythology. The name Enceladus—like the names of each of the first seven satellites of Saturn to be discovered—was suggested by William Herschel's son John Herschel in his 1847 publication Results of Astronomical Observations made at the Cape of Good Hope. He chose these names because Saturn, known in Greek mythology as Cronus, was the leader of the Titans. *Wik

It is about 500 kilometers (310 miles) in diameter, about a tenth of that of Saturn's largest moon, Titan.

**1830 ** Peter Cooper, an American inventor and industrialist, died Apr. 4, 1883, at age 92. Cooper first came on the engineering scene in 1830, when he assembled from spare parts a locomotive that he called Tom Thumb, and on behalf of which he challenged a horse-drawn rail car to a race, which took place on Aug. 28, 1830 (first image). Tom Thumb lost the race (the caption to our first image notwithstanding), due to mechanical problems, , but he won the marathon, since the locomotive’s superiority was evident, and the Baltimore and Ohio Railroad decided to put their money on steam locomotives. Their rapid expansion enabled them to buy iron rails from Cooper's iron works in Maryland, which was the whole idea behind Tom Thumb in the first place. In the early 20th century, the Bureau of Public Roads (now the Federal Highway Administration) commissioned a painting of the race by their staff artist Carl Rakeman (as well as a hundred other events in highway and rail history). You may see them all here. *Linda Hall Org

The Iron Horse Wins, by Carl Wakeman, date unknown, 1930s?,*Federal Highway Administration collection (fhwa.dot.gov) |

**1837** Pharmacists John Lea and William Perrins began manufacturing Worcester sauce on this day. Lea and Perrins sauce is still manufactured at the Midlands Road factory in Worcester, where production first began. In 1916 Perrins used some of the profits to found the Dyson Perrins organic chemistry laboratory at Oxford University. *rsc.org

*Lucio Gelmini

Scientific American sciam |

**1845**the first issue of the Scientific American was published by Rufus Porter (1792-1884), a versatile if eccentric Yankee, who was by turns a portrait-painter, schoolmaster, inventor and editor. While the paper was still a small weekly journal with a circulation less than 300, he offered it for sale. It was bought for $800 in July 1846 by 20-year-old Alfred Ely Beach (1826-1896) as editor, and Orson Desaix Munn (1824-1907). Together, they built it over the years into a great and unique periodical. Their circulation reached 10,000 by 1848, 20,000 by 1852, and 30,000 by 1853.*TIS

**1893**The first day of the Evanston Colloquial lectures by Felix Klein which would continue until 9 September.

*Karen Hunger Parshall, David E. Rowe; The Emergence of the American Mathematical Research Community, 1876-1900

**1961**The Board of Governors of the MAA voted to name Dr. Mina S. Rees, (ﬁrst) Dean of Graduate Studies at the City University of New York, the ﬁrst recipient of their Award for Distinguished Service to Mathematics. From 1946 to 1953 she held several important positions at the Office of Naval Research and was instrumental in getting ONR to adopt the policy that mathematics was part of this country’s total scientiﬁc effort and should be properly supported by government-sponsored research programs. [AMM 69(1962), pp. 185-187]. *VFR

**1974**Sweden issued a stamp picturing a spool and thread, with the thread stretched to form a string ﬁgure of a hyperbola. [Scott #1094]. *VFR

HT to Emma L Bell, Storax Sedan, and Glen Carlson for image

**1993**, a picture was taken showing the first moon of an asteroid. The asteroid 243 Ida and its newly-discovered moon, Dactyl was imaged by NASA's Galileo spacecraft, about 14 minutes before its closest approach (within 2,400-km or 1,5

**2009**The Australian Govt replies to a letter written "To A Top Scientist" by an Australian schoolboy shortly after the launch of Sputnik fifty-two years earlier with his suggested designs for a rocket ship. See all the details at this page from *Letters of Note

**Apple Talk Says Good by**

**1796 Irénée-Jules Bienaymé**(28 August 1796, 19 October 1878), was a French statistician. He built on the legacy of Laplace generalizing his least squares method. He contributed to the fields and probability, and statistics and to their application to finance, demography and social sciences. In particular, he formulated the Bienaymé-Chebyshev inequality concerning the law of large numbers and the Bienaymé formula for the variance of a sum of uncorrelated random variables.*Wik

**1801 Antoine-Augustin Cournot**(28 Aug 1801; 31 Mar 1877) French economist and mathematician, who was the first economist who applied mathematics to the treatment of economic questions. In 1838, he published Recherches sur les principes mathématiques de la théorie des richesses (Researches into the Mathematical Principles of the Theory of Wealth) which was a treatment of mathematical economics. In particular, he considered the supply-and-demand functions. Further, he studied the conditions for equilibrium with monopoly, duopoly and perfect competition. He included the effect of taxes, treated as changes in production costs, and discussed problems of international trade. His definition of a market is still the basis for that presently used in economics. In other work, he applied probability to legal statistics *TIS

**1862 Roberto Marcolongo **(August 28, 1862 in Rome – May 16, 1943 in Rome) was an Italian mathematician , known for his research in vector calculus and theoretical physics .

He graduated in 1886, and later he was an assistant of Valentino Cerruti in Rome. In 1895 he became professor of rational mechanics at the University of Messina . In 1908 he moved to the University of Naples , where he remained until retirement in 1935.

He worked on vector calculus together with Cesare Burali-Forti , which was then known as "Italian notation". In 1906 he wrote an early work which used the four-dimensional formalism to account for relativistic invariance under Lorentz transformations .

In 1921 he published to Messina one of the first treaties on the special relativity and general, where he used the absolute differential calculus without coordinates, developed with Burali-Forti, as opposed to the absolute differential calculus with coordinates of Tullio Levi-Civita and Gregorio Ricci-Curbastro .

He was a member of the Accademia dei Lincei and other Italian academies.

**1863 Andre-Eugene Blondel**(28 Aug 1863; 15 Nov 1938) was a French physicist who invented (1893) the electromagnetic oscillograph, a device that allowed electrical researchers to observe the intensity of alternating currents. In 1894, he proposed the lumen and other new photometric units for use in photometry, based on the metre and the Violle candle. Endorsed in 1896 by the International Electrical Congress, his system is still in use with only minor modifications. Blondel was a pioneer in the high voltage long distance transport of electric power, and also contributed to developments in wireless telegraphy, acoustics, and mechanics. He proposed theories for induction motors and coupling of a.c. generators.*TIS (Invention of the Oscillograph is also credited to William Du Bois Duddell.)

**1867 Maxime Bochner**(August 28, 1867 – September 12, 1918) was an American mathematician who published about 100 papers on differential equations, series, and algebra. He also wrote elementary texts such as Trigonometry and Analytic Geometry. Bôcher's theorem, Bôcher's equation, and the Bôcher Memorial Prize are named after him. *Wik

**1883 Jan Arnoldus Schouten**(28 August 1883 – 20 January 1971) was a Dutch mathematician and Professor at the Delft University of Technology. He was an important contributor to the development of tensor calculus and Ricci calculus, and was one of the founders of the Mathematisch Centrum in Amsterdam.

**1901 Kurt Otto Friedrichs**(September 28, 1901 – December 31, 1982) was a noted German American mathematician. He was the co-founder of the Courant Institute at New York University and recipient of the National Medal of Science.

**1910 Clarisse Doris Hellman Pepper**(August 28, 1910 – March 28, 1973) was an American historian of science, "one of the first professional historians of science in the United States". She specialized in 16th- and 17th-century astronomy, wrote a book on the Great Comet of 1577, and was the translator of another book, a biography of Johannes Kepler. She became a professor at the Pratt Institute and later at the Queens College, City University of New York, and was recognized by membership in several selective academic societies. *Wik

**1911 Shizuo Kakutani**August 28 1911, August 17 2004) was a Japanese-born American mathematician, best known for his eponymous fixed-point theorem.

The Kakutani fixed-point theorem is a generalization of Brouwer's fixed-point theorem, holding for generalized correspondences instead of functions. Its most important uses are in proving the existence of Nash equilibria in game theory, and the Arrow–Debreu–McKenzie model of general equilibrium theory.

Kakutani's other mathematical contributions include the Kakutani skyscraper, a concept in ergodic theory (a branch of mathematics that studies dynamical systems with an invariant measure and related problems). They also include his solution of the Poisson equation using the methods of stochastic analysis.

The Collatz (or 3n+1) conjecture is also known as the Kakutani conjecture. *Wik

**1912 George Eric Deacon Alcock**(August 28, 1912 – December 15, 2000)

George Alcock was an English astronomer. He was one of the most successful visual discoverers of novae and comets. He was also a very good (probably under-respected) teacher of the 4th year at Southfields Junior School in Stanground, Peterborough. In 1953 he decided to start searching for comets and in 1955 began searching for novae. His technique was to memorize the patterns of thousands of stars, so that he would visually recognize any intruder.

In 1959 he discovered comet C/1959 Q1 (Alcock), the first comet discovered in Britain since 1894, and only five days later discovered another, C/1959 Q2 (Alcock). He discovered two more comets in 1963 and 1965. He later discovered his first nova, Nova Delphini 1967 (HR Delphini), which turned out to have an unusual light curve. He discovered two more novas, LV Vul (in 1968) and V368 Sct (in 1970). He found his fifth and final comet in 1983: C/1983 H1 (IRAS-Araki-Alcock). In 1991 he found the nova V838 Her.

Alcock won the Jackson-Gwilt Medal of the Royal Astronomical Society in 1963 and Amateur Achievement Award of the Astronomical Society of the Pacific in 1981. After his death, a plaque was placed in Peterborough Cathedral in his memory. *TIA

**1919 Sir Godfrey Newbold Hounsfield**(28 August 1919 – 12 August 2004) English electrical engineer who shared the 1979 Nobel Prize for Physiology or Medicine (with Allan Cormack) for creation of computerised axial tomography (CAT) scanners. He originated the idea during a country walk in 1967 when he realized that the contents of a box could be reconstructed by taking readings at all angles through it. He applied the concept for scanning the brain using hundreds of X-ray beams imaging cross-sections that were reconstructed as high-resolution graphics by a computer program handling complex algebraic calculations. By 1973 his CAT scanner could produce cross-section images of a brain in 4-1/2-min, invaluable for the diagnosis of brain diseases. He later built a larger machines able to make a full body scan. *TIS

**1921 Ralph Asher Alpher**(February 3, 1921 – August 12, 2007) was an American cosmologist. Alpher's dissertation in 1948 dealt with a subject that came to be known as Big Bang nucleosynthesis. In a strange mathematical pun, his pre-publication of his thesis may have caused his independent role to have been minimized.

Although his name appears on the paper, Hans Bethe had no direct part in the development of the theory, although he later worked on related topics; Gamow added his name to make the author list Alpher, Bethe, Gamov, a pun on alpha, beta, gamma (α, β, γ), the first three letters of the Greek alphabet. Thus, Alpher's independent dissertation was first published on April 1, 1948 in the Physical Review with three authors. The humor engendered by the prodigious Gamow may at times have obscured the critical role Alpher played in developing the theory. This seminal paper was based on his dissertation (defended shortly thereafter).

With the award of the 2005 National Medal of Science, Alpher's original contributions (nucleosynthesis and the cosmic microwave background radiation predicition) to the modern big bang theory are beginning to receive due recognition. Neil deGrasse Tyson was instrumental in a NSF committee recommendation.

In 2005 Alpher was awarded the National Medal of Science. The citation for the award reads "For his unprecedented work in the areas of nucleosynthesis, for the prediction that universe expansion leaves behind background radiation, and for providing the model for the Big Bang theory." The medal was presented to his son Dr. Victor S. Alpher on July 27, 2007 by President George W. Bush, as his father could not travel to receive the award. Ralph Alpher died following an extended illness on August 12, 2007. He had been in failing health since falling and breaking his hip in February 2007. *Wik

**1939 John Frank Charles Kingman**(28 August 1939, )worked in Statistics and made significant advances in queuing theory.

He was N. M. Rothschild and Sons Professor of Mathematical Sciences and Director of the Isaac Newton Institute at the University of Cambridge from 2001 until 2006, when he was succeeded by Sir David Wallace. He is famous for developing the mathematics of the coalescent, a theoretical model of inheritance, which is fundamental to modern population genetics. *Wik

**1875 Beppo Levi** (14 May 1875 – 28 August 1961) was an Italian mathematician. He published high-level academic articles and books, not only on mathematics, but also on physics, history, philosophy, and pedagogy. Levi was a member of the Bologna Academy of Sciences and of the Accademia dei Lincei.

His early work studied singularities on algebraic curves and surfaces. In particular, he supplied a proof (questioned by some) that a procedure for resolution of singularities on algebraic surfaces terminates in finitely many steps. Later he proved some foundational results concerning Lebesgue integration, including what is commonly known as Beppo Levi's lemma.

**2005 George Szekeres**(29 May 1911 – 28 August 2005) was a Hungarian-born mathematician who worked for most of his life in Australia on geometry and combinatorics. *SAU

Szekeres worked closely with many prominent mathematicians throughout his life, including Paul Erdős, Esther Szekeres (née Esther Klein), Paul Turán, Béla Bollobás, Ronald Graham, Alf van der Poorten, Miklós Laczkovich, and John Coates.

The so-called Happy Ending problem is an example of how mathematics pervaded George's life. During 1933, George and several other students met frequently in Budapest to discuss mathematics. At one of these meetings, Esther Klein proposed the following problem:

Given five points in the plane in general position, prove that four of them form a convex quadrilateral.

After allowing George, Paul Erdős, and the other students to scratch their heads for some time, Esther explained her proof. Subsequently, George and Paul wrote a paper (1935) that generalizes this result; it is regarded as one of the foundational works in the field of combinatorial geometry. Erdős dubbed the original problem the "Happy Ending" problem because it resulted in George and Esther's marriage in 1937.

George and Esther died within an hour of each other, on the same day, 28 August 2005, in Adelaide, Australia.*Wik

**2005 Esther (Klein) Szekeres**(20 February 1910 – 28 August 2005) was a Hungarian–Australian mathematician with an Erdős number of 1. She was born to Ignaz Klein in a Jewish family in Budapest, Kingdom of Hungary in 1910. As a young woman in Budapest, Klein was a member of a group of Hungarians including Paul Erdős, George Szekeres and Paul Turán that convened over interesting mathematical problems.

In 1933, Klein proposed to the group a combinatorial problem that Erdős named as the Happy Ending problem as it led to her marriage to George Szekeres in 1937, with whom she had two children.

Following the outbreak of World War II, Esther and George Szekeres emigrated to Australia after spending several years in Hongkew, a community of refugees located in Shanghai, China. In Australia, they originally settled in Adelaide before moving to Sydney in the 1960s.

In Sydney, Esther lectured at Macquarie University and was actively involved in mathematics enrichment for high-school students. In 1984, she jointly founded a weekly mathematics enrichment meeting that has since expanded into a program of about 30 groups that continue to meet weekly and inspire high school students throughout Australia and New Zealand.

In 2004, she and George moved back to Adelaide, where, on 28 August 2005, she and her husband passed away within an hour of each other *Wik

The "Happy ending" couple near the end and still happy. |

**2006Melvin Schwartz**(November 2, 1932 – August 28, 2006) was an American physicist. He s hared the 1988 Nobel Prize in Physics with Leon M. Lederman and Jack Steinberger for their development of the neutrino beam method and their demonstration of the doublet structure of the leptons through the discovery of the muon neutrino.

**2007 Paul Beattie MacCready**(29 Sep 1925, 28 Aug 2007) was an American engineer who invented not only the first human-powered flying machines, but also the first solar-powered aircraft to make sustained flights. On 23 Aug 1977, the pedal-powered aircraft, the Gossamer Condor successfully flew a 1.15 mile figure-8 course to demonstrate sustained, maneuverable manpowered flight, for which he won the £50,000 ($95,000) Kremer Prize. MacCready designed the Condor with Dr. Peter Lissamen. Its frame was made of thin aluminum tubes, covered with mylar plastic supported with stainless steel wire. In 1979, the Gossamer Albatross won the second Kremer Prize for making a flight across the English Channel. *TIS

**2011 Anthony Edgar Sale**(or Tony Sale) (30 January 1931 - 28 August 2011) led the construction of a Colossus computer replica at Bletchley Park, completed in 2007 *Wik

In 1994, a team led by Tony Sale began a reconstruction of a Colossus at Bletchley Park. Here, in 2006, Sale (right) supervises the breaking of an enciphered message with the completed machine. *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

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