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| 1935 Little Orphan Annie Decoder |
and being dull and pedantic are surely among them.
Mark Kac
The 215th day of the year; There are 215 sequences of four (not necessarily distinct) integers, counting permutations of order as distinct, such that the sum of their reciprocals is 1. Obviously, one of them is 1/4+1/4+1/4+1/4=1. How many can you find?
How many solutions with four distinct integers, not counting permutations?
215[10] = 555[6]
Every multiple of 5 greater than 30 is expressible as the difference of the squares of two numbers that differ by 5. (Nice algebra problem for younger students.) 215 = 24^2 - 19^2.
Lagrange's theorem tells us that each positive integer can be written as a sum of four squares, but Lagrange allowed the use of zeros, such as 12 + 12 + 12 + 02 =3. Allowing only positive integers, there are 57 year days that are not expressible in less than four squares. 215 is the 34th of these year days that is NOT expressible with less than four positive squares. 215 = 12 + 32 + 62 + 132.
Lagrange's theorem tells us that each positive integer can be written as a sum of four squares, but Lagrange allowed the use of zeros, such as 12 + 12 + 12 + 02 =3. Allowing only positive integers, there are 57 year days that are not expressible in less than four squares. 215 is the 34th of these year days that is NOT expressible with less than four positive squares. 215 = 12 + 32 + 62 + 132.
The last such number was 207, the next is 220.
You can create more on your own. Take any number in the sequence and multiply it by an odd number and you have another that is in the seque. nce.
In 1937 Lothar Collatz conjectured the process of starting with any number and repeatedly multiplying by 3n+1 if odd, or dividing by two if even in iteration will always lead to one. I mention that here because if you start with 215, it will take 101 operations (a prime number) before you get back to one.
215 = (3!)^3-1 *Wik
Every multiple of 5 greater than 30 is expressible as the difference of the squares of two numbers that differ by 5. (Nice algebra problem for younger students.) 215 = 24^2 - 19^2.
215 is the second (and last) yearday that N^2 - 17 is a square. The next such number is over 4000, but can you find the smaller?
Like all odd numbers, 215 is the difference of two consecutive squares, 108^2 - 107^2 = 215. Because it ends in five (and is bigger than 35) it is also the differences of two squares of numbers that differ by 5, 24^2 - 19^2 = 215
All twin primes after 3 are of the form 6n-1 and 6n+1. A pair of twin primes are formed by 6(215)+1 and 6(215)-1
A nice foot note to this fact is that the 215th and 216 primes are twin primes.
215 is the sum of discrete factorials, 8! + 7! + 6! + 5! + 4! + 1!.
See More Math Facts for every Year Day here
431 BC Oldest European record of a verifiable solar eclipse (annular), by the Greek historian Thucydides. *NSEC
1492 Old School mneumonic "In fourteen hundred ninety-two, Columbus sailed the ocean blue." Columbus set out from Palos de la Frontera, Spain, on this day. I always reminded my students of the perils of memorization with the line:
"In Fourteen hundred ninety-three, Columbus sailed the deep blue sea" *PB
1596 David Fabricus (also spelled Fabricius) of Germany discovered that the star Mira varied in brightness. In 1638 Johann Holwarda of Germany determined its period, and Mira, from the Latin word for wonderful or astonishing, became the first periodic variable star discovered. However, a few stars of variable brightness were discovered earlier by Chinese and Korean astronomers, who mistakenly identified them as novae.*Access Science
A nice piece on Fabricius life and unusual death are at the Renaissance Mathematicus.
This graph shows how Mira’s brightness has changed over the past 10 years
1747 Diderot and d’Alembert replace de Gua, who had earlier done much to systematize analytic geometry, as director of the publishing project which was to become the celebrated Encyclop´edie*VFR
1750 The first (U.S.) teaching methods book was completed by Christopher Dock. It was originally written in German and was printed twenty years later in Germantown, Pennsylvania. The preface was dated March 27, 1770. The full title was: “Schul-ordnung; or A Simple and Thoroughly Prepared School-Management clearly setting forth not only in what manner children may best be taught the branches usually given at school, but also how they may be well instructed in the knowledge of godliness.” *VFR
1823 German chemist Johann Dobereiner discovered the role of platinum (Pt) as a catalyst. He realized that a platinum (Pt) sponge could cause the ignition of hydrogen (H) at room temperature by lowering the activation energy. This effect was the precursor to the theory of catalysis, but it was not until 1835 that the term “catalyst” was coined by Swedish chemist Jacob Berzelius. *rsc.org
1872 Charles A. Young (US) observes a flare on the Sun with a spectroscope; he calls attention to its coincidence with a magnetic storm on Earth. *NSEC
In 1903, Thomas Edison's opinion of radium was quoted within an article in the New York World newspaper. "I have had several pieces of it from Mme. Curie in Paris, and I have experimented with it. I do not see its commercial utility, but it opens up a great field of thought and scientific research. It overturns all the old theories of force and energy... I have a peculiar theory about radium, and I believe it is the correct one. I believe that there is some mysterious ray pervading the universe that is fluorescing to it. In other words, that all its energy is not self-constructed but that there is a mysterious something in the atmosphere that scientists have not found that is drawing out those infinitesimal atoms and distributing them forcefully and indestructibly."
1914 In the final hours of peace, Karl Pearson rushed back from the continent. "I at once put the whole laboratory (Biometrics Laboratory) staff at the service of any Government department that was in need of computing or statistical aide." The Laboratory at that time consisted of ten human computers, six women and four men. *When Computers were Human
1953 In honor of the 7th International Congress of History of Science, which was held in Jerusalem, August 4-11, 1953, Israel issued a stamp picturing Maimonides, Rabbi Moshe ben Maimon (1135-1204), a Jewish philosopher especially interested in the work of Aristotle. [Scott #74]. *VFR
1958 The First ship to reach the North Pole was the submarine Nautilus, which reached 90 degrees North enroute from Hawaii to the Atlantic Ocean.*VFR In 1958, the USS Nautilus (SSN571), became the first submarine to travel under the geographic North Pole when the ice-pack conditions were favorable. This was the first atomic-powered submarine in the U.S. Navy. Attempts earlier in the year failed due to the ice-pack conditions. The crew created a post office while under the North Pole and canceled their letters with a home-made North Pole Stamp. (The Post Master General later declared it to be a legal post office.) Santa Claus boarded through one of the forward torpedo tubes and complained about the effect on his lawn. *TIS
Nautilus was decommissioned in 1980 and designated a National Historic Landmark in 1982. The submarine has been preserved as a museum ship at the Submarine Force Library and Museum in Groton, Connecticut, where the vessel receives around 250,000 visitors per year.
1977 Radio Shack announces TRS-80 computer... This was the first computer I ever owned, and my son and I learned to program together on one.(He has gone on to be quite a capable programer)
Radio Shack announces its TRS-80 Model I, the company's first personal computer. Equipped with 4KB of RAM, cassette-tape storage, and a built-in BASIC interpreter, the TRS-80 was one of the first mass-marketed personal computer (along with the Commodore PET and Apple II). At a time when most microcomputers came in kit form and appealed to hobbyists, these three computers addressed the average person and were very popular in schools Radio Shack sold more than 200,000 TRS-80 computers.*chm
2018 Italy issues new stamp honoring Maria Gaetana Agnesi. It is one of four stamps honoring Italian women of learning, "Excellencies of the knowledge - Italian female genius"
1805 William Rowan Hamilton born. The date on his tombstone is 4 August 1805, the confusion being due to the fact that he was born at midnight.*VFR
Sir William Rowan Hamilton (3 August 1805 – 2 September 1865) was an Irish physicist, astronomer, and mathematician, who made important contributions to classical mechanics, optics, and algebra. His studies of mechanical and optical systems led him to discover new mathematical concepts and techniques. His greatest contribution is perhaps the reformulation of Newtonian mechanics, now called Hamiltonian mechanics. This work has proven central to the modern study of classical field theories such as electromagnetism, and to the development of quantum mechanics. In mathematics, he is perhaps best known as the inventor of quaternions. Hamilton is said to have shown immense talent at a very early age, prompting astronomer Bishop Dr. John Brinkley to remark in 1823 of Hamilton at the age of 18: “This young man, I do not say will be, but is, the first mathematician of his age.”
William Rowan Hamilton's scientific career included the study of geometrical optics, classical mechanics, adaptation of dynamic methods in optical systems, applying quaternion and vector methods to problems in mechanics and in geometry, development of theories of conjugate algebraic couple functions (in which complex numbers are constructed as ordered pairs of real numbers), solvability of polynomial equations and general quintic polynomial solvable by radicals, the analysis on Fluctuating Functions (and the ideas from Fourier analysis), linear operators on quaternions and proving a result for linear operators on the space of quaternions (which is a special case of the general theorem which today is known as the Cayley–Hamilton theorem). Hamilton also invented "Icosian Calculus", which he used to investigate closed edge paths on a dodecahedron that visit each vertex exactly once. *Wik
1811 Elisha Otis (August 3, 1811 – April 8, 1861) American inventor of the automatic safety brake for elevators, which later made high-rise buildings practical. Before this invention, elevators of his time were extremely dangerous. In 1852, he was employed at a New York bed factory. He realized the need for a "safety elevator" to move people and equipment safely to the upper floors of the building. He strikingly demonstrated his solution at the Crystal Palace Exposition in New York in 1854. In front of a large crowd, Otis ascended in his new elevator. He called for the elevator's cable to be cut with an axe, but the elevator platform did not fall. The brake he invented used toothed guiderails in the elevator shaft and a spring-loaded bar that automatically caught in the toothed rail if the elevator car if the cable failed. *TIS
1823 Abel dated a letter to his friend Holmboe “Copenhague, l’an √3
6064321219 (en comptant lafraction d´ecimal).” Can you make sense of this? The year is immediate, but how do you get
the date?
1900 John T. Scopes, (August 3, 1900 – October 21, 1970) was a teacher in Dayton, Tennessee Scopes got a job coaching the high-school football team in Dayton, Tennessee, and like many coaches, he was required to teach some science courses as well. In May of 1925, a delegation of Dayton town fathers asked Scopes if he would agree to be arrested and put on trial for violating the Butler Act recently passed by the state of Tennessee. The Butler Act forbade the teaching of evolution in Tennessee schools. Scopes said yes, even though it appears he never actually taught evolution in his classes. But he did use a textbook that discussed evolution, and that was good enough. The town leaders were hoping that a trial would put Dayton on the map, and that it certainly did. The details with Scopes were worked out at Robinson’s Drug Store in Dayton, the subject of many historical photos once the trial began (third image).
On May 25, 1925, Scopes was charged with violating the Butler Act, and the result was one of the most famous trials of the entire century, the Scopes Trial. The prosecuting attorney was Tom Stewart, but he was greatly overshadowed by William Jennings Bryan, who came to town for the occasion as a special prosecutor. Scopes’ defense attorney was in turn eclipsed by Clarence Darrow, who was present on behalf of the American Civil Liberties Union and who effectively took over Scopes' defense.
The trial began on July 10, 1925, and Scopes played almost no role in its proceedings. Most of the photographs of the trial focus on Darrow or Bryan; our first image, featuring Scopes, is an exception. The most notable occasion of the trial, when Darrow cross-examined Bryan about Biblical literalism (fifth image), did not involve Scopes at all. The trial concluded on July 21, when Scopes was found guilty of violating the Butler Act and fined $100. The expectation all along had been that Scopes would be convicted, and the intention was to appeal the conviction and put the Butler Act on trial. But the conviction was overturned by a higher court (only a jury could assess a fine of $100 in Tennessee), and the case was never retried. The Butler Act stood its ground until it was finally repealed in 1967.
The name "Scopes" has become as famous as any legal eponym ever, but Scopes himself rather disappeared from the historical record after the trial. He worked as a field geologist for most of his life. He did publish an autobiography in 1967, Center of the Storm: Memoirs of John T. Scopes, which appeared three years before his death in 1970. It is a book we ought to have in the Library, but do not. We shall attempt to remedy this.
The textbook that Scopes used (and which Bryan waved around in court on one notable occasion) was Civic Biology, by George Hunter. Published in 1914, it did indeed present the facts of evolution; we see above a page that explains Darwin’s nefarious proposal . Ironically, its use in Tennessee schools was mandated by the state Board of Education, so it was inevitable that the Butler Act and Civic Biology would clash somewhere in Tennessee. It just happened to be in John Scopes’ adopted hometown.
Scopes was born to Thomas Scopes and Mary Alva Brown, who lived on a farm in Paducah, Kentucky. He died on October 21, 1970 of cancer in Shreveport, Louisiana at age 70. His body is buried in the town of his birth.
1918 Artemas Martin (August 3, 1835; Steuben County, New York - November 7, 1918; Washington, DC, United States) was a self-educated American mathematician.
Martin grew up in Venango County, Pennsylvania. He was home-schooled until the age of 14, when he began studying mathematics at the local school, later moving to the Franklin Select School a few miles away and then to the Franklin Academy, finishing his formal education at age approximately 20. He worked as a farmer, oil driller, and schoolteacher.
Martin was a prolific contributor of problems and solutions to mathematical puzzle columns in popular magazines beginning at the age of 18 in the Pittsburgh Almanac and the Philadelphia Saturday Evening Post. From 1870 to 1875, he was editor of the "Stairway Department" of Clark's School Visitor, one of the magazines to which he had previously contributed. From 1875 to 1876 Martin moved to the Normal Monthly, where he published 16 articles on diophantine analysis. He subsequently became editor of the Mathematical Visitor in 1877 and of the Mathematical Magazine in 1882.
In 1881, he declined an invitation to become a professor of mathematics at the Normal School in Missouri. (This was probably from the work of Prof E B Seitz, who had just been appointed professor at the Missouri Normal School in Kirksville. Martin had contacted Seitz, then a teacher in Greenville, Ohio and had contributed a solution to a difficult problem on averages in the "Stairway" department of the Schoolday Magazine, for which Martin was an editor. They continued to communicate for the rest of Seitz brief life)In 1885, he became the librarian for the Survey Office of the United States Coast Guard, and in 1898 he became a computer in the Division of Tides.
In 1877 Martin was given an honorary M.A. from Yale University. In 1882 he was awarded another honorary degree, a Ph.D. from Rutgers University, and his third honorary degree, an LL.D., was given to him in 1885 by Hillsdale College. He was elected to the London Mathematical Society in 1878, the Société Mathématique de France in 1884, the Edinburgh Mathematical Society in 1885, the Philosophical Society of Washington in 1886, the American Association for the Advancement of Science in 1890, and the New York Mathematical Society in 1891. He was also a member of the American Mathematical Society, the Circolo Matematico di Palermo, the Mathematical Association of England, and the Deutsche Mathematiker-Vereinigung.
He died on November 7, 1918.
Martin maintained an extensive mathematical library, now in the collections of American University. *Wik (He was also a very early writer on "pursuit" curves. PB)
1851 George Francis FitzGerald (3 August 1851 – 22 February 1901) Irish physicist whose suggestion of a way to produce waves helped lay a foundation for wireless telegraphy. He also first developed a theory, independently discovered by Hendrik Lorentz, that a material object moving through an electromagnetic field would exhibit a contraction of its length in the direction of motion. This is now known as the Lorentz-FitzGerald contraction, which Einstein used in his own special theory of relativity. He also was first to propose the structure of comets as a head made of large stones, but a tail make of such smaller stones (less than 1-cm diam.) that the pressure of light radiation from the sun could deflect them. FitzGerald also studied electrolysis as well as electromagnetic radiation.*TIS
FitzGerald was the nephew of George Johnstone Stoney, the Irish physicist who coined the term "electron". After the particles were discovered by J. J. Thomson and Walter Kaufmann in 1896, FitzGerald was the one to propose calling them electrons. *Wik
1914 Mark Kac (pronounced kahts, Polish: Marek Kac, b. 3 August 1914, Krzemieniec, Russian Empire, now in Ukraine; d. 26 October 1984, California, USA) was a Polish mathematician. His main interest was probability theory. His question, "Can you hear the shape of a drum?" set off research into spectral theory, with the idea of understanding the extent to which the spectrum allows one to read back the geometry. (In the end, the answer was "no", in general.)*Wik
1926 Maurice Auslander (August 3, 1926 – November 18, 1994) was an American mathematician who worked on commutative algebra and homological algebra. He proved the Auslander–Buchsbaum theorem that regular local rings are factorial, the Auslander–Buchsbaum formula, and introduced Auslander–Reiten theory and Auslander algebras.*Wik
1914 Louis Couturat (17 Jan 1868 in Ris-Orangis (near Paris), France - 3 Aug 1914 in Between Ris-Orangis and Melun, France), a logician whose historical researches led to the publication of Leibniz’s logical works in 1903.*VFR Couturat was killed in a car accident, his car being in hit by the car carrying the orders for mobilization of the French army the day World War I broke out. Ironically he was a noted pacifist. *SAU
1917 Georg Frobenius (October 26, 1849 – August 3, 1917) German mathematician who made major contributions to group theory, especially the concept of abstract groups (with Ludwig Stickleberger) and the theory of finite groups of linear substitutions (with Issai Schur), that later found important uses in the theory of finite groups as it applies to quantum mechanics. He also contributed to means of solving linear homogenous differential equations. The fact so many of Frobenius's papers read like present day text-books on the topics which he studied is a clear indication of the importance that his work, in many different areas, has had in shaping the mathematics which is studied today.*TIS
1922 Mathias Lerch (Matyáš Lerch, (20 February 1860, Milínov - 3 August 1922, Schüttenhofen) was an eminent Czech mathematician who published about 250 papers, largely on mathematical analysis and number theory. He studied in Prague and Berlin, and held teaching positions at the Czech Technical Institute in Prague, the University of Fribourg in Switzerland, the Czech Technical Institute in Brno, and Masaryk University in Brno; he was the first mathematics professor at Masaryk University when it was founded in 1920. In 1900, he was awarded the Grand Prize of the French Academy of Sciences for his number-theoretic work. The Lerch zeta-function is named after him as is the Appell–Lerch sum.*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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