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| Jacob Bernoulli's tomb marker |
At ubi materia, ibi Geometria.
Where there is matter, there is geometry.
~Johannes KeplerWhere there is matter, there is geometry.
The 361st day of the year, 2361 is an apocalyptic number, it contains 666. 2361=4697085165547666455778961193578674054751365097816639741414581943064418050229216886927397996769537406063869952 That's 109 digits.
One of Ramanujan's many approximations of pi was (92+ (192/22))1/4, and 361 = 192
and as 361 is the last year day that is a perfect square, important to point out for students that all perfect squares are also the sum of consecutive triangular numbers, 361= 171 + 190 (The visual of this is a must see for students)
1612 Galileo observed Neptune, but did not recognize it as a planet. Galileo's drawings show that he first observed Neptune on December 28, 1612, and again on January 27, 1613. On both occasions, Galileo mistook Neptune for a fixed star when it appeared very close—in conjunction—to Jupiter in the night sky; hence, he is not credited with Neptune's discovery. (The official discovery is usually cited as September 23, 1846, Neptune was discovered within 1° of where Le Verrier had predicted it to be.) During the period of his first observation in December 1612, Neptune was stationary in the sky because it had just turned retrograde that very day. This apparent backward motion is created when the orbit of the Earth takes it past an outer planet. Since Neptune was only beginning its yearly retrograde cycle, the motion of the planet was far too slight to be detected with Galileo's small telescope.*Wik
On this day in 1725, Christian Goldbach was the recording secretary at the opening session of the St Petersburg Academy. The form of the Academy was imported ready-made from the Berlin model proposed to Peter the Great by Leibniz several years earlier.
The Academy started as the The Saint Petersburg Academy of Sciences and was based in St Petersburg. The name varied over the years, becoming The Imperial Academy of Sciences and Arts 1747-1803), The Imperial Academy of Sciences (1803- 1836), and finally, The Imperial Saint Petersburg Academy of Sciences (from 1836 and until the end of the empire in 1917). Following the Revolution in 1917 it was renamed the Russian Academy of Sciences. It kept this name only until 1925 when it became the USSR Academy of Sciences. In 1934 it moved from Leningrad (which is what St Petersburg had been renamed) to Moscow. In 1991 its name of the Russian Academy of Sciences was reinstated.*SAU
Some of the initial Academy members were Daniel and Nicolaus Bernoulli, Christian Goldbach, Johann Duvernoy, Christian Gross, and Gerhard Müller. Euler arrived in St. Petersburg in 1727 to take up a post in physiology, a field in which he had little experience. Before long, though, he was transferred to other areas of study; he was made full Professor of Physics in 1731, and Professor of Mathematics in 1733. Euler also took on another role as a member of the Academy's Geography and Cartography department.*Euler Archive
In 1831, Charles Darwin set sail from Plymouth harbour on his voyage of scientific discovery aboard the HMS Beagle, a British Navy ship. The Captain Robert FitzRoy was sailing to the southern coast of South America in order to complete a government survey. Darwin had an unpaid position as the ship's naturalist, at age 22, just out of university. Originally planned to be at sea for two years, the voyage lasted five years, making stops in Brazil, the Galapagos Islands, and New Zealand. From the observations he made and the specimens he collected on that voyage, Darwin developed his theory of biological evolution through natural selection, which he published 28 years after the Beagle left Plymouth. Darwin laid the foundation of modern evolutionary theory. *TIS
HMS Beagle was a Cherokee-class 10-gun brig-sloop of the Royal Navy, one of more than 100 ships of this class. The vessel, constructed at a cost of £7,803, was launched on 11 May 1820 from the Woolwich Dockyard on the River Thames. Wikipedia
In 1956, the formerly believed "law" of conservation of parity was disproved in the first successful results from an experiment conducted by Madame Chien-Shiung Wu at Columbia University on the beta-decay of cobalt-60. It had been suggested in a paper published by Lee and Yang on 1 Oct 1956. There had been problems to overcome working with the cobalt sample and detectors in a vacuum at a working temperature of one-hundredth of a kelvin. Wu's team repeated the experiment, doing maintenance on the apparatus as necessary, until on 9 Jan 1957 further measurements confirmed the initial results. Leon Lederman performed an independent test of parity with Columbia's cyclotron. They held a press conference on 15 Jan 1957.*TIS
1995 France concludes a series of nuclear weapons tests in the South Pacific ( Moruroa and Fangataufa Atoll test site). In a controversial move, French President Jacques Chirac had lifted a moratorium on testing. Most countries test weapons with computer simulations instead of actual bomb drops, but France claimed that tests that had been suspended several years earlier left the country without sufficient data to conduct future tests on computers.
Tahitians, as well as much of the international community, were outraged. Many expected the tests to harm the underwater geography and sea life of the atoll, as well as pose health risks to Tahitians. A French map from 1980 shows that testing had cracked the atolls in the past, destroyed coral reefs, and altered land plates. Harmful radioactive material had also been shown to spread via wind and rain. Some also saw France’s decision as a dangerous new step in nuclear proliferation in the West.
Both Tahitians and activists around the world responded strongly to France’s testing announcement. Activists in Tahiti were organizing a response while Greenpeace, an international environmental organization, sent a ship to Tahiti to protest the testing.
1571 Johannes Kepler (27 Dec 1571; 15 Nov 1630) German astronomer who formulated three major laws of planetary motion which enabled Isaac Newton to devise the law of gravitation. Working from the carefully measured positions of the planets recorded by Tycho Brahe, Kepler mathematically deduced three relationships from the data: (1) the planets move in elliptical orbits with the Sun at one focus; (2) the radius vector sweeps out equal areas in equal times; and (3) for two planets the squares of their periods are proportional to the cubes of their mean distances from the sun. Kepler suggested that the tides were caused by the attraction of the moon. He believed that the universe was governed by mathematical rules, but recognized the importance of experimental verification.*TIS
Fig. 1: Illustration of Kepler's laws with two planetary orbits.
- The orbits are ellipses, with foci F1 and F2 for Planet 1, and F1 and F3 for Planet 2. The Sun is at F1.
- The shaded areas A1 and A2 are equal, and are swept out in equal times by Planet 1's orbit.
- The ratio of Planet 1's orbit time to Planet 2's is .
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| *Wik |
1654 Jacob Jacques Bernoulli (27 Dec 1654; 16 Aug 1705) was a Swiss mathematician and astronomer who was one of the first to fully utilize differential calculus and introduced the term integral in integral calculus. Jacob Bernoulli's first important contributions were a pamphlet on the parallels of logic and algebra (1685), work on probability in 1685 and geometry in 1687. His geometry result gave a construction to divide any triangle into four equal parts with two perpendicular lines. By 1689 he had published important work on infinite series and published his law of large numbers in probability theory. He published five treatises on infinite series (1682 - 1704). Jacob was intrigued by the logarithmic spiral and requested it be carved on his tombstone. He was the first of the Bernoulli family of mathematicians. *TIS
He was an early proponent of Leibnizian calculus, which he made numerous contributions to; along with his brother Johann, he was one of the founders of the calculus of variations. He also discovered the fundamental mathematical constant e. However, his most important contribution was in the field of probability, where he derived the first version of the law of large numbers in his work Ars Conjectandi.*Wik
(see more about the family of Bernoulli's at the Renaissance Mathematicus )
I found an interesting anecdote related to teaching and learning at the MAA website by Paul Bedard (Saint Clair County Community College)
Even as the finite encloses an infinite series
And in the unlimited limits appear,
So the soul of immensity dwells in minutia
And in the narrowest limits no limit in here.
What joy to discern the minute in infinity!
The vast to perceive in the small, what divinity!
I found an interesting anecdote related to teaching and learning at the MAA website by Paul Bedard (Saint Clair County Community College)
"To learn more about mathematics than was possible at the University, Jakob traveled to Geneva. However, before he found a tutor, he became one. He entered the employ of the Waldkirch family in 1676 as tutor to the young, blind Elizabeth Waldkirch. His task was to help her learn to read and write – not a common accomplishment for the blind at that time. He continued in this occupation until 1678. M.B.W. Tent suggested, in her fictionalized account of the lives of Euler and the Bernoullis, that the elder Waldkirch wanted someone trained in mathematics, since he had learned that the mathematician Girolamo Cardano (1501-1576) had been involved in teaching literacy to the blind. It is worth noting that it is still true today that many professions seek mathematically trained candidates or use mathematics tests for eligibility, not because the job requires the specific skills involved, but because the assumption is that minds that can grasp mathematics are disciplined and sharp. This is a fact which the author shares with his students regularly."
"What skills as a teacher might Jakob Bernoulli have gained from this experience? There is a certain poetry in the idea that the man who would bring light to so much that was dark in mathematics began his teaching career by alleviating the disadvantages of physical blindness. If Tent was correct that he obtained this opportunity due to being a mathematician, then there is a second level of unexpected appropriateness here. "
"The early tutoring experiences of Jakob Bernoulli suggested to the author an at-home activity to assign our students. Rather than merely requiring the students to solve problems, ask them to find volunteers and teach the volunteers how to solve the problems. Each student will write a brief log entry of how the process goes, what explanations worked or failed, and how her “student” responded. Even if the person “tutored” in this way is unprepared for this level of mathematics, his response to it may be instructive for, or resonate with, our students."
1773 Sir George Cayley (27 Dec 1773; 15 Dec 1857)(6th Baronet ) English aeronautical pioneer who built the first successful man-carrying glider (1853). He made extensive anatomical and functional studies of bird flight. By measuring bird and human muscle masses, he realized it would be impossible for humans to strap on a pair of wings and take to the air. His further studies in the principles of lift, drag and thrust founded the science of aerodynamics from which he discovered stabilizing flying craft required both vertical and horizontal tail rudders, that concave wings produced more lift than flat surfaces and that swept-back wings provided greater stability. Cayley also invented the caterpillar tractor (1825), automatic railroad crossing signals, self-righting lifeboats, and an expansion-air (hot-air) engine.
*TIS (He was a distant cousin of the father of mathematician Arthur Cayley)
1915 Jacob Lionel Bakst Cooper (27 December 1915, Beaufort West, Cape Province, South Africa, 8 August 1979, London, England) was a South African mathematician who worked in operator theory, transform theory, thermodynamics, functional analysis and differential equations.*Wik
1771 Henri Pitot (3 May 1695, 27 Dec 1771) French hydraulic engineer who invented the Pitot tube (1732), an instrument to measure flow velocity either in liquids or gases. With subsequent improvements by Henri Darcy, its modern form is used to determine the airspeed of aircraft. Although originally a trained mathematician and astronomer, he became involved with an investigation of the velocity of flowing water at different depths, for which purpose he first created the Pitot tube. He disproved the prevailing belief that the velocity of flowing water increased with depth. Pitot became an engineer in charge of maintenance and construction of canals, bridges, drainage projects, and is particularly remembered for his kilometer-long Roman-arched Saint-Clément Aqueduct (1772) at Montpellier, France. *TIS
1930 Gyula Farkas (28 March 1847 in Sárosd, Fejér County, Hungary - 27 Dec 1930 in Pestszentlorinc, Hungary) He is remembered for Farkas theorem which is used in linear programming and also for his work on linear inequalities. In 1881 Gyula Farkas published a paper on Farkas Bolyai's iterative solution to the trinomial equation, making a careful study of the convergence of the algorithm. In a paper published three years later, Farkas examined the convergence of more general iterative methods. He also made major contributions to applied mathematics and physics, particularly in the areas of mechanical equilibrium, thermodynamics, and electrodynamics.*SAU
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1952 Mary Engle Pennington (October 8, 1872 – December 27, 1952) was an American bacteriological chemist, food scientist and refrigeration engineer. She was a pioneer in the preservation, handling, storage and transportation of perishable foods and the first female lab chief at the U.S. Food and Drug Administration. She was awarded 5 patents, received the Notable Service Medal from President Herbert Hoover and the Garvin-Olin Medal from the American Chemical Society. She is an inductee of the National Inventor's Hall of Fame, the National Women's Hall of Fame and the ASHRAE Hall of Fame.
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1973 Raymond Woodard Brink (4 Jan 1890 in Newark, New Jersey, USA - 27 Dec 1973 in La Jolla, California, USA) was an American mathematician who studied at Kansas State University, Harvard and Paris. He taught at the University of Minnesota though he spent a year in Edinburgh in 1919. He worked on the convergence of series. *SAU
He also authored numerous math textbooks. He served as president of the Mathematical Association of America from 1941–42.*Wik
1992 Alfred Hoblitzelle Clifford (July 11, 1908 – December 27, 1992) was an American mathematician who is known for Clifford theory and for his work on semigroups. The Alfred H. Clifford Mathematics Research Library at Tulane University is named after him.*Wik
1995 Boris Vladimirovich Gnedenko (January 1, 1912 - December 27, 1995) was a Soviet mathematician and a student of Andrey Nikolaevich Kolmogorov. He was born in Simbirsk (now Ulyanovsk), Russia, and died in Moscow. He is perhaps best known for his work with Kolmogorov, and his contributions to the study of probability theory. Gnedenko was appointed as Head of the Physics, Mathematics and Chemistry Section of the Ukrainian Academy of Sciences in 1949, and also became Director of the Kiev Institute of Mathematics in the same year.*Wik
1996 Sister Mary Celine Fasenmyer, R.S.M., (October 4, 1906, Crown, Pennsylvania – December 27, 1996, Erie, Pennsylvania) was a mathematician. She is most noted for her work on hypergeometric functions and linear algebra.*Wik
For ten years after her graduation she taught and studied at Mercyhurst College in Erie, where she joined the Sisters of Mercy. She pursued her mathematical studies in Pittsburgh and the University of Michigan, obtaining her doctorate in 1946 under the direction of Earl Rainville, with a dissertation entitled Some Generalized Hypergeometric Polynomials.
After earning her Ph.D., Fasenmyer published two papers which expanded on her doctorate work. These would be further elaborated by Doron Zeilberger and Herbert Wilf into "WZ theory", which allowed computerized proof of many combinatorial identities. After this, she returned to Mercyhurst to teach and did not engage in further research.
Fasenmyer is most remembered for the method that bears her name, first described in her Ph.D. thesis concerning recurrence relations in hypergeometric series.The thesis demonstrated a purely algorithmic method to find recurrence relations satisfied by sums of terms of a hypergeometric polynomial, and requires only the series expansions of the polynomial. The beauty of her method is that it lends itself readily to computer automation. The work of Wilf and Zeilberger generalized the algorithm and established its correctness.
The hypergeometric polynomials she studied are called Sister Celine's polynomials.
*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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