মিডিয়া
- টুইট
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- মিডিয়া, বর্তমান পৃষ্ঠা।
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Rational numbers are countable - you can put the rationals in order just like natural numbers are in order. In this paper, Neil Calkin and Herbert Wilf present a very elegant algorithm to list the rational numbers. Paper here: http://fermatslibrary.com/s/recounting-the-rationals#email-newsletter …pic.twitter.com/LBVJmepUyQ
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On February 14, 1990 Voyager 1 turned around and took a picture of Earth, 6B km away. In it, Earth is a mere point of light, a crescent less than 1 pixel in size. The picture (640,000 pixels) was saved to tape and then sent to Earth. 5:30 h later, it was recorded by 70m antennaepic.twitter.com/tBM42r63eT
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In 1937, Dirac formulated the hypothesis that the strength of gravity is inversely proportional to the age of the universe (G ∝ 1/t) and that the mass of the universe is proportional to the square of the universe's age (M ∝ t²) to explain the following coincidencespic.twitter.com/B4m3CuC3IB
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The time it takes for the Earth to perform one rotation on its axis has been growing (1.7 ms per century). This is caused by ocean tides generated by both the moon and sun's gravity. 350 million years ago, in the early Carboniferous period, a day was less than 23 hours longpic.twitter.com/BixfyZPofk
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In 1981, Yoshio Koide discovered this unexplained empirical equation relating the masses of the electron, muon and taupic.twitter.com/zvlYWzcVZB
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Visualization of the Dzhanibekov Effect onboard the International Space Station.
The effect is named after the Russian cosmonaut Vladimir Dzhanibekov who discovered this phenomenon while in space in 1985.
Find an explanation of the physics here: https://www.youtube.com/watch?v=-Si6iRL5Fj8&feature=youtu.be …pic.twitter.com/gzTGEp9Seg -
In the 16th century, before the Logarithm, people used an algorithm called Prosthaphaeresis to approximate products quickly. Its origin is associated with the calculation of position and course of ships using celestial navigation
.pic.twitter.com/om7nUNKU0W
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"Does the Flap of a Butterfly's wings in Brazil Set Off a Tornado in Texas?" This was the question Edward Lorenz presented to an audience in 1972. Lorenz was the father of chaos theory and showed how impossible perfect weather prediction is. PAPER here: http://fermatslibrary.com/s/predictability-does-the-flap-of-a-butterflys-wings-in-brazil-set-off-a-tornado-in-texas …pic.twitter.com/3GZFYHmZSR
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In 1948, Feynman showed Freeman Dyson his own proof of the Maxwell equations assuming only Newton's law of motion and the commutation relation between position and velocity of a nonrelativistic particle. Here it is: http://fermatslibrary.com/s/feynmans-proof-of-the-maxwell-equations#email-newsletter …pic.twitter.com/M0qgR3NUvM
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The following one-line is sufficient to prove that there are infinitely many prime numbers Here's why: https://www.youtube.com/watch?v=-v6yPtM4VLA&feature=youtu.be …pic.twitter.com/DYaTezPww6
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Giulio Fagnano discovered in 1750 the following formula for πpic.twitter.com/iecpXtZ6Pi
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FUN FACT In 2002 Grigori Perelman solved the the Poincaré Conjecture. Mathematicians had been struggling with this problem for a century. It took mathematicians several years to verify his proof. He was offered the prestigious Fields medal and $1,000,000. He declined both.pic.twitter.com/RTHdY11r51
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In 1990, IBM predicted that computers at the time typically experienced about 1 cosmic-ray-induced error per 256 megabytes of RAM per month.pic.twitter.com/6zYbiFqLOz
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Here's a good way to visualize factorial growth: imagine a cell that divides in 2, each child cell will then divide in 3, each grandchild cell will divide in 4 and and so on.pic.twitter.com/HQ0L1SrNWc
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PAPER Some mathematicians are birds
, others are frogs
. In this fascinating essay Freeman Dyson discusses the difference the two and how Mathematics needs both of them.
A great read: https://fermatslibrary.com/s/birds-and-frogs …pic.twitter.com/tDNVI1s640
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"When the present determines the future, but the approximate present does not approximately determine the future" Chaos summarized by Edward Lorenzpic.twitter.com/B8KAyAD6aJ
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Christoff Rudolff introduced in 1525 the sign of √ for the square root - it got this shape because of the resemblance with the letter "r" in "radix" (root in Latin)pic.twitter.com/L44JBhofR7
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Voronoi Diagram: a subdivision of a plane into regions based on the distance to points (seeds) in a specific subset of the plane. The seeds are specified beforehand, and for each seed there is a corresponding region consisting of all points closer to that seed than to any otherpic.twitter.com/Tzl8vMVd6W
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Ludolph van Ceulen, using Archimedes’ methods, approximated the circle with a regular polygon which had 2⁶² sides. It took 25 years of hand calculations to produce a 35 digit approximation of π, which was inscribed in his tombstone in 1610.pic.twitter.com/ybGNyDpG7t
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Here's an example of a conjecture that has been disproved with an extremely large counterexamplepic.twitter.com/GRcuJmC9iT
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