History Trivia / Math

17th Oct '16 5:44:27 PM nombretomado
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** [[IrregularWebcomic You'd think they could do it in just four pieces though.]]

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** [[IrregularWebcomic [[Webcomic/IrregularWebcomic You'd think they could do it in just four pieces though.]]
8th May '16 1:21:02 AM Perey
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* There's a joke computer file system called [[https://github.com/philipl/pifs PiFS]] that claims it's data free (except for the metadata file) and you can store and retrieve ''any'' file. The play on this is that any irrational number (a number that does not end or have repeating digits) contains any finite sequence of numbers. All you have to do is find out where in pi this sequence is.
** People have noted that pi, e, and other irrational numbers are [[https://en.wikipedia.org/wiki/Illegal_number illegal numbers]] because they have to contain said illegal number.

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* There's a joke computer file system called [[https://github.com/philipl/pifs PiFS]] that claims it's data free (except for the metadata file) and you can store and retrieve ''any'' file. The play on this joke is that any irrational number (a number that does not end or have repeating digits) contains any finite sequence of numbers. All you have pi is (thought to do is find out where in pi this sequence is.
** People have noted that pi, e, and other irrational numbers are
be) a [[https://en.wikipedia.org/wiki/Normal_number normal number]]; that is, its digits are truly random[[note]]in the sense that all digit sequences are uniformly distributed[[/note]], and so somewhere in its infinite decimal places, it must contain every possible finite sequence of numbers. And since a file on disk is just a sequence of numbers, all you have to do is find out where in pi this sequence is. [[BlatantLies Simple]].
** People have noted that pi, e, and other normal numbers (okay, numbers that we ''think'' are normal) are [[https://en.wikipedia.
org/wiki/Illegal_number illegal numbers]] numbers]], because they have to contain said illegal number.
10th Apr '16 11:28:09 AM Robinton
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** Another weird probability distribution is the Cauchy Distribution, which does not have a well-defined mean because the integral does not converge.

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** Another weird probability distribution is the [[http://en.wikipedia.org/wiki/Cauchy_distribution Cauchy Distribution, Distribution]], which does not have a well-defined mean because the integral does not converge.



** There's also the Pigeonhole Principle, complete with proof, on explaining that if you have ''x+1'' elements and ''x'' slots, one slot will have at least two elements.

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** There's also the [[http://en.wikipedia.org/wiki/Pigeonhole_principle Pigeonhole Principle, Principle]], complete with proof, on explaining that if you have ''x+1'' elements and ''x'' slots, one slot will have at least two elements.
10th Apr '16 11:24:47 AM Robinton
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** If you have a 50% chance of winning one cent, a 25% chance of winning two, etc., the expected winnings is infinite, despite the fact that it's impossible to win an infinite amount of money.

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** If you have a 50% chance of winning one cent, a 25% chance of winning two, a 12.5% chance of winning four, etc., the expected winnings is infinite, despite the fact that it's impossible to win an infinite amount of money.
24th Mar '16 2:55:01 AM 06tele
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* And then there's Whitehead and Russell's ''Principia Mathematica'', a multi-volume opus intended to construct all of mathematics from the most basic of axioms (such as "every statement is either true or false"). After 379 pages of incomprehensibly dense notation, it succeeds in proving that [[https://en.wikipedia.org/wiki/Image:Principia_Mathematica_theorem_54-43.png 1+1=2]]. And then Gödel's [[https://en.wikipedia.org/wiki/Incompleteness_theorem Incompleteness Theorem]] undermined the whole thing using a real-life LogicBomb.

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* And then there's Whitehead and Russell's ''Principia Mathematica'', a multi-volume opus intended to construct all of mathematics from the most basic of axioms (such as "every statement is either true or false"). After 379 pages of incomprehensibly dense notation, it succeeds in proving that [[https://en.wikipedia.org/wiki/Image:Principia_Mathematica_theorem_54-43.png 1+1=2]].1+1=2. And then Gödel's [[https://en.wikipedia.org/wiki/Incompleteness_theorem Incompleteness Theorem]] undermined the whole thing using a real-life LogicBomb.
8th Jan '16 6:46:05 PM nombretomado
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* The [[SpiritedAway Chihiro]] numbers, abbreviated C(n), are a series of numbers that grow ridiculously large. Named after mathematician Chihiro Kagachi, the name is amusing to many anime fans. They follow as the extension of 1+1, 2*2, and 3^3 (2, 4, 27...). The fourth term is equal to 4^(4^(4^(4)), which is already larger than a googolplex. This can be even more ridiculous by looking at C^n(n), but you'd need to iterate the Chihiro function 64 times to approach...

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* The [[SpiritedAway [[Anime/SpiritedAway Chihiro]] numbers, abbreviated C(n), are a series of numbers that grow ridiculously large. Named after mathematician Chihiro Kagachi, the name is amusing to many anime fans. They follow as the extension of 1+1, 2*2, and 3^3 (2, 4, 27...). The fourth term is equal to 4^(4^(4^(4)), which is already larger than a googolplex. This can be even more ridiculous by looking at C^n(n), but you'd need to iterate the Chihiro function 64 times to approach...
19th Aug '15 12:35:50 PM Enthryn
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** And the proof is ridiculously easy: Suppose there were finitely many primes. If you multiply them all together you get a number that can be divided by any prime. If you add one you then get a number that cannot be divided by any prime. Therefore this big number is either prime and not a member of the set of all primes, or has prime factors that arenít members of the set of all primes. Thatís absurd. Hence there aren't finitely many primes.

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** And the proof is ridiculously easy: Suppose there were finitely many you're given a finite list of primes. If you multiply them all together together, you get a number that can be divided by any prime. prime on the list. If you add one to this, you then get a number that cannot be divided by any prime. prime on the list. Therefore every prime divisor of this big number is either a prime and not a member of ''not'' on the set of all primes, or has prime factors that arenít members of the set of all primes. Thatís absurd. list. Hence there aren't finitely many no finite list can contain all the primes.
18th Aug '15 12:11:07 AM naclhv
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Added DiffLines:

** Other highly counter-intuitive probability problems include cases like the {{Monty Hall problem}} or the [[http://www.naclhv.com/2015/08/the-two-envelopes-problem-and-its.html two envelopes problem.]]
8th Aug '15 2:37:12 PM Llygodenfawr
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* [[http://www.naclhv.com/2014/06/how-to-make-fractal.html Fractals]] are pictures that look immensely complex and detailed, But they arise from simple mathematical equations and procedures. No matter how far you zoom in on them, there are more, smaller features to see. Some well-known fractals include the [[https://en.wikipedia.org/wiki/Mandelbrot_set Mandelbrot set]], the [[https://en.wikipedia.org/wiki/Sierpinski_carpet Sierpinski carpet]], and the [[https://en.wikipedia.org/wiki/Koch_snowflake Koch snowflake]], some of which are described in the entries below.

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* [[http://www.naclhv.com/2014/06/how-to-make-fractal.html Fractals]] are pictures that look immensely complex and detailed, But but they arise from simple mathematical equations and procedures. No matter how far you zoom in on them, there are more, smaller features to see. Some well-known fractals include the [[https://en.wikipedia.org/wiki/Mandelbrot_set Mandelbrot set]], the [[https://en.wikipedia.org/wiki/Sierpinski_carpet Sierpinski carpet]], and the [[https://en.wikipedia.org/wiki/Koch_snowflake Koch snowflake]], some of which are described in the entries below.
27th Jun '15 4:42:07 AM onyhow
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::@@else: answer is A(m-1, A(m, m-1))@@

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::@@else: answer is A(m-1, A(m, m-1))@@n-1))@@
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