September 2012 - mathfun@mailman.xmission.com

[math-fun] ABC Conjecture
by Stuart Anderson 19 Sep '12

19 Sep '12

http://terrytao.wordpress.com/2012/09/18/the-probabilistic-heuristic-justif… > What does Terry Tao's blog say? That would probably have the latest buzz. > > --Dan > > Stuart Anderson

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[math-fun] Euclid's Elements online
by Christoph Pacher 18 Sep '12

18 Sep '12

I have found a very nice edition of Euclid's Elements (both Greek and English version side-by-side) created by Richard Fitzpatrick: http://farside.ph.utexas.edu/euclid.html Links to PDF and even the LaTeX source are provided at the bottom. Hope you (and your children :) ) enjoy the read! Christoph

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[math-fun] Five non-transitive icosahedral dice
by Adam P. Goucher 16 Sep '12

16 Sep '12

I've found a set of non-transitive dice which 'emulates' the game of 'Rock, Paper, Scissors, Lizard, Spock' in an anologous way to how the simplest set of non-transitive dice emulates 'Rock, Paper, Scissors'. http://cp4space.wordpress.com/2012/09/16/lizard-and-spock-dice/ The dice were obtained from columns of a 5 by 5 magic square: 17 24 1 8 15 23 5 7 14 16 4 6 13 20 22 10 12 19 21 3 11 18 25 2 9 Sincerely, Adam P. Goucher http://cp4space.wordpress.com/

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[math-fun] see single molecules
by Warren Smith 16 Sep '12

16 Sep '12

http://www.bbc.co.uk/news/science-environment-19584301

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[math-fun] prime number visualization tool
by Ray Tayek 15 Sep '12

15 Sep '12

http://www.numbersimulation.com/ --- co-chair http://ocjug.org/

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[math-fun] The Erdos discrepancy problem
by Allan Wechsler 14 Sep '12

14 Sep '12

Let x be an infinite sequence whose entries are all +1 or -1. For this problem it is convenient to use 1-origin indexing, so the first element of x is x[1]. Now contruct the sequence d1 of partial sums: d1[0] = 0, d1[i+1] = d1[i] + x[i+1]. A similar sequence d2 adds only the even entries of x: d2[0] = 0, d2[2i+1] = d2[2i], d2[2i+2] = d2[2i] + x[2i+2] In general, we define dk[i] to equal the sum of all the elements x[j] such that j is a multiple of k not exceeding i. The "Erdos discrepancy" E[i] is the maximum over all k not exceeding i of | dk[i] |. Erdos conjectured that for all sequences x, E[i] eventually exceeds any given limit. The conjecture is still open, but generally believed to be true. Search the Web for "polymath5" (one word) for many references. You can quickly prove that E[i] exceeds 1 for some i < 12. For a limit of 2, things are not as clear. We have a many sequences of length 1124 that manage to keep below E[i]=3, but none of length 1125. It has been proved that all sequences reach E[i]=3 before somewhere between 2000 and 2100 (I forget the best known upper bound). OEIS's A181740 tabulates how many sequences of length n manage to keep E[i] <= 2. It gives values up to A[29], provided by Jeffrey Shallit. The current state of belief is that A[N] is 0 for all N exceeding 1124. I just wrote a program to calculate some more values; it agrees with Shallit's results as far as they go. I am planning to enter my new values (so far, up to A[50]), but I'm hoping that somebody can replicate my results. I list them below. A[30 .. 39] : 81326, 122422, 244844, 234934, 356154, 309068, 388042, 589796, 900000 [sic!], 813466 A[40 .. 49] : 1212450, 1837030, 1882194, 2921946, 4544342, 2274560, 3542738, 5495686, 8436986, 9597362 A[50] : 11352364 My program is really dumb; perhaps somebody can come up with a faster version. Mine is in Java; just rewriting it in C will probably speed it up enormously.

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[math-fun] LLL algorithm, Hebrew calendar, Antikythera mechanism
by Robert Munafo 14 Sep '12

14 Sep '12

Another reader points out the existence of Mathematica Home Edition, which I had not heard of. My prominent website might put me in the "non-profit organization" category. But we can also run Adam Goucher's examples in Wolfram Alpha, which accepts most Mathematica syntax. His first example is "LatticeReduce[{{1,0,0,100000,-100000,0},{0,1,0,0,3652421897/100,-3652421897/1000},{0,0,1,-295305890/100,0,295305890/1000}}]", here is the link: http://www.wolframalpha.com/input/?i=LatticeReduce%5B%7B%7B1%2C0%2C0%2C1000… A less precise answer, like the Metonic cycle, is obtained by changing the obvious scaling constants, giving "LatticeReduce[{{1,0,0,10000,-10000,0},{0,1,0,0,3652421897/1000,-3652421897/10000},{0,0,1,-295305890/1000,0,295305890/10000}}]" : http://www.wolframalpha.com/input/?i=LatticeReduce%5B%7B%7B1%2C0%2C0%2C1000… -- Robert Munafo -- mrob.com Follow me at: gplus.to/mrob - fb.com/mrob27 - twitter.com/mrob_27 - mrob27.wordpress.com - youtube.com/user/mrob143 - rilybot.blogspot.com

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[math-fun] LLL algorithm, Hebrew calendar, Antikythera mechanism
by Adam P. Goucher 13 Sep '12

13 Sep '12

A while ago I mentioned how to use continued fractions to design efficient calendars. If we want lunisolar calendars or eclipse cycles, we need to find an integer relation between more than two values. Instead of continued fractions, we can employ the LLL algorithm. I've used this to 're-discover' the Saros cycle, Metonic cycle and Exeligmos cycle: http://cp4space.wordpress.com/2012/09/12/lunisolar-calendars/ The Metonic cycle features in the Hebrew lunisolar calendar. All three are incorporated into the Antikythera mechanism. Sincerely, Adam P. Goucher http://cp4space.wordpress.com/

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[math-fun] Corrected link (Tour the Solar System from home)
by Robert Munafo 12 Sep '12

12 Sep '12

The link Mr Baker gave is not the Java solar system simulator. Here is the correct link: http://eyes.nasa.gov/launch2.html (or use the slightly shorter http://1.usa.gov/U85iUg ) On 9/12/12, Henry Baker <hbaker1(a)pipeline.com> wrote: > FYI -- NASA Java (not Javascript) browser app that allows you to tour the > solar system, including the location of all the NASA missions. > > It takes a while to download the info to display, but it's pretty cool. > > http://solarsystem.nasa.gov/ -- Robert Munafo -- mrob.com Follow me at: gplus.to/mrob - fb.com/mrob27 - twitter.com/mrob_27 - mrob27.wordpress.com - youtube.com/user/mrob143 - rilybot.blogspot.com

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[math-fun] Fwd: Topology in the Times
by meekerdb 12 Sep '12

12 Sep '12

-------- Original Message -------- http://opinionator.blogs.nytimes.com/2012/09/10/singular-sensations/?ref=op…

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