May 2008 - mathfun@mailman.xmission.com

Re: [math-fun] The value of PI
by Eugene Salamin 01 May '08

01 May '08

----- Original Message ---- From: Henry Baker <hbaker1(a)pipeline.com> To: Dan Asimov <dasimov(a)earthlink.net>; math-fun <math-fun(a)mailman.xmission.com> Sent: Thursday, May 1, 2008 11:09:40 AM Subject: Re: [math-fun] The value of PI Even more bizarre, IMHO, is the fact that in the volume formula for n dimensions, it isn't pi itself, but sqrt(pi), that is important. I don't think that the Greeks figured that part out. If you go through all the formulae in a large book -- e.g., Stegun, et al -- I think that "2pi" shows up more often than "pi". Sooner or later, we're bound to run up against a civilization that chose differently which to commemorate with a name. ------------------------------ But the sqrt(pi) is never explicit. The volume is (n/2)! pi^(n/2) R^n, and since (-1/2)! = sqrt(pi), only integer powers of pi appear. Gene ____________________________________________________________________________________ Be a better friend, newshound, and know-it-all with Yahoo! Mobile. Try it now. http://mobile.yahoo.com/;_ylt=Ahu06i62sR8HDtDypao8Wcj9tAcJ

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Re: [math-fun] The value of PI
by rwg＠sdf.lonestar.org 01 May '08

01 May '08

hgb>Even more bizarre, IMHO, is the fact that in the volume formula for n dimensions, it isn't pi itself, but sqrt(pi), that is important. That's sort of a notational artifact: (c41) sphere_volume(n,r) n/2 n %pi r (d41) --------- n (-)! 2 How times have changed. Last night I showed a 6th grader how to numerically solve for the length of the chord that cuts off area pi/3 from the unit circle (1.92853414856779, not in ISC), and the first thing he asked was "Can you prove it's irrational?". I'll bet the smart Greeks had the concept of real number, but had no way to market it. --rwg PS, if you start with 2 in the Newton's method for the disk trisection problem, you're stuck on 2 ! Look Ma, no Yahoo spamdangles!

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Re: [math-fun] The value of PI
by Henry Baker 01 May '08

01 May '08

Even more bizarre, IMHO, is the fact that in the volume formula for n dimensions, it isn't pi itself, but sqrt(pi), that is important. I don't think that the Greeks figured that part out. If you go through all the formulae in a large book -- e.g., Stegun, et al -- I think that "2pi" shows up more often than "pi". Sooner or later, we're bound to run up against a civilization that chose differently which to commemorate with a name. At 04:08 PM 4/30/2008, Dan Asimov wrote: >Bernie asks: > ><< >. . . >the area of a circle is 3.14... times the square of the radius and >the volume of a sphere is 4.18... times the cube of the radius. >. . . >But when did mathematicians realize that those weren't two separate >gnarly constants, but actually "reflections" [if you will] of a single >underlying constant? I don't think the Greeks had enough math machinery >to figure all that out, did they? >. . . >>> > >Yes, the fact that the ratio of the volume of a sphere >to the volume of the circumscribed cylinder is 2/3 was >one of Archimedes' proudest achievements: This is said >to be inscribed on his gravestone. > >--Dan

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[math-fun] interesting trailer for new movie on hilbert's 10th problem & julia robinson
by Thane Plambeck 01 May '08

01 May '08

http://www.zalafilms.com/films/julia.html (quicktime movie) http://www.zalafilms.com/news.html#041808a (some more about it) -- Thane Plambeck tplambeck(a)gmail.com http://www.plambeck.org/ehome.htm

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