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RE: [math-fun] Permuation Probabilities ... with apologies ...
by Daniel Asimov 07 Jun '04

07 Jun '04

Guy Haworth asks: << re the upcoming FIDE World Chess Championship). In the 'knockout' first round involving 128 players and 64 matches, what is the probability that none of 19 specific players are matched against each other? >> If we assume the first 19 assignments of first-round opponent are to these 19 players, the probability you request must be ((128-19)/128-1) * (128-19-1)/(128-3))* ... *((128-19-18)/(128-37)) since the first player must be assigned to any of 128-19 out of 128-1; the second must now be assigned to any of 128-(19+1) out of 128-3; until the last of the 19 must be assigned to any of 128-(19+18) out of 128-36, which is all that matters. --Dan

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[math-fun] Fifty year anniversaries
by Thane Plambeck 07 Jun '04

07 Jun '04

Under what circumstances exactly will a 50 year anniversary fall on the same day of the week as the original date? Today (6 June 2004) is a Sunday, and so was 6 June 1954. Ignore all the old calendar stuff, let's say I'm only interested in this question for dates after 1800. There seem to be lots of web pages about "repeating calendar years" but that's not at all the same question since dates can agree on day of the week even when they differ on leap year status... I was asked this at a wedding anniversary party and stammered something about 100 year leap year cycles with 400 year exceptions but couldn't work out the general answer, at least with dance music playing Thane Plambeck 650 321 4884 office 650 323 4928 fax http://www.plambeck.org

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[math-fun] Does 1=1?
by Jon Perry 06 Jun '04

06 Jun '04

If so, a lot of contemporary mathematics would flow easily... But jokes aside, what is the concept that binds my 1 to your 1? Jon Perry perry(a)globalnet.co.uk http://www.users.globalnet.co.uk/~perry/maths/ http://www.users.globalnet.co.uk/~perry/DIVMenu/ BrainBench MVP for HTML and JavaScript http://www.brainbench.com

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[math-fun] when is a certifiable prime 'surprisingly easy to prove'?
by wouter meeussen 05 Jun '04

05 Jun '04

the elliptic curve method in Mathematica's (NumberTheory`PrimeQ`) package says after 20 seconds that 15085130035827878542455979623747888891433345604817588712723282399687865427853871 is prime. An 80 digit number. Should I expect such timing, or does this large integer have special properties that make it easy to get a certificate? W. quote When \!\(TraditionalForm\`n\) is larger than the value of the option SmallPrime, ProvablePrimeQ uses the Atkin\[Hyphen]Morain test as described above. This primality proving algorithm is suboptimal if the number is within the range of efficient factoring algorithms. When this is the case, a method of V.\[NonBreakingSpace]Pratt is preferable: V.\[NonBreakingSpace]Pratt, \[OpenCurlyDoubleQuote]Every Prime Has a Succinct Certificate,\[CloseCurlyDoubleQuote] SIAM Journal of Computation 4 (1975), pages 214\[Dash]220. An implementation of this algorithm in Mathematica is described in S. Wagon, Mathematica in Action, W. H. Freeman, 1991, Section\[NonBreakingSpace]8.7. end quote

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[math-fun] abcdef conjecture
by Jon Perry 04 Jun '04

04 Jun '04

I've not seen this anywhere else, can we generalize the abc conjecture into something whereby; f=a+b+c+d+e or any number of variables, and a form of the original abc conjecture still exists? I am aware of a conjecture that for the abc conjecture there is an upper bound of zeta(2): http://www.mathematik.uni-jena.de/~aros/abc.html Do other zeta(x) limits exist for the general abc conjecture? Jon Perry perry(a)globalnet.co.uk http://www.users.globalnet.co.uk/~perry/maths/ http://www.users.globalnet.co.uk/~perry/DIVMenu/ BrainBench MVP for HTML and JavaScript http://www.brainbench.com

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[math-fun] odometer word game
by Richard Schroeppel 03 Jun '04

03 Jun '04

zimb zinc chromatic chromatid Rich

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[math-fun] biroller (cylinder intersection)
by R. William Gosper 02 Jun '04

02 Jun '04

The volume formula for the perpendicular intersection of two cylinders of radius r can be found by replacing pi by 4 in the volume of the inscribed sphere. It is said that Archimedes found this thirteen centuries before Newton's calculus. Did he also know that the same 4/pi trick gives the surface area? If not, perhaps he noticed the universal prismatoid volume formula A + 4 A + A t m b V = h --------------, 6 (= one panel of Simpson's rule, with A:=area, t:=top, m:=middle, b:=bottom, h=height), which works on all the elementary solids, and deduced that it also works for the "biroller". (Is there a classical name for this solid?) I've said this before, but a fairly dense, fairly hard biroller (say, lathed from 2" aluminum bar stock) makes an intriguing chaotic toy, when rolled diagonally down a shallow, inclined trough (like a bathtub, but longer and shallower). The roller oscillates with gradually decaying amplitude until a downswing pauses on one of the two poles, whereupon it rocks with renewed amplitude, downslope on a perpendicular arc, taking a completely unpredictable time to reach the bottom. This was shown to me by an adolescent David Silver ca. 1970. --rwg PS, a Macsyma command to draw a biroller is block([plotnum1:2,f],[sin(t),sin(t),cos(t)],f:(1-u)*%%+u*[-1,1,1]*%%, makelist(f:part(f*[-1,1,1],[2,1,3]),k,1,4),plotsurf(%%,t,0,%pi,u,0,1))

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[math-fun] new Mersenne prime: P = 24,036,583
by Richard Schroeppel 01 Jun '04

01 Jun '04

The GIMPS project has confirmed the 41st known Mersenne prime, 24,036,583 2 - 1 with roughly 7.2M digits. This becomes the new largest-known-prime, roughly 1M digits larger than the previous record holder. The exponent was discovered two weeks ago, and has been checked since by two independent machines with independent software. We won't know for a year or two if this is the 41st largest MP, since there are lots of not-yet-tested and not-yet-checked exponents less than 24M. The official announcement is at http://www.mersenne.org/24036583.htm Rich Schroeppel rcs(a)cs.arizona.edu

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[math-fun] mathematics hypertext
by BobMayans＠aol.com 31 May '04

31 May '04

Greetings. I have been working on the design of a large-scale hypertext for mathematics: a linked structure of Web pages of mathematical writing. A paper on the design issues and proposed architecture of a mathematical hypertext, at http://jodi.ecs.soton.ac.uk/Articles/v05/i01/Mayans/ may be of interest to math-funsters. This is a very large and long-term project. A first text, in linear algebra, is in the works. The starting point of this work is the question: what is the ideal way to write mathematics? I'm looking for thoughts, suggestions, and maybe collaborators in this work. Bob Mayans

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[math-fun] Don Reble points to Meccano difference engine
by Richard Schroeppel 30 May '04

30 May '04

Don Reble accidentally sent this to the old Arizona Math-Fun list. When I notice this, I forward it. -- Rich --- Sender: djr(a)gallifrey.nk.ca Date: Sat, 29 May 2004 23:03:18 -0600 To: MathFunList <math-fun(a)CS.Arizona.EDU> Subject: Meccano difference engine MathFuners: Have y'all seen this? http://mirror.digitalroutes.co.uk/www.meccano.us/difference_engines/rde_1/i… -- Don Reble djr(a)nk.ca

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