March 2008 - mathfun@mailman.xmission.com

Re: [math-fun] Dan A. is being modest
by Lee Sallows 24 Mar '08

24 Mar '08

Phosphor. Lee Sallows At 10:09 PM 3/23/2008 -0700, you wrote: >Okay, here's another one in the same vein: > >Find an 8-letter (Scrabble-eligible) word >whose first hslf is the same as its second half, >except that the 4th letter immediately follows, >alphabetically, the 8th letter. > >Additional hint: it's something that glows. > >No fair using software to solve it! > >--Dan > >_____________________________________________________________________ >"It don't mean a thing if it ain't got that certain je ne sais quoi." --Peter Schickele > >_______________________________________________ >math-fun mailing list >math-fun(a)mailman.xmission.com >http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun > >

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Re: [math-fun] more word fun
by Michael Reid 24 Mar '08

24 Mar '08

yes, that's the pair i had in mind. mike > > find two six-letter words, each of which has the same first half > > as second half, and additionally, the two words differ in only > > two places. (one is common, the other is obscure.) > > Are you thinking of (rot13ed) zhhzhh and zhezhe? If so, I would probably > think of both of those words as relatively common. The less common one has

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[math-fun] Zeta-zoo
by wouter meeussen 24 Mar '08

24 Mar '08

is it just me? I find it confusing when it is claimed that "all non-trivial zero's of Zeta[x+I y] lie 'on' the line x=1/2 " (* original claim *) since much more seems to be happening. Is that because of my lack of understanding the shorthand used? I would say three things instead: 1/ only for x=1/2 does the function Zeta[x+ I y] pass through *one single intersection point* for each revolution of its modulus [0 , 2Pi] 2/ and for x=1/2 that special point also 'magically' happens to be {0,0} 3/ apart from x=1/2, Zeta[x+ I y] always 'magically' misses the point {0,0} (* equivalent to original claim *) ... and, if x>1/2, it crosses y=0 somehere Re[ it ] >0, and if x<1/2, then at Re[ it ] <0. Everytime. Ha! The original formulation leaves it open whether Zeta[1/2+ I y] could ever *not* pass through {0,0} during a complete turn of its modulus (passing somehere through {u, 0} with u < 0.1 say, like between y= 110 and 112) But, maybe my concept of "revolution around a center from where its modulus is seen to monotonously increase" is completely naive. Can such thing be defined for good old Zeta? Would { 0+epsilon, 0 } do? hmmmppfff (puffing...). Why don't people simply say such things up front? Wouter.

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[math-fun] more word fun
by Michael Reid 24 Mar '08

24 Mar '08

find two six-letter words, each of which has the same first half as second half, and additionally, the two words differ in only two places. (one is common, the other is obscure.) mike

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[math-fun] paramagic square
by Lee Sallows 24 Mar '08

24 Mar '08

Hello mathfunsters. Here is a new puzzle (of my own) that you may enjoy: Paramagic square. In the 5x5 paramagic square below, each of the 8 sets of 3 numbers in a straight line sum to 15. * 3 * * * * * 4 * 1 * 2 5 8 * 9 * 6 * * * * * 7 * Rearrange the numbers to produce a second 5x5 paramagic square in which 8 new sets of 3-in-a-line now total to 16 rather than 15. Lee Sallows

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Re: [math-fun] quasi-icosahedral frustration
by Dan Asimov 24 Mar '08

24 Mar '08

Wouter writes: << when building a 3D set of points using a simple rule, I accidentally found a subset that seems to approach icosahedral symmetry. Why 'approach' ? because all points in my set are rationals, and those can never be icosahedral since they lack the necessary Sqrt[5] irrationality. The procedure is simple enough: start from the tetrahedron (zeroth generation) {0, 0, 0}, {1, 1, 0}, {1, 0, 1}, {0, 1, 1} and on each triangular face, add the point to form the fourth vertex of a new tetrahedron: . . . . . . . . . with the n-th generation having denominators 3^n, and the number of points tripling each generation. The quasi-icosahedron becomes apparent when selecting all points at Sqrt[2] from the origin. . . . . . . I didn't succeed in understanding where the underlying connection to their pseudo-icosahedral grouping comes from. You got to plot them to believe it >> Interesting, but I don't see how this procedure, whose input is solely the vertices of a regular tetrahedron, can have anything but the original tetrahedral symmetry at each stage and therefore in the limit as well. (E.g., given a regular tetrahedron, one can find a regular icosahedron inscribed in it -- each of 4 faces of the icosahedron is a portion of one face of the tetrahedron -- but the icosahedron is not determined uniquely.) --Dan _____________________________________________________________________ "It don't mean a thing if it ain't got that certain je ne sais quoi." --Peter Schickele

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Re: [math-fun] Dan A. is being modest
by Lee Sallows 24 Mar '08

24 Mar '08

Xerxes. Lee Sallows At 11:42 PM 3/23/2008 -0400, you wrote: >>From NPR's puzzle of the week: > >>From listener Dan Asimov of Vancouver Island, British Columbia. >Name a well known historical figure with a one-word six-letter >name. The first and fourth letters are the same, the second and >fifth letters are the same, and the third letter is one letter >before the sixth, alphabetically. Who is it? > >Victor

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Re: [math-fun] Dan A. is being modest
by Dan Asimov 24 Mar '08

24 Mar '08

Okay, here's another one in the same vein: Find an 8-letter (Scrabble-eligible) word whose first hslf is the same as its second half, except that the 4th letter immediately follows, alphabetically, the 8th letter. Additional hint: it's something that glows. No fair using software to solve it! --Dan _____________________________________________________________________ "It don't mean a thing if it ain't got that certain je ne sais quoi." --Peter Schickele

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[math-fun] Dan A. is being modest
by victor miller 24 Mar '08

24 Mar '08

>From NPR's puzzle of the week: >From listener Dan Asimov of Vancouver Island, British Columbia. Name a well known historical figure with a one-word six-letter name. The first and fourth letters are the same, the second and fifth letters are the same, and the third letter is one letter before the sixth, alphabetically. Who is it? Victor

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[math-fun] ERH news ... did I miss this before?
by Guy Haworth 23 Mar '08

23 Mar '08

http://www.bristol.ac.uk/news/2008/12017945200.html http://science.slashdot.org/article.pl?sid=08/03/20/1728236&from=rss Guy

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