Some non-member messages were dropped over the holidays. -- Rich --------------- Date: Mon, 27 Dec 2004 18:05:29 -0800 From: Richard Fateman <fateman@cs.berkeley.edu> To: "R. William Gosper" <rwg@osots.com> CC: math-fun@mailman.xmission.com Subject: Re: [math-fun] Learning computer programming for a bright 13-year old ? You might be surprised to learn that speaking fractions is ambiguous. 30/400 and 34/100 are quite different numbers, but each can be pronounced thirty four hundredths Best wishes for the new year! RJF R. William Gosper wrote:
My very bright 13-year-old nephew would like to learn computer programming (from scratch). He's quite familiar with using software,
Dan, there are some kids where the absolutely best place to start would be the console toggle switches and indicator lamps on an ancient mainframe, if you can find a live one in a computer museum, e.g. There are other kids who take best to the opposite extreme, say generic functions (object-oriented LISP). For a certain concrete thinker, I'm planning the following first program: Combine Macsyma's string manipulation functions, especially CARDINAL_STRING (12 -> "twelve") and ORDINAL_STRING (12 -> "twelfth") to make a FRACTION_STRING function (11/12 -> "eleven twelfths"). There are nice opportunities for bugs ("one twelfths", 1/2 -> "one second", 3 -> "three firsts") and features (improper vs proper format, "three quarters"), generalization (RATIONAL_STRING, NUMBER_STRING even taking floats), and finally Robinson Crusoeing one's own CARDINAL_ and ORDINAL_ STRINGs. (Captious: "third", "thirteenth", "twenty third".) --rwg
------------------ From: "Rainer Rosenthal" <r.rosenthal@web.de> To: "wouter meeussen" <wouter.meeussen@pandora.be>, <njas@research.att.com>, <seqfan@ext.jussieu.fr>, <math-fun@mailman.xmission.com> Date: Tue, 28 Dec 2004 20:15:36 +0100 Subject: Re: Possibly new sequence related to dodecahedron
more detail is in a 70kb Excel spreadsheet : http://users.pandora.be/Wouter.Meeussen/DodecahedralVectorSum.xls
Dear Wouter, I couldn't open your interesting file, because I did not have access to the following: http://users.pandora.be/Program Files\ Wolfram Research\MathematicaLinkForExcel\Excel97\MLX.xla Please help, thanks, Rainer Rosenthal r.rosenthal@web.de ------------------------- Date: Thu, 30 Dec 2004 20:16:36 -0500 From: franktaw@netscape.net (Franklin T. Adams-Watters) To: seqfan@ext.jussieu.fr, math-fun@mailman.xmission.com Subject: RE: Possibly new sequence related to dodecahedron A pair of related, also finite, sequences: the number of "polypents" (connected sets of pentagons, up to symmetry) on an dodecahedron, and "polyiamonds" on an icosohedron. These sequences can also be done for smaller Platonic solids, but are too simple to be interesting. This is especially so for the tetrahedron, where the sequence is: 1,1,1,1,1 For the square, we have: 1,1,1,2,2,1,1. For the octahedron, the sequence is (I think): 1,1,1,1,3,3,3,1,1 "N. J. A. Sloane" <njas@research.att.com> wrote:
The following is an interesting question raised by Wouter Meeussen <wouter.meeussen@pandora.be> on Dec 27 2004:
He said:
Based on the symmetry point-group, how many 'different' sets of 1, 2, .., 10 vertices exist on a dodecahedron?
If I count different norms of sums of 1, 2, .., 10 unit vectors, I find: 1,5,12,22,34,50,65,78,78,86 but there might be 'different' sets that accidentaly sum to the same resultant's norm. So the given integers are a lower bound.
We can rephrase the question as follows.
Let G be the full icosahedral group, of order 120. Let v_1, ..., v_20 be the vertices of the dodecahedron. Let S(n) be the set of vectors
v_{i_1} + v_{i_2} + ... + v_{i_n}
where 1 <= i_1 <= i_2 <= ... <= i_n <= 20. Then what is s(n), the number of orbits of G on S(n)? (so s(1) = 1, s(2) = 6, ...)
Presumably this is different from A039742: ... %S A039742 1,6,50,475,4881,52835,593382,6849415,80757819,968400940,11773656517, %T A039742 144791296055,1797935761182 %N A039742 Lattice animals in the fcc lattice (12 nearest neighbors), connected rhombic dodecahedra, edge-connected cubes. ...
Repeat for icosahedron, etc.!
NJAS
-- Franklin T. Adams-Watters 16 W. Michigan Ave. Palatine, IL 60067 847-776-7645