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[math-fun] A relayed message from James Anderson re transreal arithmetic
by Guy Haworth 14 Dec '06

14 Dec '06

I have been astonished at the response to publicity surrounding my research. A great many of you have commented on one example of transreal arithmetic that I used in the TV package. I have replied to many of you individually, but I regret that I do not have time to reply to you all. Debate will be improved if you read my papers. The first paper describes the arithmetic in terms of operations on fractions. It predates the axioms paper. http://www.bookofparagon.com/Mathematics/PerspexMachineVII.pdf The second paper gives the axioms: http://www.bookofparagon.com/Mathematics/PerspexMachineVIII.pdf The third paper gives a development of the exponential, logarithmic, and trigonometric functions. There is an error in the guarding clause of equation 10, but this does not affect anything else in the paper. Nor does it affect the demonstration I gave in the TV package. http://www.bookofparagon.com/Mathematics/PerspexMachineIX.pdf Here is another proof of the 0^0 result. It is justified in the analysis paper. 0^0 = e^(ln 0^0) = e^(0 x ln 0) = e^( 0 x (-infinity)) = e^nullity = nullity James Anderson, Univesity of Reading [via Guy Haworth]

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[math-fun] NYTimes: Dodecahedral salt
by Henry Baker 11 Dec '06

11 Dec '06

FYI -- December 10, 2006 Salt That DoesnÂt Stick By CLIVE THOMPSON Everyone knows the havoc that humidity wreaks on salt. You pick up a saltshaker, tip it upside down and Â nothing. The problem is molecular. Salt grains are cube shaped, so it doesnÂt take much to get them to stack together like Legos. Salt producers have created nonsticking salt before by adding chemicals to prevent binding. But this year, in the July issue of Crystal Growth and Design, a team of Indian scientists announced that they had discovered a better way to attack the problem: they produced salt that is round. To accomplish this, they added the amino acid glycine to a pan of brine and then let the salty liquid evaporate. The resulting crystals were shaped like dodecahedrons: 12-sided grains. In this nearly spherical form, the grains no longer stacked like bricks but like oranges in a sack. The researchers put some of the round salt into a container, left it for a year and found that it still poured freely. The glycine has a side effect: it makes the salt slightly sweeter. Pushpito K. Ghosh, one of the lead scientists on the project, claims he canÂt detect it Â ÂAnd IÂve eaten a lot of it!Â Â but he suspects that chefs might.

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[math-fun] Sudokus in other bases
by Mike Stay 11 Dec '06

11 Dec '06

http://xkcd.com/c74.html -- Mike Stay metaweta(a)gmail.com http://math.ucr.edu/~mike

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[math-fun] RE: Commas
by N. J. A. Sloane 11 Dec '06

11 Dec '06

Eric, please send that sequence in now, so that i can clean up my email stack! Best Neil

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[math-fun] News on Taxicab and Cabtaxi numbers
by Christian Boyer 11 Dec '06

11 Dec '06

The known information on Taxicab and Cabtaxi numbers goes up to Taxicab(6) and Cabtaxi(9). Here are new upper bounds, up to Taxicab(12) and Cabtaxi(20): http://cboyer.club.fr/Taxicab.htm A paper is in preparation. Christian.

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[math-fun] RE: Commas
by Eric Angelini 11 Dec '06

11 Dec '06

Hello Again Zak (and others) I've received this (coming from rec.puzzles) from "The Qurqirish Dragon": I noticed one problem with the rule. Take the sequence starting with 2: 2, (+22) 24, (+47) 71, ? Is the next value 89 or 90? Both follow the given rule: 2, (+22) 24, (+47) 71, (+18) 89, (+91) 180, ... 2, (+22) 24, (+47) 71, (+19) 90, (+09) 99, (+91) 190, ... This problem will happen whenever a given addition works resulting in a number consisting of all 9s (except for the first digit, which must be less than 9). What do you think about this remark? Can such a pb arise in the "main" sequence (the one starting with "1")? Do I have to rewrite the rule saying something like: "Keep the sequence as low as possible" Best, É.

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[math-fun] RE: Commas
by Eric Angelini 11 Dec '06

11 Dec '06

Thanks, Zak, beautiful! I had calculated by hand: 1,12,35,94,135,186,248,331,344,387,461,475,530,535,590,595,651, 667,744,791,809,908,997,1068,1149,1240,1241,1252,1273,1304,1345, 1396,1457,1528,1609,1700,1701,1712,1733,1764,1805,1856,1917,1988, 2070,2072,2094,2136,2198 ... which is exactly what you have got. I will submit this to Neil together with yr name in january. Best, É. (I'm interested in the first 1000 terms for my personal webpage, if you don't mind -- 1000 thanks again) -----Message d'origine----- De : zak seidov [mailto:zakseidov@yahoo.com] Envoyé : lundi 11 décembre 2006 17:46 À : Eric Angelini; math-fun; seqfan(a)ext.jussieu.fr Objet : Re: Commas Sequence is growing almost linearly (I calculated first 1000 terms), differences have some (nice) patterns. For checking purposes I give first and 10th hundreds terms of seq: {1,12,35,94,135,186,248,331,344,387,461,475,530,535,590,595,651,667,744,791,809,908,997,1068,1149,1240,1241,1252,1273,1304,1345,1396,1457,1528,1609,1700,1701,1712,1733,1764,1805,1856,1917,1988,2070,2072,2094,2136,2198,2280,2282,2304,2346,2408,2490,2492,2514,2556,2618,2700,2702,2724,2766,2828,2910,2912,2934,2976,3039,3132,3155,3208,3291,3304,3347,3420,3423,3456,3519,3612,3635,3688,3771,3784,3827,3900,3903,3936,3999,4093,4127,4201,4215,4269,4363,4397,4471,4485,4539,4633}<...>{44303,44337,44411,44425,44479,44573,44607,44681,44695,44749,44843,44877,44951,44965,45019,45113,45147,45221,45235,45289,45383,45417,45491,45505,45559,45653,45687,45761,45775,45829,45923,45957,46031,46045,46099,46193,46227,46301,46315,46369,46463,46497,46571,46585,46639,46733,46767,46841,46855,46909,47003,47037,47111,47125,47179,47273,47307,47381,47395,47449,47543,47577,47651,47665,47719,47813,47847,47921,47935,47989,48083,48117,48191,48205,48259,48353,48387,48461,48475,48529,48623,48657,48731,48745,48799 ,48893,48927,49001,49015,49069,49163,49197,49271,49285,49339,49433,49467,49541,49555,49609} Zak For those interesting I can send also graphs. --- Eric Angelini <Eric.Angelini(a)kntv.be> wrote: > > For non-mathematicians only: > http://www.cetteadressecomportecinquantesignes.com/Commas.htm > Best, > É. > > __________________________________________________ Do You Yahoo!? Tired of spam? Yahoo! Mail has the best spam protection around http://mail.yahoo.com

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[math-fun] Commas
by Eric Angelini 11 Dec '06

11 Dec '06

For non-mathematicians only: http://www.cetteadressecomportecinquantesignes.com/Commas.htm Best, É.

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Re: Re: [math-fun] Add no digit of n to n
by Michael Kleber 10 Dec '06

10 Dec '06

Paul R. Pudaite <pudaite(a)pipeline.com> wrote: > For binary numbers, the sequence has one term (no iterations): 1. :) Hmm, good point: 2 1 3 12 4 132 5 1324 6 12543 7 123546 8 1234576 9 12345876 10 123456978, as before; this is the first one that takes significant time to compute. f[x_,b_] := x + Module[{y=Complement[Range[b-1],IntegerDigits[x,b]]},If[Length[y]>0,Min[y],0]] g[b_] := Print @@ IntegerDigits[FixedPoint[f[#,b]&,1], b] --Michael Kleber -- It is very dark and after 2000. If you continue you are likely to be eaten by a bleen.

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[math-fun] Add no digit of n to n
by Eric Angelini 10 Dec '06

10 Dec '06

Hello Math-Fun, What is the last term of the sequence starting with "1" and obeying the rule: "Add to n the smallest positive integer sharing no digit with n" Sequence should begin like this : 1,3,4,5,6,7,8,9,10,12,15,17,19,21,24,25.... Best, E.

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