October 2003 - mathfun@mailman.xmission.com

[math-fun] 51 stars
by Thane Plambeck 20 Oct '03

20 Oct '03

Did JHC ever reveal his design? If so could someone repost it? Thane Plambeck 650 321 4884 office 650 323 4928 fax http://www.qxmail.com/ehome.htm

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[math-fun] PC continued
by Jon Perry 20 Oct '03

20 Oct '03

I found the relation between homeomorphic spaces - the slices have no encapsulated hole. This I believe solves PC, although I will be among the first to admit that the maths needs to be made presentable. Anyway, if anyone would like to publish this (plus other emials) as a proof, please contact me. 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] question about poincare conjecture
by Chris Landauer 19 Oct '03

19 Oct '03

hihi, all - yesterday, i read ``four colors suffice'' by robin wilson, which i found to be a very interesting discussion of the four color theorem, and an entertaining and informative account of the history of its proof, but i also noticed a comment about the poincare conjecture that i'd like to know more about, since it has been so often mentioned here of late Wilson writes (at the bottom of p. 178 of my hardbound edition) about Wolfgang Haken separating and reducing the poincare problem into 200 cases and then successfully addressing 198 of them, but not being able to eliminate the last two cases i'd like to know more about what kinds of features this separation into cases might depend on, whether or not anyone else has taken up this kind of approach, with what (partial) success, and whether it's something like taking out all the trivial and easy cases, so that only the really hard ones remain (as happened frequently for the four color theorem) thanx in advance it has always been interesting to me how hard it is to do any kind of useful geometric reasoning in a computer program (much of what i do is pattern recognition systems), and i've wondered for some time how a computing system might be designed to allow planar or 3d geometric reasoning to be more naturally programmed more soon, cal Chris Landauer Aerospace Integration Science Center The Aerospace Corporation cal(a)aero.org

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[math-fun] Re Mrs P's Quilt
by N. J. A. Sloane 18 Oct '03

18 Oct '03

I've updated A005670 based on the recent discussions, by adding comments, examples and references. But I did not change the list of exact values given there, which are: %S A005670 1,4,6,7,8,9,9,10,10,11,11,11,11,12,12,12,12,13,13,13 or in other words: n a(n) 1 1 2 4 3 6 4 7 5 8 6 9 7 9 8 10 9 10 10 11 11 11 12 11 13 11 14 12 15 12 16 12 17 12 18 13 19 13 20 13 Could someone please clarify just what the known exact values are? Ed? John? Thanks! Neil

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[math-fun] looking for reference to a problem
by Richard Schroeppel 18 Oct '03

18 Oct '03

Nick Baxter sent this a week ago, and I failed to notice he sent it to the old address, math-fun(a)cs.arizona.edu. I switched the list to math-fun(a)mailman.xmission.com last year because of excessive spam (and one virus). I disconnected automatic forwarding months ago, but I try to notice real messages and forward them manually. This one got by me. Sorry, Nick. I think the problem below was on the Math SAT, about a decade ago, but I'm sure someone remembers more specific information. It was written up in newspapers, and maybe Science News. Rich rcs(a)cs.arizona.edu ------------------- Date: Thu, 09 Oct 2003 11:05:00 -0700 From: Nick Baxter <nickb(a)baxterweb.com> To: math-fun <math-fun(a)CS.Arizona.EDU> Subject: looking for reference to a problem Can someone please fill in the details of a story I heard about a high school student who correctly protested the solution to the following problem that appear on a standardized test some years ago. Problem: Given an equilateral pyramid (square base), glue two regular tetrahedrons (same edge length) to two non-adjacent triangular faces. How many faces does the resulting polyhedron have? I'm looking for the name (and any other information) of the student, the year, the test, the given (incorrect) answer, and the original wording of the problem, if possible. Any references to published accounts of the incident are also appreciated. Thanks, Nick

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Re: [math-fun] looking for reference to a problem
by asimovd＠aol.com 17 Oct '03

17 Oct '03

Nick Baxter asks for references to the Colllege Board question: << Problem: Given an equilateral pyramid (square base), glue two regular tetrahedrons (same edge length) to two non-adjacent triangular faces. How many faces does the resulting polyhedron have? >> I may be wrong, but as I recall it, the problem was to glue a regular tetrahedron to a regular octahedron along one common face. --Dan

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[math-fun] Late Show physics
by Shel Kaphan 16 Oct '03

16 Oct '03

Last night David Letterman had physicist Brian Greene as a guest. The topics were the origins of the universe, inflation, and even a little about string theory. At one point in the conversation they talked about what might have existed "prior" to the big bang. A short excerpt: Letterman: But even in nothingness, nothingness in and of itself is something. Greene: Yes, it does wind up taxing language to describe these ideas using common words, but the notion would be that the familiar things we know about like space and time and matter really would not have existed. It would have been either a different realm, or a realm literally not composed of anything we know of or could describe. Letterman: Like Trenton.

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Re: [math-fun] Poincar
by asimovd＠aol.com 16 Oct '03

16 Oct '03

Gene asked: << > Can we say that two compact n-dimensional manifolds M1 and M2 are > homotopy equivalent if for all k, 1<=k<=n the homotopy groups pi[k](M1) > and pi[k](M2) are isomorphic? Dylan answered: << No, that's not true. What is true is that if there is a map between M1 and M2 which induces the identity on all homotopy groups (not just in this range) then M1 and M2 are homotopy equivalent. >> A simple example of spaces that have the same homotopy groups but are not homotopy equivalent is P^k x S^m and P^m x S^k, where say m > k > 1. (Note to Dylan: The condition you mention -- usually called "weak homotopy equivalence" -- is the same as homotopy equivalence for "nice" spaces like manifolds, and more generally simplicial or CW complexes, but there are stranger spaces that can be weakly homotopy equivalent without being homotopy equivalent.) --Dan --Dan

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[math-fun] Re: Poincare Conjecture
by Dan Hoey 16 Oct '03

16 Oct '03

"Jon Perry" <perry(a)globalnet.co.uk> writes: > Thanks - I can see the weaknesses in my argument. Very good, if true. > However, is there anything wrong with this; > PC is true because from the 3-sphere, a compact, simply connected > manifold, through only operations which preserve homeomorphicity, we > can attain every other compact, simply-connected 3-manifold. Yes, there's something wrong with that. Any statement of the form "PC is true because <sentence>" is hogwash. If you were going to prove PC, you would need more than a sentence to express a convincing proof. It might be accurate to say "If I could prove <sentence>, that would imply PC". That depends on the sentence, of course. If you ever convinced someone that you might have a proof of PC, then it might be appropriate to say something of the form, "I have proved <sentence>, and that implies PC." But you made the statement in the hogwash form. Moreover, you made that statement in reply to a message that shows that you not only did not present a realistic approach to a proof of PC, but were apparently unclear on the concept of what a proof of PC would be, and that you were beginning to sound like a crank. I hope your statement is not a proof, because it certainly isn't a proof of the Poincare conjecture. Dan Hoey Hoey(a)AIC.NRL.Navy.Mil

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[math-fun] special characters in subject lines
by Richard Schroeppel 16 Oct '03

16 Oct '03

Some mailers bounce messages that have special characters in the Subject line. Examples are the final vowel in Poincare, and the final consonant in Gauss. If you want your Math-Fun message to go to everyone in the group, avoid the fancy non-ASCII letters in your Subject lines. Rich rcs(a)cs.arizona.edu

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