April 2004 - mathfun@mailman.xmission.com

RE: [math-fun] For sale on eBay: an Erdos number
by Dan Asimov 20 Apr '04

20 Apr '04

Thane, How do you *find* these things!?! --Dan

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[math-fun] For sale on eBay: an Erdos number
by Thane Plambeck 20 Apr '04

20 Apr '04

http://cgi.ebay.com/ws/eBayISAPI.dll?ViewItem&item=3189039958 Thane Plambeck 650 321 4884 office 650 323 4928 fax http://www.plambeck.org

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[math-fun] chem Q?
by Michael Kleber 19 Apr '04

19 Apr '04

Jim Hendrickson of the chemistry department here just asked me whether there was a good algorithm for finding the set of all one- or two-edge cut sets of a graph. When pressed, he said he'd actually like to find the cut which leaves two pieces as close to the same size as possible. Anyone know a good way to do this? I think anything better than brute force would count as "good". (The graphs he's interested in are ones that indicate bonded atoms in a molecule, so each vertex has degree at most four.) --Michael Kleber kleber(a)brandeis.edu

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[math-fun] vaguely remembered carnival game
by R. William Gosper 19 Apr '04

19 Apr '04

Is r=sqrt 2 the largest disk coverable with four unit disks? --rwg

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RE: [math-fun] vaguely remembered carnival game
by Steven Finch 18 Apr '04

18 Apr '04

Hello! Let D be the largest such disk. If D is covered, then in particular its boundary C must be covered. To cover a circular subarc of length 2*pi*r/4 requires a disk of radius at least r*sin(pi/4). Therefore r is at least sqrt(2). Equality is easy to see; hence the answer to your question is yes. The problem involving five unit disks gives rise to Neville's constant. See Proc. London Math. Soc. 14 (1915) 308--326 for his original paper. See my book "Mathematical Constants", pp. 484--488 for the latest developments. Best wishes, Steve Finch http://pauillac.inria.fr/algo/bsolve/ >From: "R. William Gosper" <rwg(a)tc.spnet.com> >Reply-To: math-fun <math-fun(a)mailman.xmission.com> >To: math-fun(a)mailman.xmission.com >Subject: [math-fun] vaguely remembered carnival game >Date: Thu, 15 Apr 2004 01:03:30 -0700 (PDT) > >Is r=sqrt 2 the largest disk coverable with four unit disks? >--rwg > _________________________________________________________________ Persistent heartburn? Check out Digestive Health & Wellness for information and advice. http://gerd.msn.com/default.asp

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[math-fun] Re: Euclid numbers
by Richard Schroeppel 14 Apr '04

14 Apr '04

> 2. Is there a nice asymptotic expression for the number of E_n < x ??? The product of the primes <= X is (very roughly) e^X. There are about X/logX primes <= X, and their "average" magnitude is (very roughly) X. Suggested notation: We are using X# for this product. I suggest extending this to X## for the LCM of numbers <= X. This is the same as the product (for each prime) of the largest prime power <=X. So 6# = 2.3.5 = 30, while 6## = 4.3.5 = 60. The logs of X# and X## are standard functions in analytic number theory. Rich rcs(a)cs.arizona.edu

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[math-fun] a Cauchy equation question
by 張家齊 14 Apr '04

14 Apr '04

g(x+y)=g(x)g(y) x,y are belong to R (BUT there is no continuous condition g may not be a continuous function) how to prove that if g(1)>1 then g is increasing if g(1)=1 then g is a constant function if g(1)<1 then g is deceasing ----------------------------------------------------------------- §Ûªñ¸ô¡I¡IEmail³B³B¦¬¡I §K¶O¤U¸üYahoo!©_¼¯±¶®|¦C http://tw.companion.yahoo.com/

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[math-fun] number theoretic rug
by Erich Friedman 11 Apr '04

11 Apr '04

a number theory question for those of you who know more number theory than i do (that would be most of you): i have a rug in my bathroom in the shape of a rectangle, surrounded by a border of constant width, surrounded by another border of constant width. i have often wondered whether any such rug can have integer dimensions with the three areas being equal. in other words, if the center rectangle is L by W, the inner border has width A, and the outer border has width B (with L, W, A, and B all being positive integers), can we have 2LW = (L+2A)(W+2A) and 3LW = (L+2A+2B)(W+2A+2B) ? i looked for small solutions with a computer and couldn't find any. did i not search far enough, or is there some number theoretic reason solutions do not exist? erich

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RE: [math-fun] FW: Math Spam from David Wilson
by Meeussen Wouter (bkarnd) 11 Apr '04

11 Apr '04

Mma says they'r all prime W. -----Original Message----- From: Richard Schroeppel [mailto:rcs@CS.Arizona.EDU] Sent: vrijdag 9 april 2004 18:03 To: math-fun(a)mailman.xmission.com Subject: [math-fun] FW: Math Spam from David Wilson This is the first math message in months to appear in the old Arizona Math-Fun mailbox. No doubt a fingerslip by DW. Curiously, it has its own special spam-like qualities. It seems that within each row the rule is Next = 5 * Current + 8. I can vouch for the first three primes, 7 43 223. Rich ---------------- From: "David Wilson" <davidwwilson(a)comcast.net> To: "Math Fun" <math-fun(a)CS.Arizona.EDU> Subject: simple check Date: Fri, 9 Apr 2004 01:10:36 -0400 Could any of you verify that each of the following numbers is prime? 7 43 223 1123 5623 28123 7621 38113 190573 952873 4764373 23821873 15937 79693 398473 1992373 9961873 49809373 382933 1914673 9573373 47866873 239334373 1196671873 462271 2311363 11556823 57784123 288920623 1444603123 518803 2594023 12970123 64850623 324253123 1621265623 866941 4334713 21673573 108367873 541839373 2709196873 1025407 5127043 25635223 128176123 640880623 3204403123 16022015623 1142503 5712523 28562623 142813123 714065623 3570328123 1427347 7136743 35683723 178418623 892093123 4460465623 1742473 8712373 43561873 217809373 1089046873 5445234373 1980067 9900343 49501723 247508623 1237543123 6187715623 2343619 11718103 58590523 292952623 1464763123 7323815623 2910031 14550163 72750823 363754123 1818770623 9093853123 45469265623 3015283 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478244653 2391223273 11956116373 59780581873 298902909373 1494514546873 7472572734373 96463267 482316343 2411581723 12057908623 60289543123 301447715623 98380357 491901793 2459508973 12297544873 61487724373 307438621873 101220313 506101573 2530507873 12652539373 63262696873 316313484373 <end of DW message> _______________________________________________ math-fun mailing list math-fun(a)mailman.xmission.com http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun =============================== This email is confidential and intended solely for the use of the individual to whom it is addressed. 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Re: [math-fun] Nets for spheres
by MCKAY＠vax2.concordia.ca 09 Apr '04

09 Apr '04

1 0