February 2016 - mathfun@mailman.xmission.com

[math-fun] The importance of being a coupon-collector
by Fred Lunnon 04 Feb '16

04 Feb '16

Mama don't allow no p*l*t*c*l probability here: so I've gone back to collecting --- computationally rather expensive --- coupons. [ A man should have an occupation of some sort. ] I don't know in advance how many distinct coupons are available, but have collected m among which there are just k distinct. What is the probability that n distinct coupons are available? What is the most likely value of n ? What are asymptotic expressions for large m ? Fred Lunnon

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[math-fun] The Wittless Duck
by Fred Lunnon 04 Feb '16

04 Feb '16

I have been struggling to recall a rather surprising theorem, encountered in passing while searching for something unrelated, concerning the structure of quadratic spaces for which the Witt index exceeds 2 . Not only can I not find the theorem; I can't even locate a definition of the Witt index --- that is |p - q| + r , where the (possibly degenerate) quadratic form signature involves p positive, q negative, r absent squares. Can somebody out there please unscramble my brain (or my surfing technique) for me? Dribble, mutter ... Fred Lunnon

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[math-fun] Pegg's crashing computer
by Warren D Smith 04 Feb '16

04 Feb '16

How did you find out what the problem was and how to fix it? (I have a similar crashing problem on my computer. I suspected it was a bad graphics chip.)

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[math-fun] Research project
by rkg 03 Feb '16

03 Feb '16

Are you able to help with investigating the Lighthouse Theorem for values of n > 4 ? For information about the theorem and the important Lighthouse Duplication Theorem see the article in the Amer Math Monthly. Alternatively, I can send a copy. For n = 5, it seems that two applications of the Lighthouse Duplication theorem should lead to sets of homothetic regular pentagons which are related to quinquisectors of two angles (of a triangle? of a pentagon?) For n = 9, there can be three applications of the Lighthouse Duplication theorem. In any case a subset of the novisectors are the trisectors of Morley's theorem. Moreover the remaining novisectors Will lead to 18 Morley triangles for each of 3 x 18 triangles in the same construction. If XYZ is a Morley triangle of ABC, then the triangles I mean are BCX, CAY, ABZ, but there are 3 x 18 other triangles, AYZ, BZX, CXY, which may be worth examining. To what extent are the resulting equilateral triangles homothetic? Best wishes. R.

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Re: [math-fun] math-fun Digest, Vol 156, Issue 3
by Warren D Smith 03 Feb '16

03 Feb '16

A paper by me and some Australian showed linear time algorithm for finding the closest lattice point in a family of lattices that includes A_n: https://www.itr.unisa.edu.au/itrusers/mckillrg/public_html/papers/ISITA_Ans… http://arxiv.org/abs/0903.0673 I don't know how the 2nd australian got on the paper as author. The squared-distance metric is arguably incorrect for this purpose for many applications, such as proportional representation voting. -- Warren D. Smith http://RangeVoting.org <-- add your endorsement (by clicking "endorse" as 1st step)

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[math-fun] Iowa coin tosses
by Henry Baker 03 Feb '16

03 Feb '16

Bernie wins 1/7 coin tosses. 2^7 = 128 possibilities. 7 of them have Bernie getting exactly 1 heads. 7/128 ~ 5.469% Which is small, but considerably larger than the initial report, which said that Bernie got 0/6: 1/64 ~ 1.56%. https://www.salon.com/2016/02/02/critics_cry_foul_over_coingate_hillary_cli… "Even before all the precincts were reported, the characteristically confident Clinton campaign had immediately declared victory."

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[math-fun] DH non-prime kills "socat" command security
by Henry Baker 03 Feb '16

03 Feb '16

For the past year, the Linux command "socat" has been assuming that the following number is prime; thus breaking its crypto security. 14331936439490594261714896808578599103914668374026899657956682701558096 91247024938331090743438798945866534651922222519090748320381515854480347 31101690454685781999248641772509287801359980318348021809541131200479989 22079392594151856814372197299325182316616493333479662500817485143037796 6394594186901123322297453 isn't prime, and Maxima's primep function sez so. The number above is divisible by 271 and 13,597, but primep sez that even after dividing out these factors, the 1002-bit result 38894884397634366007356454548332370646972724268802781973440208895542936\ 165564656473524541403310393405820598366261673173802130771236325314878371830363\ 723788045821711985461441675679316058246609104355161134470046705337593170498462\ 616195650378975298117141144096886684800236261920005248055422089305813639519 still isn't prime. Does anyone have a fast factoring machine for 1000-bit numbers? http://www.theregister.co.uk/2016/02/03/socat_backdoor_fix/ Socat slams backdoor, sparks thrilling whodunit Year-old bug ruined crypto

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