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[math-fun] Unstoppable Brilliance: Irish Geniuses and Asperger's Syndrome
by Bill Gosper 30 Apr '17

30 Apr '17

Carolyn (Neil B's mom) and Jon (Julian & Corey Z H's dad) highly recommend The Curious Incident of the Dog in the Nighttime (coming to San Francisco in June). --rwg Date: 2017-04-16 16:54 From: Fred Lunnon <fred.lunnon(a)gmail.com> Having spent my professional life around comp. science and maths departments, I noticed decades ago that any "neurotypical" individual happening to stray into such realms stood out like a proverbial sore thumb. The introduction of this book reads like a personality test checklist for their academic denizens --- I found myself nodding in recognition sufficiently often to qualify under "repetitive behaviour" --- in addition, that is, to a substantial proportion of the remainder! WFL On 4/16/17, Douglas Rogers <dgrbgsu(a)gmail.com> wrote: > William Rowan Hamilton and more ... > > > * Michael Fitzgerald, Antoinette Walker > Unstoppable Brilliance: Irish Geniuses and Asperger's Syndrome > (liberties Press <http://www.libertiespress.com/>, Dublin, 2006) > <https://books.google.com/books?id=EU0xBwAAQBAJ> > > Michael Fitzgerald is Henry Marsh Professor of Child and Adolescent > Psychiatry > at Trinity College Dublin and is the leading expert on Asperger's syndrome > and > autism in Ireland. He has written extensively about these subjects and > addressed > national and international symposia on them. >

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[math-fun] Observation on 2^64
by David Wilson 30 Apr '17

30 Apr '17

18446744073709551616 = 1^844674407370955*16^16 There are also large numbers N with 1N72343 = 1^N*7^2343 1N36821221 = 1^N*36821^221 (concatenation on the left).

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[math-fun] Prime question
by David Wilson 30 Apr '17

30 Apr '17

As n grows, what is the limiting probability that n has a prime divisor >= sqrt(n)?

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Re: [math-fun] How does a dull spoon manage to cut a stringy pieceof meat
by Bill Gosper 29 Apr '17

29 Apr '17

> On Apr 28, 2017, at 9:57 AM, Bill Gosper <billgosper(a)gmail.com> wrote: > > What the heck are the correct names for grommetoid and (the simply > connected) grommetoidoid? Date: 2017-04-28 10:03 From: Dan Asimov <asimov(a)msri.org> To: math-fun <math-fun(a)mailman.xmission.com> Reply-To: math-fun <math-fun(a)mailman.xmission.com> >The word eyelet comes to mind. And to Neil B's mom's mind came eyestay. But that's Pig Latin for an ophthalmic condition. (Damn those esoteric doctors). >Or, check out this picture: http://3.bp.blogspot.com/-en07ThXYeUY/TYArIkKeuAI/AAAAAAAAFGk/K6bTVrUXfTg/s… < http://3.bp.blogspot.com/-en07ThXYeUY/TYArIkKeuAI/AAAAAAAAFGk/K6bTVrUXfTg/s… >. >—Dan Bingo: Four pairs of D-rings plus two pairs of hooks, in combination. Perfect! --rwg Wait a minute, aren't those parts of a cyclotron?

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[math-fun] sinh/asinh numbers & positional notation
by hbaker1 24 Apr '17

24 Apr '17

(Please read the following as a not-very-precise set of intuitions; I haven't been able to work out all of the details.) One thing that I forgot to say about sinh/asinh representation is the potential symmetry in "positional" representation. This symmetry is more easily seen in the "binary" version of sinh: sinh2(x)=(2^x-2^-x)/2 sinh2(k)=(2^k-2^-k)/2, k a positive integer =a long string of 1's in binary positional notation. and cosh2(x)=(2^k+2^-k)/2 So the output of cosh2(x) should -- in general -- be a *palindrome* in a "suitable" positional notation. Knuth discusses "balanced" positional notations, in which the digits 0-9 are replaced by -5..+5; these representations are often utilized in hardware multipliers to reduce the amount of circuitry required. Are there number representations which make the palidromic nature of cosh2(x) obvious? Once we have such a representation, then we can consider sinh2(x), which will have a similar type of anti-palidromic representation. We should be able to decompose *any* number into a sum(?) of elementary anti-palindromes.

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[math-fun] sinh/asinh numbers & positional notation
by hbaker1 24 Apr '17

24 Apr '17

(Please read the following as a not-very-precise set of intuitions; I haven't been able to work out all of the details.) One thing that I forgot to say about sinh/asinh representation is the potential symmetry in "positional" representation. This symmetry is more easily seen in the "binary" version of sinh: sinh2(x)=(2^x-2^-x)/2 sinh2(k)=(2^k-2^-k)/2, k a positive integer =a long string of 1's in binary positional notation. and cosh2(x)=(2^k+2^-k)/2 So the output of cosh2(x) should -- in general -- be a *palindrome* in a "suitable" positional notation. Knuth discusses "balanced" positional notations, in which the digits 0-9 are replaced by -5..+5; these representations are often utilized in hardware multipliers to reduce the amount of circuitry required. Are there number representations which make the palidromic nature of cosh2(x) obvious? Once we have such a representation, then we can consider sinh2(x), which will have a similar type of anti-palidromic representation. We should be able to decompose *any* number into a sum(?) of elementary anti-palindromes.

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Re: [math-fun] Trig question
by Dan Asimov 23 Apr '17

23 Apr '17

Yes, it's very interesting, and if I get any time soon I will write up why. —Dan ----- Is there anything mathematically interesting about the function f(a, b) = arctan(tan(a) + tan(b))? -----

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[math-fun] Simplified division?
by David Wilson 22 Apr '17

22 Apr '17

Given 64-bit unsigned integer n and 0 <= k <= 63, can floor(n/(1 + 2^-k)) be computed more quickly than by general integer division?

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[math-fun] Trig question
by David Wilson 21 Apr '17

21 Apr '17

Is there anything mathematically interesting about the function f(a, b) = arctan(tan(a) + tan(b))?

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[math-fun] Discrete Log Webpage
by rcs＠xmission.com 21 Apr '17

21 Apr '17

For those of us interested in the discrete log problem for finite fields, a new page summarizing progress. --rcs --- From: Laurent Grémy <laurent.gremy(a)inria.fr> To: NMBRTHRY(a)LISTSERV.NODAK.EDU Subject: Database of computations of discrete logarithms Dear Number Theorists, We are pleased to present the discretelogdb project. The aim of this project is to list all the computations of discrete logarithms in finite fields of any characteristic, with references. We have chosen to list the complete computations (with an individual logarithm computation of a given target in the considered finite field). We have obviously used the announcements send on this list, and also the research articles that report such computations. To consult the data we have collected, you can take a look at the website https://members.loria.fr/LGremy/dldb/index.html If you find wrong data or want to supplement the data we have, you are welcome to go to https://gitlab.inria.fr/dldb/discretelogdb and follow the CONTRIBUTING readme to improve the database. Thanks in advance for your contributions. Best regards. Laurent Grémy and Aurore Guillevic

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