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[math-fun] Factors of Mersenne Numbers
by Guy Haworth 24 Jan '05

24 Jan '05

http://www.mersenne.org/ecmm.htm sheds some light. I sent my table of 'Mersenne Numbers: Consolidated Results' for M(p) with p < 130,000 or so to the Maths Comp. UMT via the late Dan Shanks. This has first factors, 2kp+1, indicating 'k' only. Guy

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[math-fun] Rotor-router article
by Michael Kleber 23 Jan '05

23 Jan '05

Hello Jim (and math-fun) : Mathematical Intelligencer 27#1 has hit finer newsstands near you, which means I can now post my rotor-router article on the web. At the moment it's linked to from my Brandeis home page -- I'll work on getting it up on the arXiv, but I think that will require human intervention, since it comes out as a 1 Meg pdf file (mostly due to its containing a picture of the 3 million bug blob), far larger than their usual size limit. My publications list, with "Goldbug Variations" at the top, is at http://people.brandeis.edu/~kleber/pubs.html There's also a link to just download/view the blob picture alone. Jim, you are of course welcome to pass the word on to your usual list of people interested in quasi-randomness. Enjoy! --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] Mersenne divisors
by David Wilson 21 Jan '05

21 Jan '05

Where can I find a list of divisors for completely factored Mersenne numbers?

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[math-fun] most complicated variation on something like a rubic's cube?
by Ray Tayek 20 Jan '05

20 Jan '05

hi, one of the screen savers on my linux box caught my eye, since it was a box doing some strange and improbable rotations of parts of itself (the box looked like something out of some horror movie). so i was curious if anyone had figured out what limitations there were on some geometric solid that could actually be built with actual mechanical (rigid i guess) parts and what geometric shape if any would have the most states or some other measure of complexity. just a thought. thanks --- ray tayek <http://tayek.com/>, co-chair <http://www.ocjug.org/>, actively seeking telecommuting work.

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[math-fun] Spherical trig
by Don Reble 20 Jan '05

20 Jan '05

Given the three angles (A, B, C) of a spherical triangle, what's the radius (r) of the inscribed circle? My reference books are eager to tell me the radius of the circumcircle, or provide the inscribed radius if I know the three sides. Of course, one can get the sides from the angles, and do it that way. But Euclidean triangles have such a nice formula, area / r^2 = cot(A/2) + cot(B/2) + cot(C/2) you'd think there's a nice spherical formula, too. Anyway, I worked it out. For future reference: let u = sin^2 (A/2), v = sin^2 (B/2), w = sin^2 (C/2), p = uvw, q = uv+vw+wu, s = u+v+w -1 + 2s - s^2 + 4p Then sin^2 r = ------------------ 3 - 2s - s^2 + 4q That's satisfactorily symmetric, but still somewhat ugly. Is there a better formula? -- Don Reble djr(a)nk.ca

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[math-fun] Suggestion for Mathworld
by David Wilson 20 Jan '05

20 Jan '05

Eric once gave me the address for Mathworld suggestions/submissions but I have lost it. :-( Anyway, I wanted to suggest Voderberg Tile and Voderberg Spiral be added to Mathworld. The Wolfram site itself has examples.

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[math-fun] Re: harmonic sum
by James Propp 19 Jan '05

19 Jan '05

>I've always used Harmonic Sum for xy/(x+y). >I can't say what "standard" is. >It does violate the heuristic that any kind of sum operation >should exceed its inputs. (x+y)/(1+xy) might be called the "relativistic sum" of x and y (since this is how velocities add in special relativity). Does this operation arise in other places? Note that (x+y)/(1+xy) = tanh (arctanh x + arctanh y). Jim Propp

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[math-fun] Harmonic Sum
by Richard Schroeppel 19 Jan '05

19 Jan '05

I've always used Harmonic Sum for xy/(x+y). I can't say what "standard" is. It does violate the heuristic that any kind of sum operation should exceed its inputs. Rich rcs(a)cs.arizona.edu

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Re: [math-fun] ~s harmonic sum?
by Mike Stay 19 Jan '05

19 Jan '05

RWG wrote: > What is the conventional name for 1/(1/x+1/y)? Don't know. Perhaps capacitive sum (since capacitors in series follow that addition law)? Parallel sum (since resistors in parallel follow that addition law)? The paper "Associativity of the Secant Method" by Sam Northshield refers to this sum. Given a function f, define x oplus y = ( x f(y) - y f(x) )/( f(y)-f(x) ) If f has a pole at e, then define p(x) = f(x)(x-e); otherwise p(x)=f(x). If f has a pole at e, then define z=e; otherwise z=+inf. The homomorphism F(x oplus y) = F(x)+F(y) holds if F'=1/p and F(z)=0. oplus is the capacitive sum for f(x)=x^2, and F(x)=-1/x. oplus is the nirmal sum when f(x)=1/x. oplus is multiplication when f(x) = x/(1-x), and F(x) = ln x. atan is a homomorphism for f(x) = (x^2+1)/x. etc. -- Mike Stay staym(a)clear.net.nz http://www.cs.auckland.ac.nz/~msta039

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[math-fun] ~s harmonic sum?
by R. William Gosper 19 Jan '05

19 Jan '05

What is the conventional name for 1/(1/x+1/y)? (Twice the harmonic mean.) A few dubious websites call this "harmonic sum", but most waste that term on harmonic numbers. --rwg disharmony <-> hydramnios

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