August 2003 - mathfun@mailman.xmission.com

[math-fun] A complex numbers ...
by Jon Perry 12 Aug '03

12 Aug '03

What is the term for the relation of (a+bi) and (c+di), both complex numbers, where, given a+bi, (a+bi)(c+di) = x or = iy i.e., is either pure real or pure imaginary? I came up with the 'realization' or the 'imagination'. 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

1 0

[math-fun] sin/cos/tan
by Jon Perry 12 Aug '03

12 Aug '03

Anyone out there can come up with a comment on the symmetric nature of sin, cos and tan? sin(x)=sin(-x) etc... 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

3 3

Re: [math-fun] Words
by Dan Hoey 12 Aug '03

12 Aug '03

Kerry <lkmitch(a)att.net> writes: > There's a 540-word variation on the "A man, a plan, a canal--Panama." > palindrome here: > http://www.jy-muggeridge.freeserve.co.uk/pals_hoey.htm A more complete version of the story is at http://nielsenhayden.com/hoey.html and an interesting newer development at http://www.norvig.com/palindrome.html in case you're interested. Dan

1 0

Re: [math-fun] Words
by lkmitch＠att.net 12 Aug '03

12 Aug '03

There's a 540-word variation on the "A man, a plan, a canal--Panama." palindrome here: http://www.jy-muggeridge.freeserve.co.uk/pals_hoey.htm Kerry -- lkmitch(a)att.net www.fractalus.com/kerry

2 1

[math-fun] Words
by Richard Guy 11 Aug '03

11 Aug '03

I recently ran across a word problem, which I vaguely remember from years ago, and which (evidently) has the solution S T A R T L I N G S T A R L I N G S T A R I N G S T R I N G S T I N G S I N G S I N I N I Does anyone know of similar (longer?) examples? R.

9 11

[math-fun] Word
by asimovd＠aol.com 11 Aug '03

11 Aug '03

A friend recently taught me the following word (I don't know the source), which fits perfectly with the old MIT college complaint we would occasionally express about "the perversity of inanimate objects". resistentialism (reh.zis.TEN.shul.iz.um) n. The belief that inanimate objects have a natural antipathy toward human beings, and therefore it is not people who control things, but things which increasingly control people. --Dan

1 0

Re: [math-fun] Words
by Mike Stay 11 Aug '03

11 Aug '03

Not exactly what you meant, but a "knotted word" nonetheless: http://www.xaim.com/staym/art/mom's%20name.jpg http://www.xaim.com/staym/art/decode.gif ----- Original Message Follows ----- > Eckler is also a frequent contrbutor to www.wordways.com, > which has some good web accessible articles > > I like this observation, also due to Eckler apparently, > that the 26 neighbors of a lattice point in Z3 invite a > person to assign letters to the directions and then start > looking for knotted words. > > http://www.wordways.com/knotted.htm > > Thane Plambeck > 650 321 4884 office > 650 323 4928 fax > http://www.qxmail.com/ehome.htm -- Mike Stay staym(a)clear.net.nz http://www.xaim.com/staym

1 0

[math-fun] forward from a lifelong Mersennary
by R. William Gosper 11 Aug '03

11 Aug '03

Dr. Gosper, You math list might find the following announcement that I sent to Dr. Caldwell (of <A HREF="http://www.utm.edu/research/primes/">Prime Pages</A> fame) concerning a new lower factor bound for c5: http://www.isthe.com/chongo/tech/math/prime/index.html#c5 In particular: I am pleased to report a new lower factor bound for c5 = 2^(2^127-1)-1. I have confirmed my previous lower factor bound: http://www.utm.edu/research/primes/mersenne/index.html#c that I made when I was working at SGI. In addition, I have extended that result and have determined that c5 has no prime factor < 1e51. I used calc version 2.11 http://www.isthe.com/chongo/tech/comp/calc/index.html) running on AMD Athlon processors to verify and extend my previous result. Here is a quote that may be apt for index.html#c web page: Finding a factor of c5 will be a long shot. "Happiness is just around the corner" was one of the encouragements that Dr. Lehmer used to give to those who were deep in computational quests. Nevertheless the hope for finding c5 happiness is softened somewhat by the fact that c5 has an intractable number of corners. Landon Curt Noll http://www.isthe.com/chongo

1 0

[math-fun] surprisingly hard knapsack puzzle
by R. William Gosper 11 Aug '03

11 Aug '03

Last month I had the pleasure to visit the Microsoft Theory Group. Mike Sinclair and Gary Starkweather in a neighboring group generously helped me laser-cut a puzzle consisting of an 8" circular tray and twelve unequal circular disks ranging from .86" to 2.8". To my amazement, *no one* has yet succeeded in fitting all twelve disks back into the tray, although Christian Borgs, a Microsoft physicist, solved two slightly easier versions, one of which, unfortunately, gave him the answer to the harder version. I believe the solution to the current version is unique, but my first "cut" neglected to allow for the .006" diameter of the laser beam, and this small amount of slop permitted at least three unintended solutions. The current version is fairly pleasant to see and work, and draws small crowds when worked in public. Thus it invites frequent and prolonged attacks, but protects itself with the "too many cooks" effect. This puzzle is also fairly resistant to computer solution--I'm not even sure how to quantify the combinatorics of the search. --rwg

1 0

Re: [math-fun] Words
by Jeffrey Shallit 11 Aug '03

11 Aug '03

Along the same lines, can anyone top A AN ANT ANTS ANTSY ? > From: Richard Guy <rkg(a)cpsc.ucalgary.ca> > To: Math Fun <math-fun(a)mailman.xmission.com>, > Andrew Bremner <bremner(a)tulwar.la.asu.edu>, <bremner(a)asu.edu> > > I recently ran across a word problem, which I > vaguely remember from years ago, and which > (evidently) has the solution > > S T A R T L I N G > S T A R L I N G > S T A R I N G > S T R I N G > S T I N G > S I N G > S I N > I N > I > > Does anyone know of similar (longer?) examples? R.

3 2