Re: [math-fun] How we "do mathematics"
----- Original Message ---- From: David Gale <gale@math.berkeley.edu> To: math-fun <math-fun@mailman.xmission.com> Sent: Thursday, August 9, 2007 3:17:48 AM Subject: RE: [math-fun] How we "do mathematics" ...
A (very) old one I like :
Two Death Valley marathonians friends complete their run together and seek shadow in their tent nearby the finish line.
The first one had prepared a fresh 5-liter tank of water in a cooling box and his friend a similar 3-liter one.
They were about to start drinking when a journalist enters the tent desperately asking for water.
OK, the water is divided into three equal parts -- and drunk.
The thankful journalist insists to pay his share and leaves 8 dollars to be split between the two friends.
How?
----
Why is this problem so fascinating? The two friends are paid $8. The guy who contributed 5 l gets $5, and the guy who contributed 3 l gets $3. Or maybe the $8 goes towards paying for their campsite. I must be missing something. Gene ____________________________________________________________________________________ Pinpoint customers who are looking for what you sell. http://searchmarketing.yahoo.com/
You are missing something. That's what makes it a good problem. Since it was Eric's problem I don't feel I should be the spoiler but will send the solution to anyone privately. dg At 10:02 AM 8/9/2007, you wrote:
----- Original Message ---- From: David Gale <gale@math.berkeley.edu> To: math-fun <math-fun@mailman.xmission.com> Sent: Thursday, August 9, 2007 3:17:48 AM Subject: RE: [math-fun] How we "do mathematics" ... >A (very) old one I like : > >Two Death Valley marathonians friends complete their run >together and seek shadow in their tent nearby the finish >line. > >The first one had prepared a fresh 5-liter tank of water >in a cooling box and his friend a similar 3-liter one. > >They were about to start drinking when a journalist enters >the tent desperately asking for water. > >OK, the water is divided into three equal parts -- and drunk. > >The thankful journalist insists to pay his share and leaves >8 dollars to be split between the two friends. > >How? > >---- Why is this problem so fascinating? The two friends are paid $8. The guy who contributed 5 l gets $5, and the guy who contributed 3 l gets $3. Or maybe the $8 goes towards paying for their campsite. I must be missing something. Gene ____________________________________________________________________________________ Pinpoint customers who are looking for what you sell. http://searchmarketing.yahoo.com/
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
Funsters, Some months ago (if I recall correctly) a post on Math-Fun posed a nice visualization puzzle about what the cross section is when a Menger's sponge is sliced on a plane that is the perpendicular bisector of a long diagonal. I have since made a physical model of the answer and put photos of it on this page: (about half-way down) http://www.georgehart.com/rp/rp.html I'd like to add a credit line to the web page, citing whoever first posed this. If you know, please let me know. George http://www.georgehart.com P.S. Some photos you might like of workshops I did in January: http://www.georgehart.com/Japan http://www.georgehart.com/athens
I think I might have posted a link to this image on Sebastien Perez Duarte's photostream http://flickr.com/photos/sbprzd/1432723128/ On Feb 1, 2008 3:18 PM, George W. Hart <george@georgehart.com> wrote:
Funsters,
Some months ago (if I recall correctly) a post on Math-Fun posed a nice visualization puzzle about what the cross section is when a Menger's sponge is sliced on a plane that is the perpendicular bisector of a long diagonal. I have since made a physical model of the answer and put photos of it on this page: (about half-way down)
http://www.georgehart.com/rp/rp.html
I'd like to add a credit line to the web page, citing whoever first posed this. If you know, please let me know.
George http://www.georgehart.com
P.S. Some photos you might like of workshops I did in January: http://www.georgehart.com/Japan http://www.georgehart.com/athens
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
-- Thane Plambeck tplambeck@gmail.com http://www.plambeck.org/ehome.htm
Since a Penrose tiling is a slice through a regular grid at a slope of (phi, 1/phi) and the holes in a (finite-iteration) Menger sponge effectively just join together some of the cells, can we get a doubly-fractal tiling out of such a slice? -- Mike Stay - metaweta@gmail.com http://math.ucr.edu/~mike http://reperiendi.wordpress.com
participants (5)
-
David Gale -
Eugene Salamin -
George W. Hart -
Mike Stay -
Thane Plambeck