Search found 12 matches

by georgehorse
Sat Aug 07, 2010 2:16 pm UTC
Forum: Mathematics
Topic: Tiling a rectangle: Another surprisingly tricky problem
Replies: 45
Views: 6967

Re: Tiling a rectangle: Another surprisingly tricky problem

Call any 1*1 rectangle a unit square. Then any improper rectangle will cover an uneven number of unit squares whereas any proper rectangle will cover an even number of unit squares. What about the proper 1x1 rectangle? Or 1x3? I think 'even' is meant to be read as 'a whole number', not 'divisible b...
by georgehorse
Sun Jul 18, 2010 3:28 am UTC
Forum: Mathematics
Topic: Mrs. Perkins' beehive
Replies: 3
Views: 867

Re: Mrs. Perkins' beehive

My bad. It makes much more sense for me to think about these things in terms of density and thus areas rather than side lengths. And so that's what I assumed your numbers were.
by georgehorse
Sun Jul 18, 2010 3:01 am UTC
Forum: Mathematics
Topic: Mrs. Perkins' beehive
Replies: 3
Views: 867

Re: Mrs. Perkins' beehive

You can get sqrt(3)/4 (about 0.433) by being what I would think is even less clever.
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by georgehorse
Sun Jul 18, 2010 2:44 am UTC
Forum: News & Articles
Topic: Econophysics
Replies: 45
Views: 5275

Re: Econophysics

In this context, it most likely means a perfect free market, no government interference at all. Other assumptions are probably that all agents are perfectly rational and a very large (possibly infinite) number of suppliers and buyers. But you'd have to read the article to see what assumptions exact...
by georgehorse
Wed May 20, 2009 5:32 am UTC
Forum: Mathematics
Topic: Quick question on homeomorphism.
Replies: 10
Views: 1086

Re: Quick question on homeomorphism.

To be fair, I think topologists are as bad as it gets in terms of inconsistent definitions.

http://en.wikipedia.org/wiki/History_of_the_separation_axioms for an example.
by georgehorse
Wed May 20, 2009 5:26 am UTC
Forum: Mathematics
Topic: Quick question on homeomorphism.
Replies: 10
Views: 1086

Re: Quick question on homeomorphism.

I believe he meant: if f : X -> Y is a continuous bijection, X is compact, and Y is Hausdorff, then f is a homeomorphism.
by georgehorse
Tue May 12, 2009 11:10 am UTC
Forum: Mathematics
Topic: AP Calc BC 2009
Replies: 17
Views: 2801

Re: AP Calc BC 2009

Slightly off topic, but is anyone else bitter about the racket the test people and Texas Instruments have going? At least when I took the test, a few years ago, you only actually needed a TI-8x for about 3 questions, and that was only because they asked you to evaluate an integral from .9254 to 1.52...
by georgehorse
Tue May 12, 2009 11:02 am UTC
Forum: Mathematics
Topic: Converting Circle Function to Ellipse
Replies: 2
Views: 629

Re: Converting Circle Function to Ellipse

One way to think about trig functions that isn't instantly related to circles or triangles has to do with the solution to certain integrals or differential equations, since the functions satisfy some nice (differential) equations: \frac{d}{dx}\sin{x} = \cos{x} and \cos^{2}{x} = 1 - \sin^{2}{x} , or ...
by georgehorse
Tue May 12, 2009 6:17 am UTC
Forum: Language/Linguistics
Topic: Nature and languages
Replies: 80
Views: 6663

Re: Nature and languages

Bobber wrote:According to this pie chart, 29% of English comes from French... you could argue that this is a biiiiiit more than a sound and some affices :D

That's just origins of words though...all those French words are pronounced and modified grammatically as part of a predominately Germanic language.
by georgehorse
Sat Jul 05, 2008 4:43 am UTC
Forum: Coding
Topic: Non-Root chroot()
Replies: 5
Views: 1451

Re: Non-Root chroot()

You can't make a chroot() call without being root for security reasons (if you could, you can trivially get root with a fake /etc/passwd and so on).
by georgehorse
Fri Jun 20, 2008 3:13 am UTC
Forum: Mathematics
Topic: Intersecting solids
Replies: 6
Views: 1271

Re: Intersecting solids

The two points on each cylinder define a line through the center of the cylinder.

What you want to figure out is the distance between those two lines, and then how that distance relates to the intersection of those cylinders.

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