http://blogs.discovermagazine.com/cosmicvariance/2010/02/14/nothing-says-%e2%80%9ci-love-you%e2%80%9d-like-a-non-orientable-surface/ Random samplings from a universe of ideas. Fri, 25 May 2012 16:30:01 +0000 hourly 1 http://wordpress.org/?v=3.2.1 http://blogs.discovermagazine.com/cosmicvariance/2010/02/14/nothing-says-%e2%80%9ci-love-you%e2%80%9d-like-a-non-orientable-surface/comment-page-1/#comment-114113 Will Tue, 16 Feb 2010 15:42:39 +0000 http://blogs.discovermagazine.com/cosmicvariance/?p=4081#comment-114113 Thanks. Thanks.

]]> http://blogs.discovermagazine.com/cosmicvariance/2010/02/14/nothing-says-%e2%80%9ci-love-you%e2%80%9d-like-a-non-orientable-surface/comment-page-1/#comment-114108 Sean Tue, 16 Feb 2010 15:08:53 +0000 http://blogs.discovermagazine.com/cosmicvariance/?p=4081#comment-114108 <a href="http://en.wikipedia.org/wiki/Paracompact_space" rel="nofollow">Paracompact</a> is just a technical math term from topology. The major construction in topology is to introduce a collection of "open sets" that cover the space you're considering, with overlaps. Paracompactness excludes certain ugly-looking cases where points necessarily have an infinite number of open sets nearby. It's a much less restrictive condition than ordinary compactness -- a space can fail to be compact (i.e. it can go on forever), but still be paracompact. Paracompact is just a technical math term from topology. The major construction in topology is to introduce a collection of “open sets” that cover the space you’re considering, with overlaps. Paracompactness excludes certain ugly-looking cases where points necessarily have an infinite number of open sets nearby. It’s a much less restrictive condition than ordinary compactness — a space can fail to be compact (i.e. it can go on forever), but still be paracompact.

]]> http://blogs.discovermagazine.com/cosmicvariance/2010/02/14/nothing-says-%e2%80%9ci-love-you%e2%80%9d-like-a-non-orientable-surface/comment-page-1/#comment-114106 Will Tue, 16 Feb 2010 14:15:26 +0000 http://blogs.discovermagazine.com/cosmicvariance/?p=4081#comment-114106 Could you explain the "paracompact" bit, please? Could you explain the “paracompact” bit, please?

]]> http://blogs.discovermagazine.com/cosmicvariance/2010/02/14/nothing-says-%e2%80%9ci-love-you%e2%80%9d-like-a-non-orientable-surface/comment-page-1/#comment-114080 15 February 2010 « blueollie Mon, 15 Feb 2010 18:21:44 +0000 http://blogs.discovermagazine.com/cosmicvariance/?p=4081#comment-114080 [...] fun Yes, even nerds have fun on Valentines day. Roses are red. Violets are approximately blue. A paracompact manifold with a Lorentzian metric, [...] [...] fun Yes, even nerds have fun on Valentines day. Roses are red. Violets are approximately blue. A paracompact manifold with a Lorentzian metric, [...]

]]> http://blogs.discovermagazine.com/cosmicvariance/2010/02/14/nothing-says-%e2%80%9ci-love-you%e2%80%9d-like-a-non-orientable-surface/comment-page-1/#comment-114046 Mel Mon, 15 Feb 2010 05:10:48 +0000 http://blogs.discovermagazine.com/cosmicvariance/?p=4081#comment-114046 This is really creative and cute. Way to tie in the Valentines theme. This is really creative and cute. Way to tie in the Valentines theme.

]]> http://blogs.discovermagazine.com/cosmicvariance/2010/02/14/nothing-says-%e2%80%9ci-love-you%e2%80%9d-like-a-non-orientable-surface/comment-page-1/#comment-114040 Mark Mon, 15 Feb 2010 02:21:23 +0000 http://blogs.discovermagazine.com/cosmicvariance/?p=4081#comment-114040 In comic form: http://abstrusegoose.com/242 and http://spikedmath.com/175.html and http://xkcd.com/701/ In comic form:
http://abstrusegoose.com/242
and
http://spikedmath.com/175.html
and
http://xkcd.com/701/

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