Comments on: Alexander Horned Sphere http://www.arsmathematica.net/archives/2008/01/12/alexander-horned-sphere/ Dedicated to the mathematical arts. Sat, 30 Aug 2008 12:13:24 +0000 http://wordpress.org/?v=2.5.1 By: Walt http://www.arsmathematica.net/archives/2008/01/12/alexander-horned-sphere/#comment-58237 Walt Wed, 16 Jan 2008 04:22:13 +0000 http://www.arsmathematica.net/archives/2008/01/12/alexander-horned-sphere/#comment-58237 Condom usage is an applied science, Robert. Try it, and let us know how it works out. Condom usage is an applied science, Robert. Try it, and let us know how it works out.

]]> By: Jacob Freeze http://www.arsmathematica.net/archives/2008/01/12/alexander-horned-sphere/#comment-58236 Jacob Freeze Wed, 16 Jan 2008 03:57:13 +0000 http://www.arsmathematica.net/archives/2008/01/12/alexander-horned-sphere/#comment-58236 Setting up Alexander's Horned Sphere in the context of rubber bands and balloons and then revealing that the analogy or image or whatever really makes no sense whatsoever... What's it like? It's like something... Oh yeah. Since Alexander's sphere was inspired by Antoine's necklace, and Antoine was a blind WWI veteran, you might say the <em>excellent</em> pedagogical device with the rubber bands is sort of like offering to help a blind veteran across the street, and then pushing him under a bus. Setting up Alexander’s Horned Sphere in the context of rubber bands and balloons and then revealing that the analogy or image or whatever really makes no sense whatsoever…

What’s it like? It’s like something…

Oh yeah. Since Alexander’s sphere was inspired by Antoine’s necklace, and Antoine was a blind WWI veteran, you might say the excellent pedagogical device with the rubber bands is sort of like offering to help a blind veteran across the street, and then pushing him under a bus.

]]> By: robert young http://www.arsmathematica.net/archives/2008/01/12/alexander-horned-sphere/#comment-58227 robert young Mon, 14 Jan 2008 13:04:08 +0000 http://www.arsmathematica.net/archives/2008/01/12/alexander-horned-sphere/#comment-58227 Does this apply to condoms? Does this apply to condoms?

]]> By: John Armstrong http://www.arsmathematica.net/archives/2008/01/12/alexander-horned-sphere/#comment-58219 John Armstrong Sun, 13 Jan 2008 04:39:03 +0000 http://www.arsmathematica.net/archives/2008/01/12/alexander-horned-sphere/#comment-58219 The proof that you have to surreptitiously cut up the balloon is almost more interesting than the proof that the horned sphere exists in the first place. Make the rubber band into a perfectly thin one (as well as flat) and look at the sheet it traces out as you slide it off the original, round balloon. Now, as you twist up the balloon (without cutting it) you also twist up that sheet. At the end you have the path telling you how to remove the band from the balloon. Thus in order to make it so you have to cut the band, you have the cut the balloon. The proof that you have to surreptitiously cut up the balloon is almost more interesting than the proof that the horned sphere exists in the first place. Make the rubber band into a perfectly thin one (as well as flat) and look at the sheet it traces out as you slide it off the original, round balloon. Now, as you twist up the balloon (without cutting it) you also twist up that sheet. At the end you have the path telling you how to remove the band from the balloon. Thus in order to make it so you have to cut the band, you have the cut the balloon.

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