Timeline for What's a nice argument that shows the volume of the unit ball in $\mathbb R^n$ approaches 0?
Current License: CC BY-SA 2.5
6 events
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| Dec 10, 2009 at 17:37 | history | edited | Greg Kuperberg | CC BY-SA 2.5 |
added 82 characters in body
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| Dec 10, 2009 at 17:27 | comment | added | Greg Kuperberg | Right. Although so did Fedja. | |
| Dec 10, 2009 at 17:10 | comment | added | Reid Barton | In other words, you showed that the statement is true for n-spheres of any fixed radius, not just radius 1. | |
| Dec 10, 2009 at 17:07 | history | edited | Reid Barton | CC BY-SA 2.5 |
replace d
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| Dec 9, 2009 at 13:57 | comment | added | Michael Lugo | Because I like optimizing constants: h = 1/3 is not the best possible choice. However, for h = 1/3 we get that 2h/(1-(1-h^2)^(d/2)) < 1 for d > 18.654. The best possible d is around 18.295, which we get for h near 0.375. (No, not h = 3/8.) But no choice of h brings this critical d as low as 18. | |
| Dec 9, 2009 at 0:27 | history | answered | Greg Kuperberg | CC BY-SA 2.5 |