Open thread, Jan. 16 - Jan. 22, 2016

MrMind

If it's worth saying, but not worth its own post, then it goes here.

Notes for future OT posters:

1. Please add the 'open_thread' tag.

2. Check if there is an active Open Thread before posting a new one. (Immediately before; refresh the list-of-threads page before posting.)

3. Open Threads should start on Monday, and end on Sunday.

4. Unflag the two options "Notify me of new top level comments on this article" and "Make this post available under..." before submitting.

If it's worth saying, but not worth its own post, then it goes here.

Notes for future OT posters:

1. Please add the 'open_thread' tag.

2. Check if there is an active Open Thread before posting a new one. (Immediately before; refresh the list-of-threads page before posting.)

3. Open Threads should start on Monday, and end on Sunday.

4. Unflag the two options "Notify me of new top level comments on this article" and "Make this post available under..." before submitting.

OK, I had dropped this for a while, but here are my thoughts. I haven't scrubbed everything that could be seen through rot13 because it became excessively unreadable

For Part 1: gur enqvhf bs gur pragre fcurer vf gur qvfgnapr orgjrra bar bs gur qvnzrgre-1/2 fcurerf naq gur pragre.

Gur qvfgnapr sebz gur pragre bs gur fvqr-fcurer gb gur pragre bs gur birenyy phor vf fdeg(A)/4. Fhogenpg bss n dhnegre sbe gur enqvhf bs gur fcurer, naq jr unir gur enqvhf bs gur pragre fcurer: (fdeg(A)-1)/4. Guvf jvyy xvff gur bhgfvqr bs gur fvqr-1 ulcrephor jura gung'f rdhny gb n unys, juvpu unccraf ng avar qvzrafvbaf. Zber guna gung naq vg jvyy rkgraq bhgfvqr.

Part 2: I admit that I didn't have the volume of high-dimensional spheres memorized, but it's up on wikipedia, and from there it's just a matter of graphing and seeing where the curve crosses 1, taking into account the radius formula derived above.. I haven't done it, but will eventually.

Part 3 looks harder and I'll look at it later.