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February 9th, 2015, 12:04 AM   #1
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torus surface

I see two gaps on my torus.

My range was 1..64, so I changed it to 0..64. It fixed the surface but the problem with that is my sum doesn't equal zero.
[sin(2*Pi*x*(1/64))*(7/8+(5/*cos(2*Pi*y*(1/64)))+cos(2*Pi*x*(1/64))*(7/8+(5/*cos(2*Pi*y*(1/64)))+(5/*sin(2*Pi*y*(1/64))]

sum 1..64=0
sum 0..64=115/2
sum -64..64=227/2

I consistently find that these types of functions will always equal zero from 1..n. When I go into hyperspheres it continues to equal 0. Sometimes one of the two other options will equal zero, but 1..n always seems to work.

So did I break topology in anyway or do they not consider this sort of thing important?
Attached Images
 torus lines.jpg (21.2 KB, 23 views)

Last edited by tejolson; February 9th, 2015 at 12:07 AM.

 February 21st, 2015, 07:42 AM #2 Math Team   Joined: Jan 2015 From: Alabama Posts: 3,261 Thanks: 894 I've looked at this over and over again but still can't decide what you are doing! What do the different colors indicate? What does "[sin(2*Pi*x*(1/64))*(7/8+(5/*cos(2*Pi*y*(1/64)))+cos(2*Pi*x*(1/64))*(7/8+(5/*cos(2*Pi*y*(1/64)))+(5/*sin(2*Pi*y*(1/64))]" mean? Where did you get that?

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