## equations in the wiki

Higher-dimensional geometry (previously "Polyshapes").

### equations in the wiki

I thought I should start a thread where we can discuss the volumes and parametric equations in the wiki articles.

I'll start with a complaint about the Tetratorus. First, I still think it should be called a tritorus or a 3-torus, but I'll wait for Rob to come back before we argue about that.

The other thing is the surcell volume and bulk. I changed it from 4pi R r to 4pi R r a, and someone changed it back saying
Trust me, it isn't multiplied by a - there's a complex formula that cancels it out.

Who said that, and what's this complex formula that somehow gives you a volume measured in square meters?

Anyway, I've just calculated the integral directly with mathematica, and I get:
V = 8 pi^3 a r R
B = 4 pi^3 a^2 r R

So it turns out we were both wrong.

PWrong
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Ok, since noone replied, I assume it must have been Rob. I went and changed it anyway.

PWrong
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dude, how old are you guys? u guys go to college? what the heck is
V = 8 pi^3 a r R
B = 4 pi^3 a^2 r R?

heheh i go to elementary school
"Civilization is a race between education and catastrophe."
-H.G. Wells
papernuke
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V = 8 pi^3 a r R

Volume is equal to eight times pi (which is around 3.14) cubed (times itself twice...so three times as in pi times pi times pi) times "a" times "r" times "R" which are variables (symbols that stand for numbers that we plug in).

B = 4 pi^3 a^2 r R

Bulk is equal to four times pi cubed times "a" squared ("a" times itself) times "r" times "R".

I believe you learn that sort of thing in elementary school eventually. It's been so long, I don't even remember
houserichichi
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### Re: equations in the wiki

PWrong wrote:The other thing is the surcell volume and bulk. I changed it from 4pi R r to 4pi R r a, and someone changed it back saying
Trust me, it isn't multiplied by a - there's a complex formula that cancels it out.

Who said that, and what's this complex formula that somehow gives you a volume measured in square meters?

Sorry, that was me, I forgot to login. That's the problem with wikis, it doesn't force you to log in. >.<

And yea, the surcell volume has no a in it.

The tetratorus has two cells, one at (r+a) and one at (r-a). The volume of each is therefore:

outer cell: 4π<sup>2</sup>R(r+a)
inner cell: 4π<sup>2</sup>R(r-a)
total: 4π<sup>2</sup>R(r+a)+4π<sup>2</sup>R(r-a)
expanding: 4π<sup>2</sup>Rr+4π<sup>2</sup>Ra+4π<sup>2</sup>Rr-4π<sup>2</sup>Ra
simplification: 8π<sup>2</sup>Rr

Okay, maybe it wasn't 4πRr like I had on the page in the first place, but it DOES NOT have an a in it!

Keiji
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simplification: 8π<sup>2</sup>Rr

That's still not a volume, it's an area.

PWrong
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8π<sup>3</sup>Rr<sup>2</sup> then.

That makes sense, because I used the 3D solid cross-section of the tetratorus to work this out, and we all know multiplying by πr changes a line to a circle.

There's still no a.

Keiji
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Okay, now I feel stupid. There's originally an a SQUARED, because of A = πr<sup>2</sup>, and only one a cancels out, so that leaves the other a... So yes, it's 8π<sup>3</sup>Rra.

Keiji
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Pwned

Btw, I'll be back on Sunday night.

PWrong
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