adrian is rad


toilet paper calculus

Filed under: — adrian @ 2:42 pm

The other day I started realized that toilet paper is pretty non-linear. (As I’m not the first person to point out.) The last part of the roll disappears a lot quicker than the start because each sheet makes up more and more of a warp around the roll.

I decided to do some calculations and make it real by measuring (using my awesome new Mitutoyo calipers I love) a roll of 350 sheet two-ply toilet paper I have here.

Conceptually one can look at it as a series of concentric shells of radius Rn and length 2*pi*Rn. A roll with no center tube looks like:

L = pi*R^2/T + pi*R

where L is the length of paper, R is the radius, T is the paper thickness.


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