Adventures in Mostly Calculus Mathematics by Richard Palmaccio

Author:Richard Palmaccio
Language: eng
Format: mobi, epub
Published: 2012-02-14T08:00:00+00:00

II. The Sphere in Two Dimensions

The two dimensional “sphere” is really a circle. Proceeding inductively, we add one more integral to compute the “volume”, which in this case is an area. Considering the equation

we solve it for y to determine the extent of the sphere in the y-direction for a given value of x between –R and +R. Figure 2 shows the 2-D “sphere”.

The only thing different here is the addition of the vertical axis. The “sphere” now extends from

in the vertical direction as well as from –R to R in the horizontal direction as was the situation in case I. To obtain the “volume” we integrate a square whose dimensions are dy by dx as follows.

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