### Numerical Techniques

Today I began implementing some simple numerical differentiation and integration routines, applying them to some techniques found in differential geometry.

In the span of nearly three hours, I wrote a series of five programs. These programs must be run sequentially, as each uses the data of the previous program (except, of course, for the first which generates the data).

Five programs and three hours and I can successfully calculate the area of a sphere with radius 1.

Okay, so maybe I'm demeaning this process a little. My initial application was a unit sphere. But the first program can be modified to generate data for any kind of surface, and the remaining programs can find the area of said surface with little-to-no modification.

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