How can I create a discrete function that generates a curve over n iterations that whose sum ( the aria under the curve if it was continuous ) is constant?

Answer 1

There is no way to use an evolutionary algorithm or some other software to figure out a curve with a specified aria under the curve? Note that the curve starts at some value between 1000 and 2000 and ends at zero so it would be like manipulating the shape of a soap bubble. (Answers.com didn't let me include that level of detail in my question - it kept giving me errors). If physicists can figure that out, why can't we figure out how to do it with a function?

Answer 2

It isn't quite clear what you mean with a constant area. The area below any curve of a specific size is constant. If you want to have definite integral (the area under a curve) always the same, independent of the size of the interval, this is only possible if the function is zero everywhere.