Question from Dustan, a student:
Anyways heres my question, I am working on a way to compute very accurate
areas for irregualr surfaces by using the idea of a largest possible cicrle,
I go in "generations" with gen1 being the circle of mamximun radius enclosed by
the bounds of the shape, gen2 is then all circles fomr r-->3r/4. I continue this and graph the results.
As gen goes higher and higher, the radius of the circles formed becomes less and less
but the number of circles formed continues to climb with each successive generation
(usually it takes up to gen 3 or 4 to see a deffinate exponextial increase).
After I graph the results, with r on the y axis and number of circles created on the x axis
my plan is then to integrate the curve. I want to integrate as far as possible to get as high of accuracy as possible,
and thats where the problem arrises, when r get small # of circles gets huge, but r can decrease indeffinatly right?
the circles get smaller and smaller and climb in numbers, how do I give a definate value to the integral of an infinatly decreasing curve? I was thinking about representing the largest
possible circle as a seires that converges to 0 but what is the formuls for a circle of largest possible radius within a closed irregular shape?
Im sorry if this is hard to follow, its finals week here in Idaho, so im kind of frazzled, please let me know what you think.