by Opus_723 » Tue Mar 26, 2013 5:24 pm
If you define emptiness to be the area between the top of the graph (assuming it doesn't go up to infinity), the y-axis, and the curve you are drawing, out to the x-value you're at, (like the poster above me) then I think it's still pretty simple. It's a differential equation that you can do in your head. Like everyone else said though, you can define "emptiness" however you like and get totally different answers.
Anyway, don't laugh if I did this wrong, but:
h= height of graph
E(x) = Empty area as defined above.
Then,
E(x) = Int(h-E(t))dt from 0 to x
Which leads to:
d/dx(E(x)) = h-E(x)
With initial condition E(0) = 0
(The graph can't be empty if the graph has no width)
So we just draw the curve:
E(x) = h-h*(e^-x)
Edit: And of course, we fill in the graph below this curve, if that wasn't clear.
Last edited by
Opus_723 on Tue Mar 26, 2013 5:58 pm, edited 1 time in total.