This is a question regarding how to calculate the area of a circle occupied by a rectangle when that rectangle is larger than the circle (see this link for a example image http://i57.tinypic.com/30297hh.jpg). I made a first post here: Area of Circle Overlapped by Rectangle, where "achille hui" was nice enough to point out a way of calculating this value.
However, I have noticed that when the radius of the circle is very close to half the width of the rectangle, a smaller circle actually means the final percentage value is smaller (which should not be the case, correct?).
Examples:
With a rectangle of $2$ units tall and $0.8$ units wide, using the formula:
percentage = $(((2*(\text{diameter}) + (2*\sqrt{\text{radius}^2 - 0.4^2} ) ) / 3) * 0.8) / (\pi*\text{radius}^2)$
) A circle with radius $0.810687473$ yields a result of: $0.60096155$, ~$60.1$%.
) A circle with radius $0.436310160932088$ yields a result of: $0.933587972813617$, ~$93.4$%.
) Yet a circle with radius $0.414496705$ yields a result of: $0.926510065$, ~$92.7$%. Shouldn't this percentage be higher?
So I'm not sure how to account for this (and to be honest don't understand why this is happening). Though I think when the radius of the circle is equal to or less than the width of the rectangle the area covered should be 100% (in this case, am I correct?). Any ideas area appreciated, thank you for reading.