Hi i am investigating a parbelos, which is like a arbelos, except instead of two semi circles inscribing a large semi-circle, the semicircles are replace with parabolas. I am trying to come up with a general case for the perimeter and area of the parbelos, i have determined as you move C on baseline AB towards the extremities, the area decreases, while the perimeter increases. There is a formula that calculates the area of a parabola in terms of height and width, i.e. (2/3)hw=Area, but this cannot be generalised. Any Ideas?
How do i come up with a general case for the area and perimeter of a parbelos?
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