[math-fun] Electrocuted figures
To determine the area of most plane figures, one needs to place a ruler precisely on the plane. For example, for a circle, the easiest method is by ensuring it passes directly through the centre. For a square, it should be parallel to one of the sides, or pass through two vertices, et cetera. However, suppose the person required to determine the area is being electrocuted, so they cannot control precisely (to within epsilon) the position and orientation of the ruler. It is a remarkable fact that the area of any annulus can still be determined whilst being electrocuted. Indeed, as long as the ruler is dropped such that it intersects the inner circle of the annulus, the following formula works: Area = pi*a*b, where a and b are the distances from an intersection of the ruler with the inner circle to the intersection points of the ruler with the outer circle. (The reason this works is as a result of the power of a point theorem.) Are there any other *interesting* 'electrocuted figures'? Sincerely, Adam P. Goucher
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Adam P. Goucher