Trim a convex shape
By picking 2 points on the perimeter of a 2D shape that are no more than 1 unit apart and connecting them with a straight line, a cut can be made, dividing the shape into 2 parts. The part with more area is kept. Starting with a 3x3 square, can at least half its area be removed within 100 cuts?
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1 solution
Even on a circle with no sharp corners to cut, the area between a chord of length 1 and the minor arc next to it is sqrt(r^2-1)/2-2sqrt(2(r-2))+r^2 ∗ arcsin(1/r)/2, and cutting the corners off the square will allow it to fit within a circle of radius sqrt((3-sqrt(2))^2+9)/2.