Consider regular polygons with number of sides n = 3, 4, 5 ..... as shown in the figure. The center of mass of all the polygons is at height h from the ground. They roll on a horizontal surface about the leading vertex without slieeping and sliding as depicted. The maximum increase in height of the locus of the center of mass for each polygon is △ Then △ depends on n and h as
θ=π2−πhsinθ=cosπhl=hsinθΔ=l−h=h[1sinθ−1]=h=⎡⎢ ⎢ ⎢⎣1cosπh−1⎤⎥ ⎥ ⎥⎦