Area of a circle each polygon side is a radius, of length "r". And since the total side length is greater than the circumference, the polygon consists of "n" identical triangles with total area greater than "T". Again we have a contradiction, so our supposition that "C" might be less than "T" must be wrong as well. Therefore, it must be the case that the area enclosed by the circle is precisely the same as the area of the triangle. This concludes the proof. Following Satō Moshun and Leonardo da Vinci , we can use inscribed regular polygons in a different way. Suppose we
Instant centre of rotation and P-B. The direction of speed of point A is indicated by vector V. Its instant center of rotation must be perpendicular to this vector (as V is tangentially located on the circumference of a circle). The only line that fills the requirement is a line colinear with link P-A. Somewhere on this line there is a point P, the instant center of rotation for the body BAC. What applies to point A also applies to point B, therefore this instant center of rotation P is located on a line perpendicular to vector V, a line colinear with link P-B.