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
Measurement of a Circle be produced by an iterative geometrical construction suggested by Archimedes' Stomachion in the setting of the regular dodecagon. In this case, the task is to give rational approximations to the tangent of π/12. Measurement of a Circle Measurement of a Circle or Dimension of the Circle (Greek: , "Kuklou metrēsis") is a treatise that consists of three propositions by Archimedes, ca. 250 BCE. The treatise is only a fraction of what was a longer work. Proposition one states: The area of any circle is equal to a right-angled triangle in which one of the sides about the right angle is