E1: Increase the order n step by step and observe the impr0ving approximation of the circle by the polygons, and of the polygon circumference to 2π (number fields). Use the zoom option and show and hide the unit circle for each step.
E2: Choose n =2 and then n = 3. Look at the construction window, and derive the formulas for the partial triangles of the square and the octagon. From this derive the formulas for the circumferences.
E3: Generalize your derivation to the n- polygon. Compare your formula with that of the Description page.
E4: Now derive the construction and the formula for the circumscribed square, octagon and n- polygon.
E5: Reproduce Archimedes´ historical way by starting with a triangle instead of a square.
E6: Derive formulas for the approximative calculation of the area of the partial triangles, and hence of the area of the circle.