E1: Increase the order n step by step and observe the improving approximation of the circle by the polygons, and of the polygon circumference to 2π (number fields).

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.