Area of a circle Archimedes is not rigorous by modern standards, because it assumes that we can compare the length of arc of a circle to the length of a secant and a tangent line, and similar statements about the area, as geometrically evident. The area of a regular polygon is half its perimeter times the apothem. As the number of sides of the regular polygon increases, the polygon tends to a circle, and the apothem tends to the radius. This suggests that the area of a disk is half the circumference of its bounding circle times the radius. Following Archimedes' argument in "The
The Doll that Came Straight from Fairyland a cannon and a magical balloon, but only replies that his godmother should give him what she thinks best. In response, Fairy Zigzag instead asks Princess Pansy what she would like. Princess Pansy asks for a fine clay doll. The Fairy Zigzag creates a magical doll straight from fairyland and then leaves the party. The Prince is left without a gift from his fairy godmother. Princess Pansy names the doll Lady Emmelina and in the days following the party becomes bewitched by the doll. Prince Perfection gets jealous of Lady Emmelina when his sister no longer plays with him. Missing