Here is a regular polygon of n sides inscribed in a unit circle. In the limit of a very large number of sides the area and perimeter of the polygon approach those of the circle.[br][br]Write an expression for A(n), the area of an n sided regular polygon inscribed in a unit circle.[br]Write an expression for P(n), the perimeter of an n sided regular polygon inscribed in a unit circle.[br][br]Contrast the rates at which A(n) and P(n) approach their limits. [br][br][br]Challenges:[br][br]The number of sides, n, grows while the length of each side, S gets smaller and smaller. How does the product of n and S behave? How do you know? Can you prove it?[br][br]The area of a [i]UNIT[/i] circle is [math]π[/math] and its perimeter is [math]2π[/math]. How do you convince a student that[br]the area of a circle is [b][i]NOT[/i][/b] half its perimeter?[br][br][color=#ff0000][i][b]What other questions [could,would] you ask you students based on this applet ?[/b][/i][/color]