Discovering Pi Through Exploration!

Pi is a very important and commonly used mathematical constant. It represents the ratio of any circle's circumference to its diameter (or twice its radius; d = 2r) and the ratio of a circle's area to the square of its radius.

This relationship, although difficult to disvoer can also be inferred by manipulain the equations for the area and circumference of a circle, area = pi * r^2 and circumference = 2r * pi, respectively. Thus resulting in pi = (Area of a circle)/ (r^2) and pi = (Circumference of a circle)/2r .

Please explore this applet below by dragging the points a and b or c and d. Please take not ice of the respective changes in area and circumference and its relationship with Pi.

Exploratory Activities (Write answers in class notes section)

1) Drag point B until the radius AB equals 1, what is the area? What is the value of the equation?

Are they equal? Is there a rounding error? Stretch radius AB to 2, what is the area?

What is the value for the equation? Try at lease four more values.

2) Drag point D until radius DC equals .5 (remember 2r = d), what is the circumference? What is the value of the equation?

Are they equal? Is there a rounding error? Stretch radius DC to 4, what is the circumference?

What is the value for the equation? Try at least four more values.

3) Explain why the value for the equation never changes.