Estimating a Circle
Inscribe a triangle in a circle:
Now inscribe a square in a circle:
Then a pentagon, then a hexagon:
If we keep going, the shapes approach that of a circle. We'll draw a shape with 100 sides, and a shape with 1000 sides. We won't ever actually reach a perfect circle, but we're approaching it.
If we keep adding sides to these shapes, we'll end up better and better approximations of the circle. We guess you could say that the limit of the shape as the number of the sides approaches infinity is a circle.
For someone who didn't know the area of a circle is πr2, or that the circumference is 2πr, this would be a pretty good way to approximate the area and circumference of a circle, since we can easily find the area and perimeter of a polygon.
And hey, if we take the limit, we could get exact numbers for the area and circumference of a circle. Wouldn't that be handy?