# A Geometric Limit Problem

A Geometric Limit Problem

The following constitutes a popular problem in calculus courses. Consider the sector of a unit circle with angle with the measurements as shown above. Let be the area of triangle , while is the area of the curved shape . What is the limit of the ratio as the angle approaches 0? The answer is 3/4. The ratio takes the value when and when .

θ

T

ABC

S

ABC

T/S

θ

T/S

2/π

θ=π/2

2(

2

-1)(π-2)θ=π/4