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