The mathematical constant is defined as the ratio of the cir

The mathematical constant is defined as the ratio of the circumference of a circle to its diameter. What is the value of in the taxicab metric?

Solution

we know that taxicab shape consist of right angles. Also a circle does not contain any right angle. therefore technically the value of pi does not exist in taxicab metric.

But if we place a square around a circle with diameter 1 where each side of square is a tangent to the circle and removing the corners of the square then the value of pi will be equal to 4.