Pi is the ratio of a circle's circumference to its diameter. Which constant is this?

• A. tau
• B. pi
• C. i
• D. phi

Answer: (B)

The key idea is that the relationship between a circle’s circumference and its diameter is a universal constant. For any circle, the circumference C equals π times the diameter d, written as C = πd. Therefore the ratio C/d is always π, no matter how big or small the circle is. That constant is about 3.14159 and is irrational, appearing in many formulas like area (A = πr^2) and circumference (C = 2πr) as well.

Tau corresponds to the ratio of circumference to radius, which is 2π, so it’s not the same as C/d. I is the imaginary unit, not a geometric constant for circles. Phi is the golden ratio, a different constant that shows up in proportion but not in this circle ratio. pi is the correct constant for the circumference-to-diameter relationship.