What do we use pi for?

Answer 1

A long time ago it was noticed that the ratio of the circumference of any circle to its diameter was a constant value; this value was called pi (π).

π is generally used with relation to arcs (and circle). It appears in many formulae relating to them:

• The length of the circumference (perimeter) of a circle is π times its diameter;
• The area of a circle is π time its radius squared;

It is also used in relating to things that are cyclic, for example waves and pendulums.

When angles are measured in radians, π is important as it represents a straight line (like 180°) and 2π radians represents a full turn.

π crops up with probability. Suppose you have a set of parallel lines a constant distance apart and you drop a needle onto them that is the same length as the distance between the lines, then the probability that the needle will cross a line is given by Pr = 2/π

The most astounding result containing π is one that also includes the two other famous numbers e (Euler's number or approx 2.7182818 - it is the base of natural logarithms) and i (the imaginary number that is the square root of -1: i² = -1 → i = √-1): raise e to the power of i times π and the result is -1, that is e^(iπ) = -1.