Visual demonstration of pi animation ( π ). Pi is the factor by which the diameter of a circle must be multiplied to get its circumference. Pi is the same for all circles and has a value of about 3.14159265 ... π is irrational (not a ratio of two integers) and is infinitely long, which gives it a special fascination, most brilliantly expressed in Carl Sagan's "Cosmos".

The animation starts with a circle (yellow) with its diameter (d) shown as a black arrow. From this black diameter, arise three lines (1 blue, 2 purple and 3 red) which migrate outwards to map to the edge of the circle. These three diameter lengths almost completely go around the circle but they leave a small gap at the bottom (0.14159 of a diameter). These three diameter lengths + their shortfall then unwrap to form a straight line (green) of length d x 3.14159. When the diameter is 1, then the circumference is π.