Pi is a number.
A mathematical constant is a special number , usually a real number , that is `` significantly interesting in some way '' . Number theory or , in older usage , arithmetic is a branch of pure mathematics devoted primarily to the study of the integers . Pi . Being an irrational number , can not be expressed exactly as a fraction ( equivalently , its decimal representation never ends and never settles into a permanent repeating pattern ) . The ubiquity of makes it one of the most widely known mathematical constants both inside and outside the scientific community ; several books devoted to it have been published , the number is celebrated on Pi Day , and record-setting calculations of the digits of often result in news headlines .