Pi is a number.
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 ) . It appears therefore in areas of mathematics and the sciences having little to do with the geometry of circles , such as number theory and statistics , as well as in almost all areas of physics .