# Pi

Science EncyclopediaScience & Philosophy: *Philosophy of Mind - Early Ideas* to *Planck length*

Pi is one of the most fundamental constants in all of **mathematics**. It is normally first encountered in **geometry** where it is defined as the **ratio** of the circumference of a **circle** to the diameter: π = C/d where C is the circumference and d is the diameter. This fact was known to the ancient Egyptians who used for π the number 22/7 which is accurate enough for many applications. A closer **approximation** in fractions is 355/113. Students often use a decimal approximation for π, such as 3.14 or 3.14159.

Actually, the number π is not even a **rational number**. That is, it is not exactly equal to a fraction, m/n where m and n are whole numbers or to any finite or repeating decimal. This fact was first established in the middle of the eighteenth century by the German mathematician, Johann Lambert. Even further, it is a transcendental number. That is, it is not the root of any polynomial equation with rational coefficients. This was first proved by another German mathematician, Ferdinand Lindeman, in the latter half of the nineteenth century.

There are many infinite series that can be used to calculate approximations to π. One of these is where the denominators are the consecutive odd numbers.

Roy Dubisch