What are 4 mathematical formulas which use pi?

Answer 1

Ï€ is so pervasive in mathematics that there are many formulae in many different areas of mathematics as well as physics.

Here are some of them:

Area of circle: π*r2 where r is the radius of the circle.

Surface of sphere: 4*Ï€*r2

Volume of sphere: 4/3*Ï€*r3

sin(k*Ï€) = 0 for all integers k.

Here are some less common but intriguing ones:

Leibniz Formula: π/4 = 1 - 1/3 + 1/5 - 1/7 + 1/9 - 1/11 ...

Wallis Product: π/2 = 2/1 * 2/3 * 4/3 * 4/5 *

where the numerators go 2,2,4,4,6,6,8,8, ...

and the denominators go 1,3,3,5,5,7,7,9 ...

and finally, my favourite:

Euler's Identity: eiπ + 1 = 0 which, in 7 symbols, contains the two most important number in basic mathematics: 0 and 1; the two most important transcendental numbers e and π, and the basis of the complex field: i (the imaginary square root of -1).