Famous Mathematical Constants: A Complete Guide

Tap a constant to see its value and meaning.

Pi (π)

The ratio of a circle's circumference to its diameter — approximately 3.14159... — a classic irrational number whose digits continue infinitely without repeating.

Euler's Number (e)

Approximately 2.71828..., this constant naturally appears in continuous compound interest and in describing natural growth and decay, playing a central role throughout mathematics.

The Golden Ratio (φ)

Approximately 1.61803..., the ratio at which the whole is to the larger part as the larger part is to the smaller part — often cited as an aesthetically pleasing proportion in art and architecture.

The Imaginary Unit (i)

Defined by i² = -1, a number that cannot exist among the real numbers but is essential to countless calculations in electronics and physics.

Avogadro's Number (Nₐ)

Approximately 6.022×10²³, this fundamental constant of chemistry represents the number of particles (atoms or molecules) in one mole of a substance.

The Square Root of 2 (√2)

Approximately 1.41421..., this number is the length of the diagonal of a square with sides of length 1, and is historically considered the first irrational number ever discovered.

Each Constant Carries a Deep Story

These constants are the product of humanity's long effort to understand patterns in nature and the universe. Though discovered independently in entirely different fields — geometry, calculus, art, chemistry — they have each become a core concept underpinning mathematics today.

Frequently Asked Questions

Was the golden ratio really used that much in famous artworks?

It's widely claimed that the golden ratio appears in many famous works, but some of these claims have later turned out to be exaggerated or coincidental, so they should be taken with some caution.

How many digits of pi have been calculated?

Supercomputers have already calculated tens of trillions of digits, and because pi is an irrational number that never ends or repeats, the calculation could in theory continue forever.