πConstants

π (pi) is the ratio of a circle's circumference to its diameter. It's irrational and transcendental, one of mathematics' most important constants.

e is the base of natural logarithm, appearing naturally in continuous compound interest. It plays a central role in calculus.

The golden ratio φ (phi) is when the ratio of whole to larger part equals the ratio of larger to smaller part.

i is the imaginary unit satisfying i² = -1. It's fundamental to complex numbers and essential in math and engineering.

The Euler-Mascheroni constant γ is the limit of the difference between harmonic series and natural log. Whether it's irrational is still unknown.

Apéry's constant is ζ(3) from the Riemann zeta function. Roger Apéry proved its irrationality in 1978.

Catalan's constant is defined by an alternating series. Whether it's irrational remains unproven.

√2 is the diagonal length of a unit square. The first discovered irrational number, it shocked the Pythagorean school.

The Feigenbaum constant δ is a universal constant in chaos theory, the limiting ratio between bifurcation points.