Explore Mathematical Constants

Every constant, theorem, and identity on PlayMemorize. Each page has a full explainer, diagrams, and flashcards.

🔢The fundamental constants

Numbers that appear everywhere in mathematics and physics.

Base of natural logs. Governs growth.

The most irrational number.

Square Root of 2

The first number proved irrational.

2π. One full turn.

Euler-Mascheroni

The gap between harmonic and log.

Natural Log of 2

Every half-life hides this number.

✨Famous identities and theorems

Equations so elegant they changed how mathematicians think.

Euler's Identity

Five constants, one equation.

Sum of inverse squares.

Gaussian Integral

The bell curve's total area.

› ∫=F(b)-F(a)

Fundamental Theorem

Integration and differentiation unified.

› a²+b²=c²

Pythagorean Theorem

Right triangles, forever.

› (cosθ+isinθ)ⁿ

De Moivre's Theorem

Rotation on the complex plane.

› Σf⁽ⁿ⁾/n!

Every smooth function as a polynomial.

Pi from an infinite product of fractions.

› n!≈√(2πn)(n/e)ⁿ

Stirling's Approximation

Factorials without multiplying.

› π(n)~n/lnn

Prime Number Theorem

How thin primes become.

🔍Number theory constants

Constants that describe the hidden structure of the primes.

The atoms of arithmetic.

› C₂≈0.660

Twin Prime Constant

Governs pairs like 11 and 13.

› ζ(3)≈1.202

Apery's Constant

Proved irrational in 1978.

Catalan's Constant

Irrational? Nobody knows.

Riemann Zeta Function

The $1 million hypothesis.

Meissel-Mertens

Prime reciprocals' gap constant.

Proved irrational by Erdos.

📐Sequences and growth rates

Growth patterns that emerge from simple rules.

Tribonacci Constant

Like Fibonacci but sum three.

The Padovan spiral's ratio.

› δₛ≈2.414

The A-paper series constant.

Conway's Constant

Look-and-say sequences.

Levy's Constant

Continued fraction denominators.

› K₀≈2.685

Khinchin's Constant

Almost every continued fraction.

Feigenbaum Constant

Universal route to chaos.

How sunflowers pack their seeds.

∞Transcendental numbers

Numbers that lie beyond all algebraic equations.

Liouville's Constant

The first proved transcendental.

Champernowne Constant

Write all integers in a row.

› e^π≈23.14

Gelfond's Constant

e raised to pi.

Where xe^x = 1.

› e^(π√163)

Ramanujan's Constant

Almost a whole number.