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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.

e
Euler's Number
Base of natural logs. Governs growth.
 › φ
Golden Ratio
The most irrational number.
 › √2
Square Root of 2
The first number proved irrational.
 › τ
Tau
2π. One full turn.
 › γ
Euler-Mascheroni
The gap between harmonic and log.
 › ln2
Natural Log of 2
Every half-life hides this number.
 ›

✨Famous identities and theorems

Equations so elegant they changed how mathematicians think.

eiπ+1=0
Euler's Identity
Five constants, one equation.
 › π²/6
Basel Problem
Sum of inverse squares.
 › √π
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!
Taylor Series
Every smooth function as a polynomial.
 › π/2
Wallis Product
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.

2,3,5,7…
Prime Numbers
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.
 › G≈0.916
Catalan's Constant
Irrational? Nobody knows.
 › ζ(s)
Riemann Zeta Function
The $1 million hypothesis.
 › M≈0.261
Meissel-Mertens
Prime reciprocals' gap constant.
 › E≈1.607
Erdos-Borwein
Proved irrational by Erdos.
 ›

📐Sequences and growth rates

Growth patterns that emerge from simple rules.

T≈1.839
Tribonacci Constant
Like Fibonacci but sum three.
 › ρ≈1.325
Plastic Number
The Padovan spiral's ratio.
 › δₛ≈2.414
Silver Ratio
The A-paper series constant.
 › λ≈1.304
Conway's Constant
Look-and-say sequences.
 › β≈1.186
Levy's Constant
Continued fraction denominators.
 › K₀≈2.685
Khinchin's Constant
Almost every continued fraction.
 › δ≈4.669
Feigenbaum Constant
Universal route to chaos.
 › 137.5°
Golden Angle
How sunflowers pack their seeds.
 ›

∞Transcendental numbers

Numbers that lie beyond all algebraic equations.

L≈0.110
Liouville's Constant
The first proved transcendental.
 › C₁₀
Champernowne Constant
Write all integers in a row.
 › e^π≈23.14
Gelfond's Constant
e raised to pi.
 › Ω≈0.567
Omega Constant
Where xe^x = 1.
 › e^(π√163)
Ramanujan's Constant
Almost a whole number.
 ›