---
tags:
  - mathematics
  - constants
  - reference
created: 2026-05-16
breadcrumb: "Mathematics > Constants"
---

# Mathematical constants

> **Mechanism:** dimensionless numbers that recur across mathematics.

## Constants

- **π (pi)** — ≈ 3.141 592 653 589 793 …  Ratio of a circle's circumference to its diameter. Transcendental.
- **e (Euler's number)** — ≈ 2.718 281 828 459 045 …  Base of the natural exponential; e = lim (1+1/n)^n.
- **φ (golden ratio)** — ≈ 1.618 033 988 749 894 …  (1+√5)/2.  Limit of consecutive Fibonacci ratios.
- **γ (Euler–Mascheroni)** — ≈ 0.577 215 664 901 532 …  γ = lim (Hₙ − ln n).  Irrationality unknown.
- **√2** — ≈ 1.414 213 562 373 095 …  Diagonal of the unit square.
- **√3** — ≈ 1.732 050 807 568 877 …  Height of an equilateral triangle with side 2.
- **ln 2** — ≈ 0.693 147 180 559 945 …  Natural logarithm of two.
- **ln 10** — ≈ 2.302 585 092 994 045 …  Bridge between natural and common logs.
- **log₂ e** — ≈ 1.442 695 040 888 963 …
- **π/180  (degree → rad)** — ≈ 0.017 453 292 519 943 …
- **Catalan constant** — G ≈ 0.915 965 594 177 219 …  Σ (−1)ⁿ / (2n+1)².
- **Apéry's constant ζ(3)** — ≈ 1.202 056 903 159 594 …  Irrational (Apéry 1978).
- **Khinchin constant** — K ≈ 2.685 452 001 …  Geometric mean of partial quotients of almost every real.
- **Twin-prime constant** — C₂ ≈ 0.660 161 815 8 …  Density coefficient for twin primes.
- **Meissel–Mertens constant** — M ≈ 0.261 497 …  Difference between harmonic prime sum and ln ln n.

## Related

- [[famous-math-equations]]
- [[calculus-basics]]
- [[linear-algebra]]