---
tags:
  - mathematics
  - equations
  - famous-equations
created: 2026-05-16
breadcrumb: "Mathematics > Famous equations > Famous math equations"
---

# Famous math equations

> **Mechanism:** Compact statements that anchor whole subjects

## Items

- **Pythagorean theorem** — a² + b² = c² — right triangle side lengths.
- **Euler's identity** — e^{iπ} + 1 = 0 — five constants, three operations, no equals signs to spare.
- **Quadratic formula** — x = (−b ± √(b² − 4ac)) / 2a.
- **Binomial coefficient** — C(n, k) = n! / (k!(n−k)!) — count of k-subsets of an n-set.
- **Binomial theorem** — (x + y)^n = Σ_{k=0}^{n} C(n, k) x^{n−k} y^k.
- **Cauchy–Schwarz** — |⟨u, v⟩| ≤ ‖u‖ ‖v‖. Equality when u and v are parallel.
- **Fourier transform** — F(ω) = ∫ f(t) e^{−iωt} dt — decompose a signal into frequencies.
- **Bayes' rule** — P(A|B) = P(B|A) P(A) / P(B). Foundation of inference.
- **Normal distribution** — p(x) = (1/√(2πσ²)) exp(−(x − µ)² / 2σ²).
- **Geometric series** — Σ_{n=0}^∞ rⁿ = 1 / (1 − r) for |r| < 1.
- **Basel problem** — Σ_{n=1}^∞ 1/n² = π²/6.
- **Gauss integral** — ∫_{−∞}^{∞} e^{−x²} dx = √π.
- **Power rule (calculus)** — d/dx (xⁿ) = n x^{n−1}.
- **Fundamental theorem of calculus** — ∫ₐᵇ f dx = F(b) − F(a) where F' = f.

## Related

- [[calculus-basics]]
- [[linear-algebra]]