円周率を含む数式
∑ n = 1 ∞ 1 ( 2 n ) 2 = 1 2 2 + 1 4 2 + 1 6 2 + 1 8 2 + ⋯ = π 2 24 {\displaystyle \sum _{n=1}^{\infty }{\frac {1}{(2n)^{2}}}={\frac {1}{2^{2}}}+{\frac {1}{4^{2}}}+{\frac {1}{6^{2}}}+{\frac {1}{8^{2}}}+\cdots ={\frac {\pi ^{2}}{24}}}
∑ n = 0 ∞ ( ( − 1 ) n 2 n + 1 ) 2 = 1 1 2 + 1 3 2 + 1 5 2 + 1 7 2 + ⋯ = π 2 8 {\displaystyle \sum _{n=0}^{\infty }{\left({\frac {(-1)^{n}}{2n+1}}\right)}^{2}={\frac {1}{1^{2}}}+{\frac {1}{3^{2}}}+{\frac {1}{5^{2}}}+{\frac {1}{7^{2}}}+\cdots ={\frac {\pi ^{2}}{8}}}
T ≈ 2 π L g {\displaystyle T\approx 2\pi {\sqrt {\frac {L}{g}}}}
Δ x Δ p ≥ h 4 π {\displaystyle \Delta x\,\Delta p\geq {\frac {h}{4\pi }}}