New posts in pi

Is $\pi^k$ any closer to its nearest integer than expected?

random-variables approximation pi hypothesis-testing

Looking for a closed form for $\sum_{k=1}^{\infty}\left( \zeta(2k)-\beta(2k)\right)$

sequences-and-series summation riemann-zeta pi dirichlet-series

why is PI considered irrational if it can be expressed as ratio of circumference to diameter? [duplicate]

irrational-numbers fractions pi

How to prove $\sum_{n=0}^\infty \left(\frac{(2n)!}{(n!)^2}\right)^3\cdot \frac{42n+5}{2^{12n+4}}=\frac1\pi$?

sequences-and-series pi

Proof of identity for $\pi$: $\frac{\pi}{3} = \frac{2}{\sqrt{2+\sqrt{3}}}\frac{2}{\sqrt{2+\sqrt{2+\sqrt{3}}}}\cdots$

calculus trigonometry pi infinite-product

Euler's Approximation of pi.

approximation pi

A curious limit for $-\frac{\pi}{2}$

How does atan(1) * 4 equal PI?

Recent progress in the irrationality measure of $\pi$

number-theory reference-request pi irrationality-measure

Geometric proof of existence of irrational numbers.

real-analysis pi geometric-construction meta-math

Non-Numerical proof of $e<\pi$

calculus geometry inequality pi eulers-number-e

1000 digits of pi in Python

Prove without using a calculator $(\ln 6)^{(\ln 5)^{(\ln 4)^{(\ln 3)^{(\ln 2)}}}}<\pi$

Continued fraction estimation of error in Leibniz series for $\pi$.

calculus reference-request pi continued-fractions

Bellard's exotic formula for $\pi$

soft-question pi

Prove that $\int _{-\infty }^{+\infty }{\frac {\mathrm {d} z}{(\phi ^{n}z)^{2}+(F_{2n+1}-\phi F_{2n})(e^{\gamma }z^{2}+\zeta (3)z-\pi )^2}}=1$

improper-integrals pi golden-ratio euler-mascheroni-constant

Proving that $\frac{\pi}{2}=\prod_{k=2}^{\infty}\left(1+\frac{(-1)^{(p_{k}-1)/2}}{p_{k}} \right )^{-1}$ an identity of Euler's.

sequences-and-series pi transcendental-numbers constants

Why is $22/7$ a better approximation for $\pi$ than $3.14$?

approximation pi

Proving that $\sum_{k=1}^{\infty} \frac{3408 k^2+1974 k-720}{128 k^6+480 k^5+680 k^4+450 k^3+137 k^2+15 k} = \pi$

sequences-and-series polynomials pi

What would a base $\pi$ number system look like?

number-theory pi