New posts in pi

Irrationality of $\pi^2$ and $\pi^3$

number-theory reference-request book-recommendation pi rationality-testing

Can we express $\pi$ in terms of $\sum_{n=1}^\infty\frac1{n^2}$?

real-analysis sequences-and-series summation pi

What are better approximations to $\pi$ as algebraic though irrational number?

algebra-precalculus approximation pi

How do I prove that $3<\pi<4$?

real-analysis inequality pi

Does $\pi$ satisfy the law of the iterated logarithm?

number-theory statistics random pi experimental-mathematics

Proof of infinitude of primes using the irrationality of π

number-theory prime-numbers pi

A Mathematical Coincidence, or more?

calculus improper-integrals approximation pi

A couple of formulas for $\pi$

sequences-and-series pi

Showing that $\sum_{n=1}^{\infty}\left(\frac{\sin(22n)}{7n}\right)^3=\frac{1}{2}\left(\pi-\frac{22}{7}\right)^3$

sequences-and-series pi

Proving a series for the Watson Triple Integrals?

sequences-and-series integration pi

Is there any similar solutions including $\pi$ like $1-\frac{1}{2}+\frac{1}{4}-\frac{1}{5}+\cdots=\frac{\pi}{3\sqrt{3}}$?

prime-numbers riemann-zeta pi coprime

why is $\sqrt[3]{31}$ so close to $\pi$?

algebra-precalculus radicals pi

Let $x$ be a positive real number. Inequality problem with $\pi$ and $x$ terms.

number-theory inequality pi

Charming approximation of $\pi$: $2\left(\frac{1}{2}\right)^{\phi/2}+2< \pi$, where $\phi$ is the golden ratio

inequality approximation alternative-proof pi golden-ratio

The most complex formula for the golden ratio $\varphi$ that I have ever seen. How was it achieved?

exponential-function pi continued-fractions golden-ratio ramanujan-summation

Showing $\sqrt{\frac{e}{2}}\cdot\frac{e}{\pi}\left(\frac{e}{2}-\frac{1}{e}\right)<1$ without a calculator

inequality pi constants

Proving that $\pi=\sum\limits_{k=0}^{\infty}(-1)^{k}\left(\frac{2^{2k+1}+(-1)^{k}}{(4k+1)2^{4k}}+ \frac{2^{2k+2}+(-1)^{k+1}}{(4k+3)2^{4k+2}}\right)$

sequences-and-series power-series pi transcendental-numbers constants

What's the formula for this series for $\pi$?

sequences-and-series pi continued-fractions

Yet another $\sum = \pi$. Need to prove.

sequences-and-series factorial pi

$e^{\left(\pi^{(e^\pi)}\right)}\;$ or $\;\pi^{\left(e^{(\pi^e)}\right)}$. Which one is greater than the other?

real-analysis inequality exponential-function pi