New posts in golden-ratio

How many pairs of numbers are there so they are the inverse of each other and they have the same decimal part?

elementary-number-theory real-numbers irrational-numbers decimal-expansion golden-ratio

A closed form of $\int_0^\infty\frac{\sqrt[\phi]{x}\ \arctan x}{\left(x^\phi+1\right)^2}dx$

calculus integration definite-integrals closed-form golden-ratio

Why does this process map every fraction to the golden ratio?

sequences-and-series golden-ratio

On the Paris constant and $\sqrt[k]{1+\sqrt[k]{1+\sqrt[k]{1+\sqrt[k]{1+\dots}}}}$?

limits logarithms nested-radicals constants golden-ratio

Prove that $\frac{1}{\phi}<\int_0^\infty \frac{e^{-x}}{\Gamma(x)} dx< \frac{24+\sqrt{2}}{41} $

inequality definite-integrals gamma-function golden-ratio

A golden ratio series from a comic book

sequences-and-series golden-ratio popular-math

Why is $\varphi$ called "the most irrational number"?

number-theory irrational-numbers golden-ratio

How to prove that $\lim \limits_{n\rightarrow \infty} \frac{F_{n+1}}{F_n}=\frac{\sqrt{5}+1}{2}$

limits fibonacci-numbers golden-ratio

Can the golden ratio accurately be expressed in terms of $e$ and $\pi$

soft-question recreational-mathematics approximation diophantine-approximation golden-ratio

Proving that $\frac{\phi^{400}+1}{\phi^{200}}$ is an integer.

golden-ratio

Is there any integral for the Golden Ratio?

calculus integration big-list golden-ratio