New posts in Golden Ratio

Verifying a long polynomial equation in (the reciprocal of) the Golden Ratio

How to prove $\phi=1+\sum_{n=1}^{\infty}\frac{(-1)^{n+1}}{F_nF_{n+1}}$

Is a visual proof to $\varphi = 1 + \tfrac{1}{{1 + \tfrac{1}{{1 + \tfrac{1}{{1 + \,\ddots\,}}}}}}$?

$a/b < (1 + \sqrt{5})/2 \iff a^2 - ab - b^2 < 0$?

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

How does one show that $\int_{0}^{1}{1\over 1+\phi x^4}\cdot{\mathrm dx\over \sqrt{1-x^2}}={\pi\over 2\sqrt{2}}?$

How can we show that $4\arctan\left({1\over \sqrt{\phi^3}}\right)-\arctan\left({1\over \sqrt{\phi^6-1}}\right)={\pi\over 2}$

Conjecture for the value of $\int_0^1 \frac{1}{1+x^{p}}dx$

New very simple golden ratio construction incorporating a triangle, square, and pentagon all with sides of equal length. Is there any prior art?

New, extremely simple golden ratio construction with two identical circles and line. Is there any prior art?