New posts in golden-ratio

Polylogarithm ladders for the tribonacci and n-nacci constants

sequences-and-series special-functions golden-ratio polylogarithm

Golden Rectangle into Golden Rectangles

sequences-and-series recreational-mathematics polygons golden-ratio tiling

On the formula, $\pi = \frac 5\varphi\cdot\frac 2{\sqrt{2+\sqrt{2+\varphi}}}\cdot\frac 2{\sqrt{2+\sqrt{2+\sqrt{2+\varphi}}}}\cdots$

pi infinite-product nested-radicals golden-ratio

Prove that the golden ratio is irrational by contradiction

analysis golden-ratio

Finding relatives of the series $\varphi =\frac{3}{2}+\sum_{k=0}^{\infty}(-1)^{k}\frac{(2k)!}{(k+1)!k!2^{4k+3}}$.

sequences-and-series catalan-numbers golden-ratio constants

Fibonacci sequence and other metallic sequences emerged in the form of fractions

sequences-and-series fractions golden-ratio

Fibonacci Sequence, Golden Ratio

sequences-and-series convergence-divergence fibonacci-numbers golden-ratio

Continued fraction involving Fibonacci sequence

fibonacci-numbers continued-fractions golden-ratio

How to find $\lim_{n \to \infty} \int_0^1 \cdots \int_0^1 \sqrt{x_1+\sqrt{x_2+\sqrt{\dots+\sqrt{x_n}}}}dx_1 dx_2\dots dx_n$

integration limits definite-integrals nested-radicals golden-ratio

Why does every "fibonacci like" series converge to $\phi$?

sequences-and-series recurrence-relations fibonacci-numbers golden-ratio

Simplify $7\arctan^2\varphi+2\arctan^2\varphi^3-\arctan^2\varphi^5$

trigonometry golden-ratio

Approximation for $\pi$

approximation math-history pi golden-ratio

Is my proof for the Irrationality of the Golden Ratio correct?

elementary-number-theory golden-ratio

Proof Phi is Irrational by using another Irrational Number

irrational-numbers golden-ratio

Finding properties of operation defined by $x⊕y=\frac{1}{\frac{1}{x}+\frac{1}{y}}$? ("Reciprocal addition" common for parallel resistors)

calculus abstract-algebra complex-numbers means golden-ratio

A conjectured continued fraction for $\phi^\phi$

number-theory continued-fractions conjectures golden-ratio

How to compute $\int_0^\infty \frac{1}{(1+x^{\varphi})^{\varphi}}\,dx$?

calculus integration definite-integrals closed-form golden-ratio

How was this approximation of $\pi$ involving $\sqrt{5}$ arrived at?

approximation pi golden-ratio diophantine-approximation

Is the Fibonacci lattice the very best way to evenly distribute N points on a sphere? So far it seems that it is the best?

fibonacci-numbers lattice-orders golden-ratio spheres equidistribution

Show that the maximum value of this nested radical is $\phi-1$

functions recursion maxima-minima nested-radicals golden-ratio