## Pearls I found on this site

Can an irrational number raised to an irrational power be rational?

A (probably trivial) induction problem: $\sum_2^nk^{-2}\lt1$

Innocent-looking Diophantine equation with smallest solution of the order $10^{50}$?

Picture/intuitive proof of $\cos(3 \theta) = 4 \cos^3(\theta)-3\cos(\theta)$?

Proving a trigonometric identity: $\frac{\cos x}{1-\sin x} -\tan x = \sec x$

Cover a plane with parabolas and hyperbolas

What is the (mathematical) point of straightedge and compass constructions?