Abraham de Moivre and formula

De Moivre's formula states that (cos x + isin x)^n = cos nx + isin nx. Where i is the imaginary number √-1. Now, for proof and simplicity's sake, let's change cosx + isin x to cis x. This is a proof by induction, as stated by Wikipedia (I use a lot of Wikipedia these … Continue reading Abraham de Moivre and formula

Joseph Liouville and his Numbers (especially his constant)

Number theory. Whoo! In number theory, let there be a number x where, for any positive integer n, there are infinitely many number pairs (p, q) where q > 1 that: 0 < |x - p/q| < 1/q^n x is the Liouville number. Liouville numbers can be described as "almost rational", and can be approximated … Continue reading Joseph Liouville and his Numbers (especially his constant)

RSA Factoring Challenge

The RSA Factoring Challenge is a set of factorisation challenges that involve numbers with hundreds of digits. The highest one cracked was RSA-250, which was 250 digits long, 829 bits, and was factored in February 2020 by Fabrice Boudot, Pierrick Gaudry, Aurore Guillevic, Nadia Heninger, Emmanuel Thomé, and Paul Zimmermann (what's with the cool names?). … Continue reading RSA Factoring Challenge

Behind the scenes of the proof that level 5 is impossible.

Level five of what? Geometry Dash, of course. JK, Back on Track is harder. I'm talking about Conway's Soldiers. And today, just for comfort, instead of calling the soldiers soldiers, I will be calling them pegs. Conway's Soldiers is simple. There are an infinite number of pegs behind a line that divides the land between … Continue reading Behind the scenes of the proof that level 5 is impossible.