# 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)

# P/NP?

Back to another Millennium Prize problem! There are two types of questions: one, where an algorithm can solve the question in polynomial time (P), and ones, where there is no way to find the answer quickly, but if information is given on showing what the answer is, it can be quickly verified, which is NP, … Continue reading P/NP?

# Poincaré Conjecture… with less detail.

Yes, this was already solved by Grigory Perelman, but I have nothing much, so... Imagine a spherical item. And, for the easiest solution, let's use an apple. Wrap the rubber band around the apple. Without tearing it or letting it leave the surface, we can slowly shrink the rubber band until it becomes a single … Continue reading Poincaré Conjecture… with less detail.

# Riemann Hypothesis

Yesterday, I said that I would do a post on the Riemann Hypothesis, so here we are now. There is a function with the name of the Riemann Zeta Function, named after Bernhard Riemann. The Riemann Hypothesis states that the Riemann zeta function has zeroes only at the negative even integers and complex numbers with … Continue reading Riemann Hypothesis

# 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.