# 1, 2, 3, 4, … , +1?

The proof on the theorem of four consecutive numbers + 1, including a little example.

# The 0x10 problem

In this post, we cover a problem that the author created, involving hexadecimal and the alphabet (not so much the alphabet but...).

# Random challenge 2 part 2

This is the "sequel" to the post "Random challenge 2", where we talked about division by zero. In this post, we talk about 0^0, or zero to the power of zero.

# 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

# Conway’s Soldiers… part 2.

Phi The sigma sum I will prove that the sigma sum is true given the value of phi, which is also the reciprocal of the golden ratio. Remember how Φ^2 = 1 - Φ? The sigma sum states that 1 - Φ + Φ - Φ^2 + Φ^2 - Φ^3 + Φ^3 - Φ^4 + … Continue reading Conway’s Soldiers… part 2.

# The unreachable, the impossible, the multidimensional…

Level five of Conway's Soldiers, once thought impossible, but proved possible with certain manipulations. Credits to Simon Tatham and Gareth Taylor for the solution.