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

# Tag: proof

# 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

# Sigma proof… explained

Unrelated, but a GD level called Sigma: https://geometry-dash-fan.fandom.com/wiki/Sigma Yesterday, I posted a proof on why the sigma sum for phi was true, but I kind of rushed it, so I will be going into details. If you can do a little bit of "hard maths", then it is easy to prove that: is true. is … Continue reading Sigma proof… explained

# 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.

# The uninteresting paradox

When I say uninteresting, I don't mean that this paradox is uninteresting. It means "relating to the interesting/uninteresting numbers" and this is a paradox that is about uninteresting numbers. When we say interesting number, they're numbers with special features. Like 1 is the first positive integer, 2 is the only even prime, 3 is the … Continue reading The uninteresting paradox

# Zero is?

Zero, right? But it's complicated again! Is it prime or composite? I was having a look-around on Math Stack Exchange Is zero a prime number? and it was absolutely confusing. Give it a read! It's not prime, so it should b -- (Screech sound) Wait. Who said it was PRIME? Not me. Let's prove it! … Continue reading Zero is?

# One is?

One!Anybody I mean, yeah. But in a prime/composite definition? It's neither, the one exception, the golden, whatever. Why is it not prime? Let's have a look. Take 25321, a prime number. 1 is also prime, right? So the factorization of 25321 would be 25321 and 25321*1 at the same time. But we have broken two … Continue reading One is?