The proof on the theorem of four consecutive numbers + 1, including a little example.
In this post, we cover a problem that the author created, involving hexadecimal and the alphabet (not so much the alphabet but...).
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.
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
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
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.
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.
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, 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!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?