###### Cartography Graph theory

## Four Color Theorem Controversy

We cover the four color theorem controversy, discuss the proof of the four color theorem and explain computer-assisted proofs in mathematics.

We cover the four color theorem controversy, discuss the proof of the four color theorem and explain computer-assisted proofs in mathematics.

Leonhard Euler literally stumbled upon graph theory by walking across the seven bridges of Königsberg. We explain discuss this directed graph problem.

We explain the coastline paradox and how the theory of fractal geometry can be used to measure the immeasurable coastlines. We also discuss the occurence of fractals in other parts of nature.

We provide a mathematical proof for the friendship paradox, give examples for possible applications, and introduce ideas of graph theory.

We derive the necessary ideas for solving the German tank problem like the Allies in World War 2 and provide insight with an example.

This article serves as an introduction to graph theory. We present basic definitions and articles that discuss applications of graph theory in everyday life.

We prove by contradiction that there are infinitely many prime numbers. This fact was already known to Euclid and our proof is based on his.

We prove with a diagonal argument by Georg Cantor that the set of real numbers, or R, is uncountable.

We prove by contradiction that the square root of 2 is irrational.

We introduce the shortest path algorithm by Dijkstra, pathfinding, and ultimately explain how Google Maps finds the shortest route from point A to point B.

We approximate pi using a Monte-Carlo method in Matlab, explain the code, provide the program for you to try for yourself, and present an error analysis.

The Math Section is the host for the Carnival of Mathematics #163.

This article serves as a follow-up to the article titled Friendship Paradox. We consider the complement graph which creates the Inverse Friendship Paradox.

We explain the basic idea of the Simplex Algorithm, present linear programming, and discuss the underlying geometric ideas used to solve LP-problems.