# Math Section Articles

## Collection by Math Section

All articles from the Math Section can be found here.

### Graph Theory Introduction

Learn about the most fundamental Graph Theory definitions and the most interesting applications of Graph Theory in everyday life.

### Maps Can Always Be Colored With Only Four Colors

Maps can always be colored with only four colors in such a way that no two adjacent regions of the map share the same color. This is the Four Color Theorem, a highly controversial mathematical theorem that was proved using computer-assistance. A first in mathematics. We delve into the controversy, explain the proof concept, and present ways to make maps that are still not 4-colorable.

### Article on the Simplex Algorithm

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

### Coastline Paradox and Fractals

How long is the coast of Britain? This question was of utmost importance in the process of creation of the field of fractal geometry. We explain the coastline paradox, fractal geometry and dimension, and how we use fractal geometry to measure coastlines. #Fractals #Geometry #Coastlines #Fry #Lewis #Richardson #Dimension

### Approximate Pi Using a Monte-Carlo Method in Matlab

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. #Pi #Matlab #Tutorial

### Friendship Paradox

Your friends are on average more popular than you. That fact is the Friendship Paradox. We give a mathematical proof for this statement, explain the relevant graph-theoretic terms, and present an example of an application of the Friendship Paradox in real life, the early detection of flu outbreaks. #Graph #Theory #Friendship #Paradox

### Game Theory and Doping

A game-theoretic discussion of doping. We discuss possible methods for solving the doping dilemma, introduce the Nash equilibrium, and establish the mathematical concept of doping games.

### The Byzantine General Problem

We present an example of a problem from theoretic computer science and epistemic logic, the Byzantine general problem.

### Inverse Friendship Paradox

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

### Account Suspended

Leonhard Euler created graph theory by walking across the seven bridges of Königsberg. We follow Euler's path and discuss this directed graph problem.

### German Tank Problem

We explain the German Tank Problem that the Allies faced in World War 2, derive a solution by analyzing serial numbers, and provide insight with an example. #Probability #Theory #World #War #2 #German #Tank #Problem #Allies

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.