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.
Graph theory Traffic
Taking A Walk With Euler Through Königsberg
Leonhard Euler literally stumbled upon graph theory by walking across the seven bridges of Königsberg. We explain discuss this directed graph problem.
Cartography Geometry
From The Coastline Paradox To Fractals
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.
Graph theory Sociology
Friendship Paradox
We provide a mathematical proof for the friendship paradox, give examples for possible applications, and introduce ideas of graph theory.
Probability theory and statistics War
German Tank Problem
We derive the necessary ideas for solving the German tank problem like the Allies in World War 2 and provide insight with an example.
Biology Cartography Graph theory Relationships Sociology Traffic
Introduction To Graph Theory Applications
This article serves as an introduction to graph theory. We present basic definitions and articles that discuss applications of graph theory in everyday life.
Simple Proofs
Infinite Number Of Primes
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.
Simple Proofs
The Set Of Real Numbers Is Uncountable
We prove with a diagonal argument by Georg Cantor that the set of real numbers, or R, is uncountable.
Algebra Simple Proofs
The Square Root Of 2 Is Irrational
We prove by contradiction that the square root of 2 is irrational.
Graph theory Mathematical Optimization Traffic
How Google Maps Calculates The Shortest Route
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.
Do it yourself Probability theory and statistics
Approximate Pi: Matlab Monte-Carlo Method
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.
Applied mathematics Geometry Other Sociology
Carnival Of Mathematics #163
The Math Section is the host for the Carnival of Mathematics #163.
Graph theory Sociology
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.
Applied mathematics Economics Geometry Mathematical Optimization Traffic War
Linear Programming: 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.