###### Graph theory Traffic

## Taking A Walk With Euler

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

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.

Proof by a diagonal argument 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.

We prove that vampires are a mathematical impossibility due to the properties of exponentially growing functions.

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

This is a book review of the book How to Solve It. The article gives insight into how the book can help both mathematicians and non-mathematicians improve their problem-solving skills.