Bertrand Russell (1872-1970) It isn’t too often that we think about or even explore the fundamental building blocks of mathematics. These building blocks are called axioms. Axioms are statements taken to be true, i.e. they cannot be proven. This causes mathematicians, whether they know it or not, to take a lot of things on faith. All of […]Read more "Axioms: Sets (Russell’s Paradox)"
It is a common occurrence in mathematics that when something does go wrong, it goes terribly wrong. This exact phenomenon occurs with the Banach-Tarski Paradox. Informally, it says that one can take a sphere (in 3 or more dimensional space) can be split into finitely many pieces and, using only rigid motions, can be rearranged […]Read more "Banach-Tarski Paradox"
Pythagoras of Samos (569-500 BCE) was an actual person, but was also the founder of the Pythagoreans. He was a political figure and a mystic. Beyond this, he stood out in his time as he involved women as equals in his activities. The Pythagorean society focused on mathematics, but also had some religious properties which include […]Read more "Pythagoras and the Square Root of 2"
The prisoner’s dilemma is a very popular situation in crime fiction, and can be found in many areas of real life. It originated from Merrill Flood and Melvin Dresher, however Albert Tucker is credited for formalizing it into its current form. So let us take a look. Two criminal partners, A and B, are arrested […]Read more "The Prisoner’s Dilemma"
This is the third and final post on the volume of a sphere. The other two can be accessed by the following links, “Coordinates in 3-Space” and “The Volume of a Sphere with Calculus” As the title suggests, this will be a derivation without the use of Calculus. This proof is Greek in origin, in […]Read more "The Volume of a Sphere (without Calculus)"
This post is second in a series of 3 beginning with “Coordinates in 3-space”. We have been taught that the volume of a sphere . We will go through two derivations of this, beginning with the Calculus version. We will make use of a theorem in calculus. Theorem: . Suppose we have a sphere of radius […]Read more "The Volume of a Sphere with Calculus"
This post was inspired by a calculus student and will be in three parts: This on the development of different coordinate systems, one with calculus and one without. We are taught in school that the volume of a sphere with radius is . In this post we shall look at a development in calculus that will not […]Read more "Coordinates in 3-Space"