Pythagoras and the Square Root of 2

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 […]

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The Prisoner’s Dilemma

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 […]

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The Volume of a Sphere (without Calculus)

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 […]

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The Volume of a Sphere with 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 […]

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The Road to Larger Infinities

Georg Cantor was a German mathematician responsible for the invention of set theory. Before him, the concept of infinity was not well studied or considered by mathematicians. The importance of Cantor’s development of set theory is very clear as it is the basis for much of modern mathematics. We will take a look at Cantor’s […]

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Infinitude of Primes

It is well known that there are infinitely many primes. The proof by Euclid is among the first we see as rising mathematicians. Though it is often put into a proof by contradiction context, the original proof does not actually contain a reducto ad absurdum argument. Below we will share Euclid’s famous proof and a […]

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