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Are Pi’s Days Numbered?

Pi defines the relationship between a circle’s radius and its area. Some people have argued that Pi’ ...
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Quadratic Number Spirals and Polygonal Numbers

Take the positive Integer number-line, place it in the xy plane (with zero at the origin), and wrap  ...
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Generating Random Walks in Mathematics

With connections to the study of gambling, Brownian motion, fractals, and more, random walks are a f ...
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Quasi-regular Rhombic Tiling and Polyhedron

It could be argued that the square is the ‘nicest’ rhombus, but the rhombus with angles ...
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Pascal’s Triangle and Polygonal opsgf’s

The diagram above illustrates a surprising correspondence – if you take the reciprocal of a particul ...
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Spherical Tetrahedron

Imagine a tetrahedron centered inside a sphere. If you were to project the edges of the tetrahedron ...
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A Family of Sequences and Number Triangles

The triangular numbers (and higher triangular numbers) can be generated using this recurrence relati ...
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False Positives in Probability

There are plenty of probability problems that have counter-intuitive solutions. Problems like these, ...
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Dividing Polynomials – The Grid Method

Students generally learn to divide polynomials using  long division or synthetic division. This post ...
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Farey definition, property, and algorithm

Here is an outline of how you can go about generating this data. The definition and properties of Fa ...
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Farey, Ford, & Fathom

Chapter 3 of Hardy & Wright’s An Introduction to the Theory of Numbers involves Farey sequ ...
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Another Triangular Number Formula

The double recurrence relation that defines the higher triangular numbers is a simple one – it ...
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The Sequence of Primes

As I make my way through Hardy & Wright’s An Introduction to the Theory of Numbers,  I am ...
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Triangular Numbers and Euler’s Number Triangle

There is a nice identity stating that a square number can be written as the sum of two subsequent tr ...
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Metaphors and Mathematics 4

If mathematics is a game, then playing some game is doing mathematics, and in that case why isn ...
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The Humble Multiplication Table, 1

A surprising relationship found in the multiplication table is that the sum of the entries in the ma ...
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