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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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Secant and Tangent

The names of the trigonometric ratios tangent and secant are derived from the Latin “to touch” and “ ...
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Metaphors and Mathematics 3

In many traditions, Biedermann’s Dictionary of Symbols tells us, “the tree was widely se ...
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Metaphors and Mathematics 1

When asked to describe mathematics we often resort to metaphor rather than attempt to provide strict ...
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Window Patterns

Start with a square piece of paper (like a Post it note), fold and unfold it in half along a mid-lin ...
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Star Polygons

Starting with p (p a positive integer) equally distributed dots (vertices) around a circle. Connecti ...
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Extended Multiplication Tables

A surprisingly interesting structure is the extended multiplication table, shown above for the numbe ...
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Phyllotaxis Spirals 2

If you have already created the phyllotaxis data in Fathom, or opened the data created in TinkerPlot ...
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Metaphors and Mathematics 2

Robert Recorde, author the first English textbook on algebra (published in 1557), chose to give his ...
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Cut-and-Glue Polyhedral Models

Building polyhedral models is a nice way to explore a lot of significant mathematics. The above mode ...
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Phyllotaxis Spirals

  Phyllotaxis is a term used for the patterns that emerge in the growth of plants. Spiral phyll ...
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Polygonal Number Formulas

Polygonal numbers are a mainstay of recreational and school mathematics, providing a nice bridge bet ...
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