Our first project from Conway and Guy’s The Book of Numbers

My son has started reading The Book of Numbers by Conway and Guy. Today we did are first project based on some examples early in the book:

The first example we looked at were the “hexagonal” numbers. Here my son explains what those numbers are and gives a little introduction into the surprising geometric idea that helps understand these numbers:

My son had some difficulty seeing the argument from the pictures in the book, so we tried out a few examples (a few days before this project) using snap cubes. Here’s his explanation of the surprising geometry:

The next thing we looked at in the book were the “tetrahedral” numbers. The book game an amazing proof showing a formula for these tetrahedral numbers. Here he explains this clever proof:

This was a really fun project, and I’m also really happy that this book is teaching my son a bit about reading math books – sometimes even reading and understanding just a couple of pages can take time.

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