Project: Mathematical Puzzles

Introduction

After developing the 3D equation grapher for my PlotEquation plugin, I created a Shapeways shop to further showcase some of the models it produced. About a year later (when I was a senior in high school), a professor contacted me through the website with the idea of creating puzzles that represent various mathematical formulas. The following images showcase the different puzzles and explain how they represent their respective formulas.

Sum of Consecutive Sums
1 + (1+2) + (1+2+3) + .... + (1+2+3+...+n) = n(n+1)(n+2)/6

The following puzzle represents this formula with n=4. The solution is a rectangular prism (shown in the image above) with dimensions of 4x5x6, which respectively correspond to the n, n+1, and n+2 components of the formula. Note that this puzzle is solved using 6 pieces of pyramid-like pieces that iterate from 1 to 4. Except for two pieces, which are mirror images of the rest, all the pieces are exactly the same.

n=4

Sum of Squares
1^2 + 2^2 + 3^2 + ... + n^2 = n(n+1)(2n+1)/6

The following puzzle represents this formula with n=3 and n=4. The solutions are rectangular prisms with dimensions of 3x4x7 and 4x5x9, which respectively correspond to the n, n+1, and 2n+1 components of the formula. Note that this puzzle is solved using 6 pieces constructed from squares that iterate from 1 to n (this is especially visible on the first piece), and only 3 of the pieces are unique - each one has an identical pair.

n=3

n=4