New York, NY

Zoe Markman created a visual proof of the “sum of squares formula” by cleverly using three wooden 3-D pyramids that fit together. Each pyramid consisted of a total of 12 + 22 + … + n2 identical wooden cubes; thus, its volume visually represented the sum of the squares of all the whole numbers from 1 to n. To find a formula for this sum of squares, Zoe manipulated and rearranged the three pyramids to form a rectangular prism, whose volume could then be easily calculated to obtain the desired formula for the sum of squares.

The judges agreed with Zoe that this sort of visual, hands-on manipulative “provides a deeper understanding of math than that provided by a written project. Since you can observe, hold, and manipulate the pyramids (even more so in person), the audience is able to understand why the formula works rather than just taking it at face value and accepting that it was true arbitrarily. Second, the presentation could be understood even by people without a significant knowledge of math. It put what looks like an intimidating problem in terms that are easily digestible.” Zoe even tested the presentation on friends who said they didn’t like math. That’s a good practice in any form of communication. Overall, this project is modest but extremely well done and produces a very pleasurable “Aha!” moment for many viewers; indeed, it led one of the judges to understand the “sum of squares formula” in a whole new way!