I received about one hundred loop-de-loops from teachers, parents, and students from several different countries. It took me an hour to take in all the awesome eye candy, which included dioramas, videos, 3D loop-de-loops made from snap cubes, and more. I pulled out my five favorites and sent them to three judges who I think embody the best of creativity in mathematics.

**The Judges**

- Malke Rosenfeld, who uses dance and choreography to explore mathematical thinking.
- George Hart, a research mathematician who also sculpts using geometry as his medium.
- Michael Serra, author of
*Discovering Geometry*, a geometry textbook infused from the front cover to the back with Michael’s love for math and art.

**Five Finalists**

Autumn, from Angela Ensminger’s class:

Theo, from Alice Hsiao’s class:

Trish Kreb’s seventh grade student:

John Grade & his daughter:

Maddie Bordelon and her math art team, “Right Up Left Down”:

[**BTW**. In an early draft of this post, I reversed the second and third prize winners. Mistakes were made. Apologies have been issued.]

**Third Prize**

Third prize, which is a medium-intensity high five delivered if we ever meet, and one copy of Weltman’s book, goes to Maddie Bordelon and her math art team, “Right Up Left Down.”

**Second Prize**

Second prize, which is sustained applause in a crowded, quiet room, and five copies of Weltman’s book, goes to Theo from Alice Hsiao’s class:

One judge wrote:

[E] completely holds my attention. The coloring choices pull me in and highlight the patterns and structure in a way that fascinates me. The long bands of white, blue and grey make a fantastic contrast to the brighter colors closer to the middle, which are also the shorter segments in the design. And, the bold outlines pull out the structure even more. I don’t know if it was intentional, but the overall effect of hand-coloring plus scanning the image made for a lovely final effect.

**First Prize**

First prize, which is 40 copies of Anna Weltman’s awesome book, goes to John Grade & his daughter.

[**2015 Oct 12**. John Grade is graciously passing his first prize down to the second prize winner.]

Our judges wrote about John Grade’s loop-de-loop:

It is very well constructed, brilliant use of color, and the number pattern chosen is pretty special.

A nice experiment to try Pi and see if a visible pattern emerges.

Congratulations, everybody.

**Honorable Mention**

I loved seeing students conjecturing mathematically about loop-de-loops, asking each other which ones converge and diverge, trying to predict the patterns they’d find in different strings of numbers. (See: Denise Gaskin’s comment for one example.)

Also, The Nerdery really sank its teeth into this assignment. This blog’s collection of programmer-types produced some great loop-de-loop visualizations:

- Josh G. used Scratch to let you manipulate every loop-de-loop of length three. (See also Scott Farrar with Geogebra; Jacob Klein with Desmos.)
- Dan Anderson used Processing to draw every loop-de-loop of length five.
- Joshua Green used PencilCode to let you draw
*non-rectangular*loop-de-loops. - Finally, Chris Lusto dazzled us with his “loop laboratory.” Great instructional design. No restrictions on the length of your loop-de-loop. Make sure you click through to screen 10.