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.