Spirolateral Math Doodles

This is not a math book coverInterrupt your regular math programming to try this fantastic math doodling investigation, and you might even win a prize!

Anna Weltman wrote a math/art book, and Dan Meyer is offering a classroom-size set of them to the winner of his fall contest (deadline Tuesday, October 6, and homeschoolers are welcome, too).

Even if you don’t want to enter Dan’s contest, spirolateral math doodles—‌or “loop-de-loops”—‌make a great mathematical exploration.

loop-de-loops1

How to Get Started

To make a spirolateral, you first pick a short series of numbers (1, 2, 3 is a traditional first set) and an angle (90° for beginners). On graph paper, draw a straight line the length of your first number. Turn through your chosen angle, and draw the next line. Repeat turning and drawing lines, and when you get to the end of your number series, start again at the first number.

Some spirolaterals come back around to the beginning, making a closed loop. Others never close, spiraling out into infinity—‌or at least, to the edge of your graph paper.

loop-de-loops2

For Further Reading

Articles by Robert J. Krawczyk:

Anna Weltman appeared on Let’s Play Math blog once before, with the game Snugglenumber. And she’s a regular contributor to the wonderful Math Munch blog.


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4 thoughts on “Spirolateral Math Doodles

  1. Thank you so much for sharing these, Denise, they look great. I haven’t stopped to comment here in far too long but I do continue to appreciate all the fab maths ideas you take the time to post. It’s been a few years since we switched to your “Let’s Play Math” approach and we’re all still loving maths. It seems to get more and more fun as the children get older!

  2. Hi, Lula! It’s great to hear from you.
    Yes, math gets more fun as the kids get older, because it’s so exciting to see them wrangle with ideas on their own. They never think things through exactly the way I would, and sometimes their ideas are so much better than mine.

    For example, with these spirolaterals, my daughter noticed a pattern in the way some loop around while others spiral off into infinity. And after thinking about it for awhile, she came up with a proof for why it happened and predicted what longer series of numbers would do.

    Her very own proof! And a conjecture, too. How cool is that?! I love watching her mind work🙂

  3. Wow! That is very cool!

    Yes, I agree that seeing how their minds work is one of the best things about this kind of maths. (Parents who delegate wholesale to workbooks or online programs are missing out on so much!)

    I’ve always known my son is a visuospatial learner but it wasn’t until we were looking at some visual patterns together this week that I really saw what that means. His way of deriving the equation for the nth step was completely different from mine and my daughter’s (and probably much more efficient). That was once I’d managed to get him to backwards engineer his answers, of course.🙂

    1. Backwards-engineering an answer — good phrase! That’s the way professional mathematicians do it, too. I can’t find the quote right now, but someone described it along these lines:
      “We notice interesting things and play around with them, and that’s the real work of mathematics. Then later we go back and write a proof, just to make sure our minds haven’t been playing tricks on us.”

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