Even if you don’t want to enter Dan’s contest, spirolateral math doodles—or “loop-de-loops”—make a great mathematical exploration.
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.
- Download and print Anna’s Loop-de-Loop Lesson Instruction Page and Student Work Page.
- Share with your kids.
- Print some extra graph paper for continued play.
- Check out Anna’s blog post for more ideas.
- Explore what happens when you make spirolaterals on triangle graph paper, too.
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.
For Further Reading
- Mike Lawler and sons explore Loop-de-Loops: Part 1, and Part 2.
- Martin Gardner, “Worm Paths” in Knotted Doughnuts and Other Mathematical Entertainments.
Articles by Robert J. Krawczyk:
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