# A One-Squiggle Cat

May 20, 2020

Cats are cute, but what’s weird about this drawing of a cat? If you look really, really closely, you’ll see that the whole thing is 1 single line! The line keeps bending in on itself to fill the paper. In places where the line pieces come close to each other, the picture becomes darker. Those different shades of color make it look like a picture of a real thing. This kind of line is called a Hilbert curve. As we see in this video, the artist actually programmed a printer to draw those squiggles. Cats may have 9 lives, but we don’t have enough lives to draw that whole long line ourselves!

Wee ones: Try drawing as straight a line on paper as you can. If you’re able, try to draw 2 straight lines close together without them touching!

Little kids: If you draw a line to make a shape with 5 sides, what do you call that shape?  Bonus:If you draw 9 straight, non-crossing lines all in the same direction, how many spaces do they make between them?

Big kids: If a picture is 2 feet across and each squiggle is 1 inch wide, how many squiggles fit across the page? (Hint if needed: A foot has 12 inches.)  Bonus: A 4-inch-wide square would hold 4 1-inch squiggles across and 4 squiggles up and down, giving us 16 squiggles. How many squiggles would fit in that square if the squiggles were just 1/2 inch tall and 1/2 inch wide?

Answers:
Wee ones: Try drawing a straight line, or two!

Little kids: A pentagon.  Bonus: 8 spaces.

Big kids: 24 squiggles, since 2 feet = 24 inches.  Bonus: 64 squiggles, since you can now fit 4 of them (not 2!) in each square inch.  Another way to think of it: you can now fit 8 squiggles across and 8 down.

### Laura Overdeck

Laura Bilodeau Overdeck is founder and president of Bedtime Math Foundation. Her goal is to make math as playful for kids as it was for her when she was a child. Her mom had Laura baking before she could walk, and her dad had her using power tools at a very unsafe age, measuring lengths, widths and angles in the process. Armed with this early love of numbers, Laura went on to get a BA in astrophysics from Princeton University, and an MBA from the Wharton School of Business; she continues to star-gaze today. Laura’s other interests include her three lively children, chocolate, extreme vehicles, and Lego Mindstorms.