The Rolling Race π
Here's a wheel with a red dot on its rim, sitting on the ground. How far does it travel in one full spin, from the red dot touching the ground to touching it again? We'll measure in sticks, where one stick is exactly as wide as the wheel, straight through the middle. That's the purple stick lying inside it.
Every wheel ever π‘
Three sticks and a little bit. Was that just this wheel, or do coins and Ferris wheels do the same thing? Change the size, roll it again, and watch the table.
π My Discovery Table
| wheel size (hands across) |
distance rolled (hands) |
distance Γ· size |
|---|
π Stare at the last column. Different wheels, different distancesβ¦ but what do you notice?
The Great Squeeze π₯ͺ
2,200 years ago Archimedes trapped this number between two shapes, and you can do the same. Put a six-sided shortcut path inside the wheel: its corners touch the rim, but its sides cut straight across. π Click each side to measure it with a radius stick.
Mission time π¦Έ
If you know how big something round is across, you can work out the distance around it, and the other way too. Use the Ο machine below on the missions.
Now YOU are the teacher π
You know four ways to show someone the secret of circles. Try each one on a different person.
1. Roll & Count π
Find any wheel or round lid. Mark a spot on the rim, roll it one full turn, then measure.2. The String Trick π§΅
Wrap a string around a can, then stretch it across the top.3. The Squeeze π₯ͺ
Draw a circle with a six-sided shortcut path inside it.4. The Endless Number π₯§
Tell them its name and its weirdest fact.Taught somebody at least one way? Then claim this:
Certificate of Discovery
This declares that
discovered the Secret of Every Circle
(known to grown-ups as Ο β 3.14159β¦)
by rolling, measuring, and squeezing,
the same way Archimedes did.