Math · AreaVISUAL DISCOVERY 01 OF 1,100
Unroll a Circle
Explorer · about 8 minutes · a little curiosity goes a long way
For grown-ups
Today’s little discovery
A ring at distance ρ has length about 2πρ. Open many thin rings and stack them: their ends trace a sloping edge. The finite stack underestimates each curved band with its inner-circumference strip, so its estimate is πr²(1−1/N); increasing N closes that gap and approaches πr².
Ask what the unrolled strip length depends on before naming the formula.
This is a learning model. Try the take-home activity together.Voice settings
Using Heart (en-US).
Your selected voice and opening narration get ready when the page opens with Sound on. The first visit downloads a voice model (about 92 MB), which your browser can cache. No lesson text is sent to a speech service.The sample plays once and does not change the Sound on/off setting.- Wonder
- Guess
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HERE’S A LITTLE WONDER…
How can curved rings become almost-straight strips?
Imagine peeling a round rug into thin circular ribbons and opening every ribbon at one cut.
No rush. Try an idea and see.