From 4 slices to 32
Tap + to add slices: 4 → 8 → 16 → 32. The right-hand row of wedges quietly straightens — the more slices, the more it resembles a real parallelogram.
Slice a circle into more and more wedges and the rearranged shape gets straighter. At 32 wedges it looks like a real rectangle — base πr, height r. The circle hasn't changed; only the cuts are finer.
Aligned with CCSS 7.G.B.4.
More slices → the pieces line up into a near-perfect parallelogram (base ≈ πr, height = r).
Geometry and measurement model
Unroll a Circle into a Rectangle is built for students who memorize formulas before seeing the shape decomposition. It gives the page a clear search purpose: learn the model, manipulate it, then continue into the matching grade-level practice.
Unroll a Circle into a Rectangle helps when a student can copy a procedure but cannot explain why it works. The demo slows the idea down into a visible model before sending the learner to guided missions.
Learning goals
How to play
Continue with guided practice
Each wedge's arc gets smaller relative to its straight sides as wedge count grows. The curved bottom edge approximates a straight line.
Cutting and rearranging never adds or removes material. The whole circle is always present, just in pieces.
Riemann sums approximate curved areas with rectangles, then take the limit. This game shows the geometry of that idea on one easy example.
Grades 6–7, aligned with CCSS 7.G.B.4. Beautiful preview of integration.
