Chapter 12
Circle Measurement and Constructions
A round table needs trim around its edge and a cover across its top. A ruler gives you straight distances, but following the curved edge or covering the whole top raises different questions. Circle measurement offers a way to reason about those quantities. What could justify an exact answer when even a very precise measurement has to stop at some point?
What You'll Explore
4 lessons.
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How could polygons help you measure a circle when every polygon has straight sides? Explore what increasingly close approximations can tell you about circumference and area, and what separates convincing reasoning from a pattern in a few measurements.
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Suppose the same central angle is marked in two circles of different sizes. Explore the connection between their arc lengths and the way angles are measured, including what an alternative to degrees might help us describe.
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Picture a curved garden bed bounded partly by a straight fence. How could you measure its space and complete boundary, and how do those questions change for other regions formed from parts of circles?
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Can a compass and straightedge place the corners of a regular polygon exactly on a circle? Explore constructions of an equilateral triangle, a square, and a regular hexagon, and the geometric evidence needed to justify each drawing.