Geometry · Foundation · 9 min
Where πr² comes from
Cut a circle into sectors, then alternate their directions. The pieces approach a rectangle.
WHAT HAPPENS IF…Double the radius. How does the area change?
Preparing your experiment…
As sector widths shrink, the alternating arrangement approaches a rectangle of height r and width πr. Finite sectors have scalloped edges, so they are only an approximation to that rectangle; the original sectors still have exact total area πr².
A detail that matters
A finite collection of sectors is not an exact rectangle.
Keep the connection going
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