1 year, 6 months ago
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Could a circle be considered a polygon with an infinite number of sides?
Where would I find the definition of a circle and a polygon? Why do some mathematicians say a circle has sides? Where can I find discussions on circles and polygons?
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M$1 Answer
Yes, a circle can be thought of as a polygon with an infinite number of sides. As the number of sides increase, the length of each side gets smaller until you technically just have a series of points right next to each other. The same kind of concept is attributed to a line. It's basically an infinite number of points next to each other. In fact, early mathematicians estimated Pi by taking regular polygons with large number of sides, getting the perimeter and dividing by the diameter. As the number of sides of a regular polygon increase, the more the shape approximates a circle. You can see below with the 10 sided polygon, the decagon and a 20 sided polygon. The 20 sided polygon looks more like a circle than the decagon and there are programs that you can add additional sides and see how it looks more and more like a circle with more sides.
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