



 
Hi Reid, Mathematicians need to define concepts clearly and without ambiguity, and this is just the task you are struggling with. What is the meaning of a side as it pertains to a circle? On a polygon like a triangle, rectangle, pentagon and so on the meaning is clear. Without getting technical the sides are the straight line segments that make up the shape. It seems that you want to include a circle as a polygon and define the sides of a circle. A polygon is defined in different ways and none of them include a circle. For example look at the Wikipedia definition or others you can find by searching the web for polygon definition. Regardless of whether you want to call a circle a polygon the idea of an infinite number of corners applies to many other shapes. For example This is an equilateral triangle with the sides fattened to be arcs of a circle. You can perform the same fattening with any polygon. I agree with the statement by Chris and Harley that "The question, "How many sides does a circle have?", is too ambiguous to have a definite answer." Penny  


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