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In modern textbooks,  π  is defined as the ratio  C / d , where  C  is the length of a circumference and  d  its diameter. Since  π  is presented as a constant, we are led to the question in the title. A complete answer is not found in Euclid nor in Archimedes works, as they did not  define  the length of a plane curve explicitly, which impedes us to put their writings into a formal proof. In this paper, we point out the disadvantages of the integral definition of length found in calculus textbooks and then we introduce a definition that allows for a simple proof that  C / d  is the same for all circles, which demands only basic notions of geometry and sequences.

Why is it that the Ratio of Any Circle’s Circumference to its Diameter is a Constant?