Summary 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.
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机译：摘要 在现代教科书中，π被定义为 C/d 的比率，其中 C 是圆周的长度，d 是它的直径。由于π表示为常数，因此我们被引导到标题中的问题。在欧几里得和阿基米德的著作中都找不到完整的答案，因为他们没有明确定义平面曲线的长度，这阻碍了我们将他们的著作转化为形式证明。在本文中，我们指出了微积分教科书中长度整数定义的缺点，然后我们引入了一个定义，该定义允许简单证明 C/d 对于所有圆都是相同的，它只需要几何和序列的基本概念。
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