# Circular Reasoning: Who First Proved That C Divided by d Is a Constant?

@article{Richeson2015CircularRW, title={Circular Reasoning: Who First Proved That C Divided by d Is a Constant?}, author={David Richeson}, journal={The College Mathematics Journal}, year={2015}, volume={46}, pages={162 - 171} }

Summary We argue that Archimedes proved that the ratio of the circumference of a circle to its diameter is a constant independent of the circle and that the circumference constant equals the area constant. He stated neither result explicitly (in surviving material), but both are implied by his work. His proof required the addition of two axioms beyond those in Euclid's Elements.

## 3 Citations

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

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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…

### $\pi$ and Arc-Length

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We use the classical definitions (i) π is the ratio of area to the square of the radius of a circle; (ii) π is the ratio of circumference to the diameter of a circle, to prove π’s existence within…

### A Bibliography of Publications on the Numerical Calculation of π

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(sinα)/α [128]. 0 [248]. 1 [261]. 1/π [221, 222, 315, 286]. 1/π [240, 255, 222]. 10, 000 [57]. 10, 000, 000 [155]. 16 [230]. 2, 000 [39]. 2, 576, 980, 370, 000 [249]. $24.95 [219]. 2H2 [259]. b…

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