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The Pi-on

Explore how general relativity affects our understanding of pi and curved spacetime manifolds, revealing the nuances of geometry.

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I am in love with this comment and want to have its babies:

pi appears as a constant in many formula of physics. General relativity says that it isn't constant. Is it the origin of the pi particle, aka pion?

A curmudgeonly literalist might, when faced with a question such as this, harrumph a simple "No." A more loquacious sort might explain that general relativity does not say that π is not a contstant. Pi is not a parameter of physics like the fine-structure constant, which could conceivably be different or even variable from place to place. It's a universal answer to a fixed question, to wit: what is the ratio of the circumference of a circle to its diameter, as measured in Euclidean geometry? The answer is of course 3.141592653589793..., or any number of representations in terms of infinite series. But the point of the question is that GR ...

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