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With regular spherical and hyperbolic geometry, yes, it is flat-ish if you look at a small enough area. On the other hand, if you have a different distance metric, the ratio of a circle's diameter to circumference can be a different constant. For example, in taxicab geometry, it is 4

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In Uber Geometry, it can vary from 5 to 14 during surge pricing.

In London geometry, the distance depends where you are in the one-way system.

I know this is sort of a low quality joke post, but I don’t think I’d ever thought about a directed taxi-cab distance before. I’m not yet convinced it’s a useful model outside GIS, but I may spend considerable time today thinking about it.

Thank you.

Happy to be of service, in filth it will be found!

TIL that Taxicab circles are squares with sides oriented at a 45° angle to the coordinate axes.

It depends if you define a circle as "constant distance from centre point" or "minimum (circumference/area)".

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