this post was submitted on 17 May 2025
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Do cylinders even exist in metrics where pi = 5 ?
Yes. The 3d shape existence is not affected by changing pi values
Cause it's just a (n-1)-dimensional ball extruded along the remaining axis, or do all 3d shapes exist on (nearly) all 3d metrics?
Mostly because the actual pi values can vary in between non/euclidean geometries. Within extremely strong gravitational fields, spacetime becomes highly non euclidean, affecting the C/d ratio of an actual circle, so I'd wager this would affect pi as well
Technically no, because pi equals pi not 5. But you can approximate its value as 3 or 5 or whatever you want, knowing it's not exact and that your result will only be an approximation. I mean you could also ask how long light takes to reach us from Alpha Centauri if the speed of light is 1000 mph. It's not, but if you make that a condition of the problem you can do the calculation just fine.
I think that reason would make it "Technically Yes", since False (pi = 5) implies False (cylinders exist) is (vacuously) True ("absurd premise").