this post was submitted on 23 Jan 2025
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[Migrated, see pinned post] Casual Conversation

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What would a universe where π=3 look like? (lemmy.world)
submitted 4 months ago by NineMileTower@lemmy.world to c/casualconversation@lemm.ee
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[–] glowing_hans@sopuli.xyz 4 points 4 months ago* (last edited 4 months ago)

if pi was 3, the area of a circle would be equal to 3 squares with side-length of the radius. this means the definition of a circle would be different, since now a circle is 3 squares. This would break geometry. Since the definition of a circle is the foundation of geometry, and trigonometric functions sin and cos.

Hmm or maybe if the area of a circle A=r*r*PI and PI = 3 so A=r*r*3 you would just scale the radius by the factor of sqrt(pi)/sqrt(3) = 1.0233267079464885... to get to a correct circle again.

So you would just scale the universe by a factor slightly larger than 1, up-scaling everything.

But then the formula for the volume of a sphere V=4/3*pi*r*r*r would break ………