this post was submitted on 07 Oct 2024
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Behold, a square (sopuli.xyz)
submitted 1 day ago by hydroptic@sopuli.xyz to c/science_memes@mander.xyz
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[–] UrLogicFails@beehaw.org 5 points 1 day ago (1 children)

Someone may want to double-check my math on this one, but the length of the sides will be dependant on the radius of the smaller circle

ϴ=π+1-√(π^2+1), l=(2π-ϴ)r_1, l is the length of the sides. r_1 is the radius of the smaller circle

[–] m0darn@lemmy.ca 4 points 18 hours ago* (last edited 17 hours ago) (1 children)

I look at your diagram and see:

ϴ= L/(L+R)

And

2π-ϴ = L/R

I solved those and got

L= π-1 ± √(1+π²) ~= 5.44 or -1.16

Whether or not a negative length is meaningful in this context is an exercise left to the reader

Giving (for L=5.44):

ϴ~= 0.845 ~~48.4°

I'm surprised that it solved to a single number, maybe I made a mistake.

[–] UrLogicFails@beehaw.org 3 points 15 hours ago

That lines up pretty similarly with what I found also. The angle should be a constant since there is only one angle where the relationship would be true. I just left it in terms of π because I try to avoid rounding.

Having said that, L would be a ratio of r; which I think lines up with what you found as well.