this post was submitted on 07 Oct 2024
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Behold, a square (sopuli.xyz)
submitted 1 month ago by [email protected] to c/[email protected]
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[–] [email protected] 11 points 1 month ago (3 children)

What are the 4 sides?

[–] [email protected] 8 points 1 month ago (1 children)

The semi-circle is one side, then the 2 straight edges, and the arc between them is the 4th side.

[–] [email protected] 6 points 1 month ago (1 children)

That's what I thought. The only way on which this has four sides is if the semi -circle is a side. But if that's the case, then I don't know wha the definition of "side" is

[–] [email protected] 10 points 1 month ago (1 children)

Knock knock. Do you have a moment to discuss non-euclidean geometry?

[–] [email protected] 10 points 1 month ago

/slams door

[–] [email protected] 17 points 1 month ago

The black lines

[–] [email protected] 4 points 1 month 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

[–] [email protected] 4 points 1 month ago* (last edited 1 month ago) (1 children)

I look at your diagram and see:

ϴ= L/(L+R)

And

2π-ϴ = L/R

I solved those (using substitution, then the quadratic formula) 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.

[–] [email protected] 3 points 1 month 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.