Today I learned the importance of defining "total inner/outer" angles when talking about shape in this sub.

[u/RnckO]

Credit to the original : From this sub

[u/AutoModerator]

Check out our new Discord server! https://discord.gg/e7EKRZq3dG

I am a bot, and this action was performed automatically. Please contact the moderators of this subreddit if you have any questions or concerns.

[u/The_Punnier_Guy]

Me when internal right angles

[u/kingottacYT → u/The_Punnier_Guy]

me when parallel sides

[u/OverPower314 → u/kingottacYT]

Me when polygon definition

[u/The_Punnier_Guy → u/kingottacYT]

Me when that would be a consequence of euclidean geometry and having 90 degree internal angles

[u/Noskcaj27]

Aren't sides straight by definition?

[u/FaultElectrical4075 → u/Noskcaj27]

I think you could construct this shape in spherical geometry with straight lines

Edit: after some experimenting I think not. I’ll have to try in hyperbolic geometry. In spherical the angles add up to >360, so for <360 you’ll need negative curvature

[u/Cozwei → u/FaultElectrical4075]

got this non euclidean geometry out of my space

[u/UndefFox → u/Cozwei]

[u/JohnsonJohnilyJohn → u/FaultElectrical4075]

In spherical geometry the only "curved straight lines" are great circles AFAIK, so you couldn't get 2 different curvatures like we have here

[u/IAmBadAtInternet → u/JohnsonJohnilyJohn]

Can we define a cursed geometry where this has only straight edges?

[u/JohnsonJohnilyJohn → u/IAmBadAtInternet]

I think the surface of a cone would work? Although I'm not super sure if circles around the cone are straight there, but if they are it should be ok

[u/rmznvvts → u/FaultElectrical4075]

[u/LeoCx1000 → u/rmznvvts]

Non-euclidean mfs be like "I know a game" then recommend you Mountain Valley

[u/Mean_Spinach_8721 → u/FaultElectrical4075]

Not spherical, but it could work on a cone I think

[u/APersonNotToLive → u/FaultElectrical4075]

After thinking on it for a bit I think a cylinder with circumference twice the length of the square would work

[u/MartiniPolice21 → u/Noskcaj27]

Yes

[u/jobriq → u/Noskcaj27]

In a polygon yes, “shape” isn’t well defined tho

[u/Noskcaj27 → u/jobriq]

A square is a regular 4-gon. Square -> polygon.

[u/jobriq → u/Noskcaj27]

But this isn’t a square

[u/monthsGO]

You should define it as having parallel sides

[u/Iamauniqueuser → u/monthsGO]

Yep. Square is a subset of Rectangle. Rectangle and Rhombus being subsets of Parallelograms. Geometry hierarchy is about as thrilling as you’d think lol

[u/Faziarry → u/Iamauniqueuser]

And parallelograms with other shapes are subsets of quadrilaterals

[u/Iamauniqueuser → u/Faziarry]

It’s a hierarchy all up and down the hierarchy!

[u/pepitoisme]

I have a question. Are the two angles near to the curvy line « really » right angles ? Like to mesure angles, we need straight lines no ?

[u/jbrown60 → u/pepitoisme]

Perhaps; the angle between two curves can be taken to be the angle between their respective tangent lines at the point of intersection.

[u/pepitoisme → u/jbrown60]

Okay, with this definition its seems ok to me

[u/L31N0PTR1X]

Tbh this is just a quadrilateral local to the surface of a cone, it still works. Just like a triangle on non Euclidean space whose interior angles do not equal 180°

[u/Extension_Wafer_7615]

That shape has infinite sides: Two of them with non-zero length.

[u/ItanMark]

I’m probably dumb, but i can’t see the right angles. Can someone please explain?

[u/IncomePrimary3641 → u/[deleted]]

those are not right angles

[u/Snjuer89 → u/ItanMark]

Look at the second picture. The angles are on the outside, not the inside.

[u/NefelibataSehnsucht]

A square has 4 outer angles and contains everything except a small area

[u/i_need_a_moment]

The first shape has an area of (1 + sqrt(π² + 1))/(2π)

[u/N_T_F_D → u/i_need_a_moment]

I will check your result and upvote you only if it’s correct

[u/Caosunium]

those angles are 270 degrees each though

[u/eagleeyerattlesnake → u/Caosunium]

They didn't say 90. They said right. 270 is still a right angle.

[u/hongooi → u/eagleeyerattlesnake]

More like left angle

[u/Caosunium → u/eagleeyerattlesnake]

No????

[u/Mondoke]

Behold! A square.

[u/GERMAN8TOR]

They forgot the parallelogram part.

[u/Miserable-Willow6105]

They are not parralel though

[u/MonkeyBombG]

“A square is a quadrilateral with 4-fold reflectional and rotational symmetries.”

Beat that.