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BEHOLD! PLATO’S MAN!
Squares are defined as polygons which are defined as having all straight lines.
I bet there exists a non-Euclidean surface such that all these lines are straight.
A cone should do the trick, no?
Spheres and hyperbolas. EDIT: oh they mean this specific shape not just any non-Euclidean square, so those won’t work.
I haven’t thought about a cone much but I think no.
The definition of a square is a polygon with four equal sides and four equal angles (nothing about 90 degrees and nothing about internal vs external angles since people love to get hung up on that)
A cone is half a hyperbola but I think without the symmetry of a hyperbola you can only get two angles equal at a time or two sides equal at a time.
You have the section of the smaller circle wrapping around the back of a narrower section of the cone, a right angle and then a straight line running down the side of the cone, another right angle in the other direction, then the section of the larger circle, this time going around the front of the cone, another right angle, and then the straight line completing the shape.
But you are right, the circle sections are not geodesics on that manifold, so not ‘straight’ by the most reasonable extension of that word to non -euclidian geometries. They’d be more like lines of latitude in that they seem straight from the outside, but in the context of that manifold are curved.
Oh no! Are you telling me, OP didn’t post a square??? ;_;
but muh mathematical breakthru!!!
AI when I ask it to do most things…
This is some typical plucked chicken shit
Yes. And the “broad flat nails” retort for this is “with parallel opposing sides.”
While I know this is supposed to be a joke, surely the angles of a shape must be on the inside of the shape.
Lol
I just read another comment here pointing out that square is a polygon, which requires having only straight lines.
I think this would be a stronger argument.
I think what the previous poster is saying is that the image does not have four 90° angles, but instead it has two 90° and two 270° angles.
…I have no idea if that’s an actual deal breaker, but the logic is sound.
I’m not aware of any shape that is defined by the angles of its outsides.
Eh, going back when I was learning proofs in high school…
A square was 4 equal length sides arranged in two sets of parallel lines with four 90° right angles.
Two sets of parallel lines are necessary to make a rectangle, and a square is just a rectangle with equal sides.
Proofs are all about working the way through each step to getting to a distinct shape defined by those smaller steps. All squares are rectangles, but not all rectangles are squares. Technically if in remembering correctly, rectangles are also trapezoids, just with 90° right angles.
Parallelograms, not trapezoids. Kind of. Maybe. Or maybe trapeziums.
See… some define trapezoid as specifically one set of parallel sides (originally trapezium). Some as no parallel sides (originally trapezoid) Those two were swapped by some asshole, and then swapped back in England but not in America.
Though most now just say a trapezoid (or trapezium in England) is at least one set of parallel sides, which makes parallelograms a type of trapezoid. Which does make a rectangle a type of trapezoid.
They call only one pair of parallel sides a proper trapezoid instead.
I totally forgot that parallelograms were a thing in all that. And I never even considered naming differences over time.
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