Oh let’s get pedantic!
The curved edges technically have infinite “side”.
…and a square has four interior 90 degree angles.
…and based on the infinite number of sides for a curved line aspect, the “90 degree” angles would all be +/- the limit as it approaches zero, so never truly 90 degrees but always an infinite fraction away.
Someone knows more calculus than they are letting on…
Hey, I failed the highest level of calculus possible. Twice.
I’ll have you know that I passed the two lowest levels of calculus required for my degree. So you know, I’m something of an expert.
Yeah, we gonna need more rigor on this one.
“A square is a shape made up of four equally long lines a, b, c, d where a is perpendicular to c and d and parallel to b. Each of these lines meet exactly two other lines at it’s ends.”
I’m not a mathematician so there might an odd case somewhere in there. Maybe it has to be confined to a shared plane?
Lines are infinitely long… do you mean line segments?
Wikipedia has a good enough definition: “It has four straight sides of equal length and four equal angles.” Nice and simple.
Pentagon fits that definition also since it doesn’t specify “it has four and only four” sides
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So you’re saying this is the outline of a square in the astral plane? Because it sounds like you’re saying this is a square in the astral plane.
No, just a 2d plane
the angles are interior if you go into the scary world of high level maths and their weird fucking geometries.
this is a square, from a certain point of view
Hey, that’s my job!
Also I don’t think that’s technically the technical classification. I think that sidedness is an attribute that simply doesnt apply to curves.
You can approximate curves with some number of sides, and the approximation gets more accurate as the number approaches infinity, but it doesn’t actually have the infinite sides.Very cool! I’m always happy to learn something new!
I mean, I’m just pedantic; double check with a mathematician, to be sure lol
I’m genuinely curious, what is your job that requires arithmetic?
I feel like most jobs require arithmetic.
But it is not my career to be a pedant, just my role in life 😜Fair
Not if this square is a projection of a curved surface
If it is a projection, then there are more than two curved sides, which also begs credence to the interpretability of the angles they intersect.
Well angles between 3 points are always going to be angles. If your choose a different configuration of dimensional parameters you can effectively project a square from the 2D plane into this exact shape, then logically the angles would follow.
You lost me at 3 points. Could you dumb it down a bit?
Yo bro let’s downscale everything to 2D then upscale it to infinity or something, everything is possible when you project to this demonic crystal justttt this way /s
I’m not a math major, but I always considered it that a square is a special case of rectangle, a rectangle is a special case of parallelogram, and a parallelogram a special case of a quadrilateral, a quadrilateral a special case of a simple polygon.
This shape isn’t a polygon, so it cannot be a square.
Rotate the cone towards you.
Now you see this. 🤯
uhhh, wait. Under what projection is OP’s “square” reduced to an actual square
It’s possible, but there needs to be a thickness in addition to the length and width.
Im gonna need more than that as an explanation. Sandwiches too if you’re making some
Imagine you have a cookie cutter in that shape. Cut a cookie as thick as the chord of the largest arc.
View the new vertical surface of the longest arc that is now a cylindrical section.
Viola, square. 😁
*munches thoughtfully*
this is terrible, but it tastes okay
Wrong. This is a definition of a [pizza] + [the extra peperoni from the other slices that got stuck to that slice because the cutting was imperfect]
Plus the table.
Listen if they put a pepperoni in the center of the pie then a poor cut is clearly the least of our concerns
Always put a pepperoni in the exact middle. It’s like a wishbone, but for pizza. The person who gets the majority of the center pepperoni gets a wish.
A center pepperoni is asking for the center of your pie to be fucked up
Peperoni are bell peppers. I have no idea why the USA chose to use this word to mean salami, instead of, you know, salami.
You’re thinking of peperoncino, a spiced chilli pepper also known as sweet Italian peppers. We still have salami in the US.
I’d guess pepperoni is called that because it’s dried salami with pepper seasoning.
I found a link just randomly googling. https://www.thoughtco.com/you-say-pepperoni-3972377
Yes, peperoncini are a bit like chili. Peperoni is literally “bell peppers” though. Peperone in singular.
https://dictionary.cambridge.org/dictionary/italian-english/peperone
Pepperoni and salami are totally different dude, you might as well be saying that Americans should just call their potatoes “yams”. And you can get both of those sausages and many, many more on your pizza, often at the same time
Not a polygon
Diogenes go home.
Don’t the internal angles need to be 90°? Two of those right angles aren’t right angles on the inside.
Mathematics by Diogenes
Didn’t a square need broad nails or something?
Okay, calm down Diogenes
Lines that intersect a circle like that aren’t “right angles” tho, they’re called “normal” to the circle - in other words pointing directly toward the center. A normal line is at right angles to a tangent line, but not to a curve.
Straight lines. Also two sets of parallel lines. This is one definition of a square, but not the common one.
This shape could exist as a projection onto an upright cylinder, wrapping around the cylinder. The two straight edges go vertically along opposite sides of the cylinder. The curved lines wrap around the circumference. The lines are now straight and parallel on the net of the cylinder.
But we can go further: Imagine taking this cylinder and extending it. Wrap it into a loop by connecting the top to the bottom so it forms a torus (doughnut) shape. This connects both sides of the shape, now all “interior” angles are on the inside of the square, and all “exterior” angles are on the outside. The inside and outside just happen to be the same side.
I believe these lines are straight with a black hole at the centre.
straight, gay, lines are lines. let them be.
If that’s so, the angles are probably not right angles.
None of the angles looks wrong either
Can straight be defined in a nonlinear environment?
I would guess on a sphere these can be straight yes: The pole goes into the center of cicular thing and radius of the sphere needs to put the other arc on one latitude.
Euclid’s first postulate: Give two points, there exists exactly one straight line that includes both of them.
This only applies in 2nd order real space. Euclidean geometry aside, I agree with at least one line could exist between two points
Counterexample: North and Southpole on Earth.
No, it’s still accurate - the straight line goes through the center of the Earth. Only in coordinate systems where ‘straight’ is defined as following the curvature of a surface are there infinite lines between the North and South Poles… and that would be non-Euclidean geometry.
Someone never had to deal with mathematical proofs, only layman’s definitions.
All properties of a parallelogram apply:
- Opposite sides are parallel
- Opposite sides are congruent
- Opposite angles are congruent
- Consecutive angles are supplementary
- Diagonals bisect each other
AND
- All angles are congruent
- All sides are congruent
- Diagonals are congruent
- Diagonals are perpendicular
- Diagonals bisect opposite angles
Of course, but such strict definitions only come about because smart people come up with examples like OP when you don’t add the full definition.
The interior angles need to be equal 🤓
Here you can see how things go haywire when skipping minor parts of definitions.
