No arguments here
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Why point (5)?
Since the straight lines are radii, they cut the circles at angle θ and 2π - θ, respectively. Adding those, you get 2π.
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Since the straight lines are radii, they cut the circles at angle θ and 2π - θ, respectively. Adding those, you get 2π.
Okay, but... Why? Is that a theorem that I don't remember from school?
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Mathematics by Diogenes
Didn't a square need broad nails or something?
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Someone knows more calculus than they are letting on...
Hey, I failed the highest level of calculus possible. Twice.
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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?
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.
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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.
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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
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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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....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.
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
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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.
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Oh let's get pedantic!
The curved edges technically have infinite "side".
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. -
The interior angles need to be equal
wrote on last edited by [email protected]Here you can see how things go haywire when skipping minor parts of definitions.
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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!
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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.
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Not a polygon
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Okay, but... Why? Is that a theorem that I don't remember from school?
wrote on last edited by [email protected]Take this shape as an example. The "square" in question consists of AC, BD, the outer AB, and the inner CD.
Point (5) means that, since the lines AC and BD are radii of the concentric circles, the arcs AB and CD should have the same inner angle. That's because the angle COD is equal to AOB.
Since, the inner angle is the same, then the outer AOB should, by definition, be 2π - (the inner AOB), because that's how radiants work; a circle is 2π rads.
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Take this shape as an example. The "square" in question consists of AC, BD, the outer AB, and the inner CD.
Point (5) means that, since the lines AC and BD are radii of the concentric circles, the arcs AB and CD should have the same inner angle. That's because the angle COD is equal to AOB.
Since, the inner angle is the same, then the outer AOB should, by definition, be 2π - (the inner AOB), because that's how radiants work; a circle is 2π rads.
Thank you! But why arc CD and arc AB length should add to 2 PI? Or why does the angle COD times two is 2PI if that's what you meant?
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Thank you! But why arc CD and arc AB length should add to 2 PI? Or why does the angle COD times two is 2PI if that's what you meant?
wrote on last edited by [email protected]Point (5) is not about the arcs' lengths. It's about the angle they create with the center.
Also, I never said that COD * 2 = 2π. I said (inner COD) + (outer COD) = 2π rads
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Very cool! I'm always happy to learn something new!
wrote on last edited by [email protected]I mean, I'm just pedantic; double check with a mathematician, to be sure lol
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Rotate the cone towards you.
Now you see this. 🤯
uhhh, wait. Under what projection is OP's "square" reduced to an actual square
