Oh Yeah?

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Oh Yeah?

Postby Jakob » Sat Oct 21, 2017 8:59 pm

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Re: Oh Yeah?

Postby Mr Reasonable » Sun Oct 22, 2017 10:33 am

You see...a pimp's love is very different from that of a square.
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Re: Oh Yeah?

Postby gib » Fri Nov 17, 2017 7:12 pm

Mr Reasonable wrote:https://www.theonion.com/new-evidence-reveals-pythagoras-wrote-dozens-of-unhinge-1819655096


From the site:

These conspiracy theorems shed new light on this historic figure, who was apparently suspicious of the fact that all triangles have interior angles adding up to 180 degrees, believing this was evidence that they were united in hiding some sort of covert agenda,” said Professor Janet Boisvert, who found among the artifacts an alternative version of the Pythagorean theorem in which Pythagoras concluded that the square of the hypotenuse of a right triangle was equal to the sum of “all the lies embodied by these cursed triangles!” “One scroll is 35 feet long and contains nothing but a rambling series of postulates attempting to demonstrate the existence of a triangle with three obtuse angles that he thought was being kept under wraps by the government.


Einstein proved that on the surface of a sphere, you could form a triangle with two right angles. Just draw two parallel lines going north starting from the equator and they will meet at the north pole. <-- Could that be considered a triangle? If so, is there a spacetime geometry in which a triangle can be formed with three obtuse angles? Hmm... :-k
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Re: Oh Yeah?

Postby Uccisore » Sat Nov 18, 2017 4:32 pm

gib wrote:Einstein proved that on the surface of a sphere, you could form a triangle with two right angles. Just draw two parallel lines going north starting from the equator and they will meet at the north pole. <-- Could that be considered a triangle? If so, is there a spacetime geometry in which a triangle can be formed with three obtuse angles? Hmm... :-k


What if I say you can't draw a triangle on a sphere at all, because anything drawn on a sphere is inherently a three dimensional figure, which violates the definition of 'triangle'?
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Re: Oh Yeah?

Postby James S Saint » Sat Nov 18, 2017 7:55 pm

gib wrote:is there a spacetime geometry in which a triangle can be formed with three obtuse angles? Hmm... :-k

Easily as long as you aren't talking about planer geometry. Wrapping things around a sphere allows for just about anything.
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Re: Oh Yeah?

Postby gib » Sun Nov 19, 2017 5:47 pm

Uccisore wrote:
gib wrote:Einstein proved that on the surface of a sphere, you could form a triangle with two right angles. Just draw two parallel lines going north starting from the equator and they will meet at the north pole. <-- Could that be considered a triangle? If so, is there a spacetime geometry in which a triangle can be formed with three obtuse angles? Hmm... :-k


What if I say you can't draw a triangle on a sphere at all, because anything drawn on a sphere is inherently a three dimensional figure, which violates the definition of 'triangle'?


That's why I posed it as a question: "Could that be considered a triangle?" I'm not sure myself.

But I think to the beings who are confined to the sphere surface, any shape you draw enclosed by 3 angles would look like a triangle. The sphere is supposed to be a representation of a 4D object and the surface is supposed to be a representation of 3D space. No matter how curved the shapes we draw on the surface, the beings who live in that surface will not see curvature.

Still, that doesn't mean the shape I described would look like a triangle to them either. At the equator, it would look like the beginning of a square and as they make their way to the north pole they'd wonder how the hell the two sides ended up crossing.

James S Saint wrote:
gib wrote:is there a spacetime geometry in which a triangle can be formed with three obtuse angles? Hmm... :-k

Easily as long as you aren't talking about planer geometry. Wrapping things around a sphere allows for just about anything.


I'm trying to picture it. If we widen the angles at the equator to be slightly more than 90 degrees so that they're obtuse, I'm pretty sure the two lines would still meet somewhere near the north pole, but I think it would still be acute.

To get an enclosed shape with three obtuse angles, you would definitely have to warp space in such a way that it perfectly accommodates the angles you want. You could probably just warp space somewhere in the middle of each line as they made their way upward such that they end up curving more towards each other. If you cause them to curve a bit beyond 45 degrees, then they'd form an obtuse angle when they met each other.
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It is impossible for a human being to go through life not thinking irrationally even if they think of themselves as rational
Also just as irrational decisions are not always bad then rational ones are not always good no matter what the intention
- surreptitious75

The rating of rationality can be higher and always is higher than the person trying to be rational. Rationality is less emotional than the person delivering it.
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Re: Oh Yeah?

Postby surreptitious75 » Tue Nov 21, 2017 7:14 am

The general definition of a triangle is a shape with three straight sides whose points touch and whose internal angles add up to I80 degrees. However this is only true
of triangles in two dimensional space. In three dimensional space such as on the surface of a sphere for example they would have three curved sides and the internal angles would add up to 270 degrees. The reason why that type is less well known is because the pages in maths textbooks are two dimensional which means that it is more practical to represent only two dimensional shapes within them
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Re: Oh Yeah?

Postby James S Saint » Tue Nov 21, 2017 9:11 am

Spherical Obtuse Triangle.png
Spherical Obtuse Triangle.png (8.98 KiB) Viewed 356 times


Each dot represents an obtuse corner.
Clarify, Verify, Instill, and Reinforce the Perception of Hopes and Threats unto Anentropic Harmony :)
Else
From THIS age of sleep, Homo-sapien shall never awake.

The Wise gather together to help one another in EVERY aspect of living.

You are always more insecure than you think, just not by what you think.
The only absolute certainty is formed by the absolute lack of alternatives.
It is not merely "do what works", but "to accomplish what purpose in what time frame at what cost".
As long as the authority is secretive, the population will be subjugated.

Amid the lack of certainty, put faith in the wiser to believe.
Devil's Motto: Make it look good, safe, innocent, and wise.. until it is too late to choose otherwise.

The Real God ≡ The reason/cause for the Universe being what it is = "The situation cannot be what it is and also remain as it is".
.
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Re: Oh Yeah?

Postby Uccisore » Wed Nov 29, 2017 12:49 am

gib wrote:But I think to the beings who are confined to the sphere surface, any shape you draw enclosed by 3 angles would look like a triangle.


Sure, but those two angles wouldn't look to be 90 degrees to them either.

Still, that doesn't mean the shape I described would look like a triangle to them either. At the equator, it would look like the beginning of a square and as they make their way to the north pole they'd wonder how the hell the two sides ended up crossing.
[/quote]

I think it would just be a regular isosceles triangle to them, with a 20 degree angle and two 80 degree angles, or what have you.
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Re: Oh Yeah?

Postby Uccisore » Wed Nov 29, 2017 12:52 am

surreptitious75 wrote:The general definition of a triangle is a shape with three straight sides whose points touch and whose internal angles add up to I80 degrees. However this is only true
of triangles in two dimensional space.


"Triangles in two dimensional space" are the only kinds of triangles there are. These other figures like the one James depicted are three-dimensional figures, and thus not triangles.
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Re: Oh Yeah?

Postby James S Saint » Wed Nov 29, 2017 5:12 am

"Triangle" means "three-angles". There is nothing incorrect in referring to 3-angled shapes of other, more usual dimension, as long as the dimensions are specified.
Clarify, Verify, Instill, and Reinforce the Perception of Hopes and Threats unto Anentropic Harmony :)
Else
From THIS age of sleep, Homo-sapien shall never awake.

The Wise gather together to help one another in EVERY aspect of living.

You are always more insecure than you think, just not by what you think.
The only absolute certainty is formed by the absolute lack of alternatives.
It is not merely "do what works", but "to accomplish what purpose in what time frame at what cost".
As long as the authority is secretive, the population will be subjugated.

Amid the lack of certainty, put faith in the wiser to believe.
Devil's Motto: Make it look good, safe, innocent, and wise.. until it is too late to choose otherwise.

The Real God ≡ The reason/cause for the Universe being what it is = "The situation cannot be what it is and also remain as it is".
.
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Re: Oh Yeah?

Postby Uccisore » Wed Nov 29, 2017 8:15 pm

If all triangle means is 'three angles', then we could resolve all these questions very simply just by drawing curved lines on 2d pieces of paper. Of course a "Triangle" can have three angles of any size you want if the lines connecting the angles are free to loop around however you please. if curved lines aren't your bag, another simple solution is just to make a 'triangle' that isn't a closed figure. If you give it three angles and a pair of sides that just extend away from each other forever,
the angles can be any size you want! Why even go to the trouble of inscribing it on a globe? Whatever the hell did those fools mean when they said the angles of a triangle must add up to 180?

But of course that's all nonsense, because relying on the geometric definition of triangle is the only thing that made the question interesting in the first place.

A triangle has to have three angles and three sides. It's a polygon, which means the sides have to connect to each other in a closed figure and have to be straight. Being a polygon also means the figure has to lie in a single plane, and figures inscribed on spheres don't do that.
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Re: Oh Yeah?

Postby James S Saint » Fri Dec 01, 2017 6:09 am

It's just a standardization of language issue. Anything other than the standard must be indicated as such. Not a problem.
Clarify, Verify, Instill, and Reinforce the Perception of Hopes and Threats unto Anentropic Harmony :)
Else
From THIS age of sleep, Homo-sapien shall never awake.

The Wise gather together to help one another in EVERY aspect of living.

You are always more insecure than you think, just not by what you think.
The only absolute certainty is formed by the absolute lack of alternatives.
It is not merely "do what works", but "to accomplish what purpose in what time frame at what cost".
As long as the authority is secretive, the population will be subjugated.

Amid the lack of certainty, put faith in the wiser to believe.
Devil's Motto: Make it look good, safe, innocent, and wise.. until it is too late to choose otherwise.

The Real God ≡ The reason/cause for the Universe being what it is = "The situation cannot be what it is and also remain as it is".
.
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Re: Oh Yeah?

Postby Uccisore » Fri Dec 01, 2017 6:01 pm

There is no issue. It's clear from the context of the thread that everybody here was talking about the geometric definition of 'triangle', and indeed it's clear that's what *you* meant as well- that's why you took the time to inscribe your 'triangle' on a sphere instead of just presenting a jagged line with three kinks in it, or some sort of flat, curved figure.

When I pointed out that a curved figure residing in three dimensions isn't a triangle, you declared the word meant something other than how everybody here was using it in order to save face. 'just any old thing with three angles' is not anybody's definition of 'triangle', much less a standard one.
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Re: Oh Yeah?

Postby gib » Sat Dec 02, 2017 7:51 pm

If we are living in a 4D universe which is symbolized by the 3D sphere, then no geometric object we see is ever really flat.

If I understand where Ucci's going with this, he'd like to say that if we are analogues of 2D creatures bound to the surface of a sphere, then whatever looks flat to us is really curved. It would be the highest dimension that counts as the absolute state of reality. Just as we would say that the surface of a sphere is really curved despite what the 2D creatures living on the surface think, we'd have to say the same of the 4D universe of which we are creatures bound to its 3D "surface". Thus, we cannot perceive triangles, or any other 2D shape--not if all such 2D shapes would, by definition, have to be flat--and if all shapes we see in our universe look to be flat, it can only be because they are curved along the "surface" of our 4D universe, and therefore not flat shapes at all. Thus, if we really are creatures living on a the surface of a 4D universe, we have never ever seen a triangle.
My thoughts | My art | My music | My poetry

It is impossible for a human being to go through life not thinking irrationally even if they think of themselves as rational
Also just as irrational decisions are not always bad then rational ones are not always good no matter what the intention
- surreptitious75

The rating of rationality can be higher and always is higher than the person trying to be rational. Rationality is less emotional than the person delivering it.
- encode_decode

Is that a demon slug in your stomach or are you just happy to see me?
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Re: Oh Yeah?

Postby Uccisore » Sat Dec 02, 2017 11:07 pm

gib wrote:If we are living in a 4D universe which is symbolized by the 3D sphere, then no geometric object we see is ever really flat.


That wouldn't really have any bearing on mathematical definitions like those used in geometry, though. I mean, there's no true perfect circles out there either, but we manage to talk about them.

If I understand where Ucci's going with this, he'd like to say that if we are analogues of 2D creatures bound to the surface of a sphere, then whatever looks flat to us is really curved.


I think I'm making a simpler statement than that. I'm just saying a figure inscribed on a sphere is 3D, not 2D, and that's why it can break the rules of geometry. Because it's not really the figure we say it is. I mean, take the sphere out of it for a moment. Imagine the proposed figure hanging in space. It would look something like this:

https://www.obelink.es/images/detailed/ ... hade_1.jpg

A curved shape with two right angles that is bowed so that the opposite end can meet at a point.

That is not a triangle.

Gluing it to the side of a globe does not make it a triangle.

Drawing on the side of a globe does not make it a triangle.

Just as we would say that the surface of a sphere is really curved despite what the 2D creatures living on the surface think,


It's worth pointing out that the creatures living on the surface of the sphere aren't 2D either, for the same reason that the 'triangles' they see are not. If they were 2D, their edges would be lifted from the sides of the sphere, and indeed they would only make contact with the sphere at a single point.


Thus, if we really are creatures living on a the surface of a 4D universe, we have never ever seen a triangle.


I dunno, maybe. That's certainly further than I intended to go with it. I'm just pointing out that drawings on spheres don't meet the geometric definition of a polygon.
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