The proof depends on the existence of triangles which only exist in a two-dimensional world. Nevertheless, it still holds true in our 3 dimensional world. Can this theorem also be used to accurately describe structures existing in multi-universe?
The proof depends on the existence of triangles which only exist in a two-dimensional world. Nevertheless, it still holds true in our 3 dimensional world. Can this theorem also be used to accurately describe structures existing in multi-universe?
Your question is illogical as universe is only consistent with how you feel persally.
Try using the pythagorean theorem on a sphere and see how well it works for you.
2-d wrote:
Try using the pythagorean theorem on a sphere and see how well it works for you.
You mean, like, the Earth?
http://en.wikipedia.org/wiki/Pythagorean_theorem#Non-Euclidean_geometry2-d wrote:
Try using the pythagorean theorem on a sphere and see how well it works for you.
And to the OP: there exists a general formula for the Pythagorean Theorem for n-dimensions.
Technically no.
The Earth is a spheroid not a sphere.
But either way it will not work there.
In the liberal world, things are always a bit askew.
2-d wrote:
Technically no.
The Earth is a spheroid not a sphere.
But either way it will not work there.
Oh it works there. I've used it in school.
Chris Wasnetsky wrote:
And to the OP: there exists a general formula for the Pythagorean Theorem for n-dimensions.
Thanks, but WTH does that mean?
Prove the n-dimensional Triangle Inequality in a general sense (independent of the Pythagorean Theorem and law of cosines). That is your answer.
Only if God wills it.
2-d wrote:
Try using the pythagorean theorem on a sphere and see how well it works for you.
I don't get it. It's not a triangle. It's three curved lines that meet.
The Ancient Kenyans discovered most mathematics that was lagter copied by the Ancient Persians, ANcient Incas, Ancient Egyptians, and Ancient Chinese who uncovered Calculus, Physics, and Chemistry.
Words are flowing out like endless rain into a paper cup
In Euclidean space (flat) like normally encountered, triangles are as they should be, with the angles adding up to 180 degrees. Similarly, the circumference of a circle is 2piR.
But on Riemann (curved) surfaces these normal geometries get really weird. For instance, the angles of a triangle won't add up to 180. Or the circumference is less than or greater than 2piR.
So, in the universe you can have situations (space near black holes or neutron stars) where general relativity can play havoc with every day geometry.
dumb blob wrote:
The proof depends on the existence of triangles
Really? The proof doesn't depend on the existence of something.
The theorem states, that, IF you have a right-angled triangle, THEN the well known relationship exists. It says nothing about the existence of (right-angled) triangles.
said88 wrote:
dumb blob wrote:The proof depends on the existence of triangles
Really? The proof doesn't depend on the existence of something.
The theorem states, that, IF you have a right-angled triangle, THEN the well known relationship exists. It says nothing about the existence of (right-angled) triangles.
Cut me some slack, will 'ya? I'm just a dumb blob trying to grasp some weird abstract concepts.
Please, humor me for a second more. Would Pythagorean's theorem exist if triangles weren't part of the human consciousness? I mean, would that Pythagorean guy have cause to even contemplate the relationship between the sides of a triangle and its hypotenuse if he had never conceptualized a triangle?
Two dimensions is just an idea used to describe the world. Three dimensions is just an idea used to describe the world. Triangles are just an idea used to describe the world. For them to be a useful description, ideas like straight lines and right angles have to be useful too. Across the entire universe, they're not.
pythagoras did not invent the problem of right triangles. They had been used for millennia in building by the mesopotamians and egyptians. The egyptians knew of the 3-4-5 right triangle, but you don't need to use calculations to construct a right triangle, all you need is to mark the midpoints of two ropes, stretch the shorter one out into a straight line, and then stretch the longer one out next to it with the endpoints touching and the midpoint stretched out laterally, draw a line between the midpoints and boom, right angle. Nobody knows how long ago this was invented but I expect stone age people could do it. They just didn't happen to build very many things.
Yes, the Pythagorean theorem is consistent across the universe. ET beings may call it something other than the Pythagorean theorem, but the actual formula is the same.