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RE: What Did Einstein Mean when He Said Space is Curved?
June 5, 2017 at 6:37 pm
(June 5, 2017 at 10:27 am)Alex K Wrote: One more along vorlon's lines: the angle sum in a triangle in general isn't 180 degrees anymore. How much it deviates from 180 is directly proportional to the amount of curvature enclosed in the triangle.
I had one helluva time grasping this until a TA I had took three push pins and a length of twine. With these, she constructed a triangle on a globe of the earth, then handed me a protractor and invited me to measure the interior angles. Crystal clear, after that.
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RE: What Did Einstein Mean when He Said Space is Curved?
June 5, 2017 at 6:50 pm
now make a triangle inside a saddle seat, and it will be off the other way
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RE: What Did Einstein Mean when He Said Space is Curved?
June 5, 2017 at 6:56 pm
(June 5, 2017 at 6:50 pm)vorlon13 Wrote: now make a triangle inside a saddle seat, and it will be off the other way
Yeah, I grasp it now, but until I started at uni, I was taught three things: 1) Don't pick your nose where people can see you, 2) always vote the straight SDLP ticket, and 3) the sum of the interior angles of a triangle is always 180 degrees.
I was so impressed with what the teaching assistant demonstrated that I asked her out on the spot, hoping she had some other mysteries to unlock for me.
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RE: What Did Einstein Mean when He Said Space is Curved?
June 5, 2017 at 6:59 pm
...and?
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RE: What Did Einstein Mean when He Said Space is Curved?
June 5, 2017 at 7:03 pm
(June 5, 2017 at 6:37 pm)BrianSoddingBoru4 Wrote: (June 5, 2017 at 10:27 am)Alex K Wrote: One more along vorlon's lines: the angle sum in a triangle in general isn't 180 degrees anymore. How much it deviates from 180 is directly proportional to the amount of curvature enclosed in the triangle.
I had one helluva time grasping this until a TA I had took three push pins and a length of twine. With these, she constructed a triangle on a globe of the earth, then handed me a protractor and invited me to measure the interior angles. Crystal clear, after that.
Boru
Amusing extremes of that: if you put the three pins on the pole, on the equator and another on the equator a quarter of its length away, you get a triangle with three right angles.
If you put all pins along the equator, you get a triangle with three 180 degree angles that's just a circle.
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RE: What Did Einstein Mean when He Said Space is Curved?
June 5, 2017 at 9:25 pm
(June 5, 2017 at 10:20 am)Lutrinae Wrote: Right over my head.
It's incredible, isn't it? We're so lucky to have this caliber of brain power around here. 
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RE: What Did Einstein Mean when He Said Space is Curved?
June 6, 2017 at 3:58 am
(June 5, 2017 at 6:59 pm)Alex K Wrote: ...and?
And nothing. Some song and dance about her being married. Blah blah blah.
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RE: What Did Einstein Mean when He Said Space is Curved?
June 6, 2017 at 8:29 am
(This post was last modified: June 6, 2017 at 8:30 am by ignoramus.)
(June 5, 2017 at 9:25 pm)LadyForCamus Wrote: (June 5, 2017 at 10:20 am)Lutrinae Wrote: Right over my head.
It's incredible, isn't it? We're so lucky to have this caliber of brain power around here.
LFC, I'm surprised you spelt "caliber" the way you did? American spelling? Being a pom, wouldn't you instinctively write calibre? like theatre, litre, etc? (US = theater)
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RE: What Did Einstein Mean when He Said Space is Curved?
June 6, 2017 at 4:22 pm
(This post was last modified: June 6, 2017 at 5:08 pm by Rhondazvous.)
(June 5, 2017 at 11:25 am)Anomalocaris Wrote: (June 5, 2017 at 10:06 am)Rhondazvous Wrote: How does he define the word curved as he used it to describe space?
He meant well known geometric principles known since Euclidean to be true for angles and lines inscribed on a flat plane would not hold true with physical representations of these lines and angles created on sufficiently large scale in space near sufficiently massivee objects. Instead these physical lines and angles would behave as if they were inscribed on a curved surface.
That makes sense. So are you saying is that what is actually curved is not empty space but objects of matter in space? Like Alex's example of parallel lines on a sphere.
(June 5, 2017 at 6:56 pm)BrianSoddingBoru4 Wrote: (June 5, 2017 at 6:50 pm)vorlon13 Wrote: now make a triangle inside a saddle seat, and it will be off the other way
Yeah, I grasp it now, but until I started at uni, I was taught three things: 1) Don't pick your nose where people can see you, 2) always vote the straight SDLP ticket, and 3) the sum of the interior angles of a triangle is always 180 degrees.
I was so impressed with what the teaching assistant demonstrated that I asked her out on the spot, hoping she had some other mysteries to unlock for me.
Boru
I could understand this if I knew what's being added. When you say sum, I'm assuming that something is being added. I'm also assuming that , like circlces, a triagle is 360 degrees all around. And this is where I get lost trying to take 3 angles and get 180. I get really lost when I think of right angles, obtuse angles, acute angles. eeteecee. I fear that I'm doing something very wrong.
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RE: What Did Einstein Mean when He Said Space is Curved?
June 13, 2017 at 3:28 pm
Remember that General Relativity is in four dimensions, not three, although, the time component is typically normalized to be in the same units as the three spatial dimensions, 'ct' (speed of light times time).
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