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Old Sep 20th 2009, 03:46 AM   #1
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sum of the angles in coordinate system

In 2D coordinate system the sum of the angles of all quadrants=360
degree
in (x,y) plane
Case 2
In 3D coordinate system (x,y,z) I took 3 possible plane
i.e.
(x,y) (y,z) (x,z)
each plane provides angle of 360 degree, so can we say that in 3D coordinate system sum of all quadrants is 1080?
Because
(x,y) gives 360
(y,z) gives 360
(x,z) gives 360
so their sum is 1080 degree
Case 3
And in 4d space the distance formula according to Minkowski formulation is
s^2=x^2+y^2+z^2-(ct)^2
Where c is speed of light and t is time and ct also has the dimension length
like other coordinates.
so can I deal it as a 4D coordinate system
(x,y,z,ct)
all possible plains are
(x,y) (y,z) (z,ct) (x,ct) (y,ct) (x,z)
so can we say,
sum of all quadrants in 4D coordinate system is 2160 degree?
Because
There 6 planes and each gives 360 degree.
Is it right to measure angles in this way or not?

Last edited by mars shaw; Sep 21st 2009 at 07:08 AM.
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Old Sep 20th 2009, 04:56 AM   #2
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Read this link:

http://www.km.fpv.ukf.sk/math2earth/...ere_Pisa_2.pdf


hope this helps you.
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Old Sep 25th 2009, 01:25 AM   #3
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The mistake is that I was not integrating correctly.
2D:
Integral[ d(theta), {theta, 0, 2pi}] = 2pi good

3D:
Integral[ d(cos[theta]) d(phi), {phi, 0, 2pi},{cos[theta], -1, 1} ] = 2 * 2pi = 4 pi

I have to move to a proper spherical coordinate system and integrate over the proper limits.
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Old Sep 29th 2009, 01:06 AM   #4
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Originally Posted by mars shaw View Post
In 2D coordinate system the sum of the angles of all quadrants=360
degree
in (x,y) plane
The coordinate system is irrelevant to what angles are. The sum of angles is independant of the number of coordinates. You're thinking of a 2-D "manifold". A 2d manifold (often simply called a "space") can be flat or curved. The xy-plane is an example of a flat manifold. The surface of a plane is an example of a curved 2d manifold
Case 2
In 3D coordinate system (x,y,z) I took 3 possible plane
i.e.
(x,y) (y,z) (x,z)
each plane provides angle of 360 degree, so can we say that in 3D coordinate system sum of all quadrants is 1080?
No. What is this 1080 angle supposed to be between?
(x,y) gives 360
(y,z) gives 360
(x,z) gives 360
so their sum is 1080 degree
Sorry but that's not how it works.
Case 3
And in 4d space the distance formula according to Minkowski formulation is
s^2=x^2+y^2+z^2-(ct)^2
Where c is speed of light and t is time and ct also has the dimension length
like other coordinates.
so can I deal it as a 4D coordinate system
(x,y,z,ct)
all possible plains are
(x,y) (y,z) (z,ct) (x,ct) (y,ct) (x,z)
so can we say,
sum of all quadrants in 4D coordinate system is 2160 degree?
Because
There 6 planes and each gives 360 degree.
Is it right to measure angles in this way or not?
No. Angles are spatial concepts and don't apply to time so you can't meaningfully speak of an angle in spacetime. Of course you can always define such a concept but when you do so you can define it in many ways and get different answers.
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