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The Thinker
Join Date: Mar 2005 Posts: 3,278
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09-30-2005, 02:48 AM
| Quote: |
Originally Posted by AntonioLao Hardly many theoretical physicists became rich doing what they do. However, engineers can become multi-billionaire like Bill Gate.
The prerequisites for calculus are good background base in geometry, algebra, trigonometry, and analytic geometry. | I'm a master in all of these. What is analytic geometry? (Maybe I have done it but know about it by another name). | | | | Raider of the lost time
Join Date: Nov 2003 Posts: 6,036
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09-30-2005, 03:52 PM
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Originally Posted by GUILLE What is analytic geometry? | It was Rene Descartes who founded analytic geometry, a combination of geometry and algebra. It is the study of the geometry of figures by algebraic representation and manipulation of equations describing their positions, configurations, and separations. Analytic geometry is also called coordinate geometry since the objects are described as  -tuples of points (where  in the plane and 3 in space) in some coordinate system. The study of the geometry of figures by algebraic representation and manipulation of equations describing their positions, configurations, and separations. Analytic geometry is also called coordinate geometry since the objects are described as -tuples of points (where in the plane and 3 in space) in some coordinate system.
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Time independence: [∂E(g)]²=[∂F(a)×∂r(a)]·[∂F(b)×∂r(b)] and Mass independence: ¶a(t)·¶r(t)=c²
| | | | The Thinker
Join Date: Mar 2005 Posts: 3,278
48 | |
09-30-2005, 04:36 PM
| | Oh....I have done analytic geometry, a lot of it in school.
Now, what is it's relationship to differential geometry? | | | | Raider of the lost time
Join Date: Nov 2003 Posts: 6,036
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10-01-2005, 02:05 PM
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Originally Posted by GUILLE what is it's relationship to differential geometry? | Analytic geometry is fine if we only need to describe static figures and shapes. However, if these shapes changes with some parameters such as time, then we must use the methods of the calculus (differential and integral) for their descriptions.
__________________
Time independence: [∂E(g)]²=[∂F(a)×∂r(a)]·[∂F(b)×∂r(b)] and Mass independence: ¶a(t)·¶r(t)=c²
| | | | Raider of the lost time
Join Date: Nov 2003 Posts: 6,036
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10-03-2005, 02:47 PM
| The hexahedron or the cube occupies a significant place among the five regular solids: octahedron (green), tetrahedron (red and blue), cube (black), dodecahedron, icosahedron. It is located in the middle. It can inscribe both the tetrahedron and the octahedron while being circumscribed by the dodecahedron and the icosahedron. dodecahedron and icosahedron not shown below. 
Furthermore, the green octahedron can circumscribe a smaller cube, ad infinitum.
__________________
Time independence: [∂E(g)]²=[∂F(a)×∂r(a)]·[∂F(b)×∂r(b)] and Mass independence: ¶a(t)·¶r(t)=c²
| | | | The Thinker
Join Date: Mar 2005 Posts: 3,278
48 | |
10-03-2005, 04:09 PM
| | I just wondered: coudl differential geometry, as it studies objects in movement, study the "inner" or "Internal" movement of na object? | | | | Raider of the lost time
Join Date: Nov 2003 Posts: 6,036
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10-03-2005, 04:16 PM
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Originally Posted by GUILLE I just wondered: coudl differential geometry, as it studies objects in movement, study the "inner" or "Internal" movement of na object? | That is exactly what Gauss and Riemann were talking about. The intrinsic curvature in contradistinction to the extrinsic curvature. To study an extrinsic curvature, one must be situated outside the dimension of the object. To study intrinsic curvature, all one needed is to determine the metrical properties.
__________________
Time independence: [∂E(g)]²=[∂F(a)×∂r(a)]·[∂F(b)×∂r(b)] and Mass independence: ¶a(t)·¶r(t)=c²
| | | | The Thinker
Join Date: Mar 2005 Posts: 3,278
48 | |
10-03-2005, 04:24 PM
| Quote: |
Originally Posted by AntonioLao That is exactly what Gauss and Riemann were talking about. The intrinsic curvature in contradistinction to the extrinsic curvature. To study an extrinsic curvature, one must be situated outside the dimension of the object. To study intrinsic curvature, all one needed is to determine the metrical properties. | DAM!
I now think I have definatelly been born in a time that doesn't belong to me. Not only I hate the music that is all around these yeas, and the horrible billion $ films that your horrible directors make, and the necesity of people to take the car and have mobile phones, but, I realise that I have had thousands of thoughts that would have lead me for discoverments just decades or centuries ago, when musicians like Debussy or Brahms existed, Antonioni and Passolini were starting the italian neorealist film movement, and the only vihecles that existed where carriages and the unique form to comunicate was by letter. | | | | Raider of the lost time
Join Date: Nov 2003 Posts: 6,036
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10-03-2005, 04:41 PM
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Originally Posted by GUILLE I now think I have definatelly been born in a time that doesn't belong to me. | What you have that they dont have is the time to prove better, or at most to prove that they were wrong.
__________________
Time independence: [∂E(g)]²=[∂F(a)×∂r(a)]·[∂F(b)×∂r(b)] and Mass independence: ¶a(t)·¶r(t)=c²
| | | | Raider of the lost time
Join Date: Nov 2003 Posts: 6,036
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10-03-2005, 08:34 PM
| The 2D building blocks of spacetime is the following 
__________________
Time independence: [∂E(g)]²=[∂F(a)×∂r(a)]·[∂F(b)×∂r(b)] and Mass independence: ¶a(t)·¶r(t)=c²
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