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The Thinker
Join Date: Mar 2005 Posts: 3,278
48  | |
10-08-2005, 10:36 AM
| | Quanta,
What kind of properties are "unvariable" in geometric figures?
Dave,
I agree with you that infinitymike's claims are far too unrealistic and gigantic for him to give them in such a normal way, someone with that information, I think, owuld be much more controlled about the knowledges, for it would actually be something serious.
Now, I've been thinking; isn't fact actually a kind of fiction, an dfiction actually a kind of fact?
Infinitymike,
I see too much "I will" 's and "I can" 's as to believe you. | | | | Brown Belt
Join Date: Apr 2005 Posts: 152
15 | |
10-08-2005, 11:55 PM
| | geometric & mathematical modeling of local space-time
Hello Guille, Quote: |
What kind of properties are "unvariable" in geometric figures?
| Referring to post #8, the invariate properties are stated and numbered from one thru 5 in the post.
The properties of point, line, plane.... projected in TIME....produce the structure of local spacetime and the mathematical function of expansion.
Examples of Projective geometry concepts were used in the posted article here on ToeQuest,
"The Pure Mathematics of Space-Time"
(recently updated)
Happy Thoughts......Q7 | | | | The Thinker
Join Date: Mar 2005 Posts: 3,278
48 | |
10-09-2005, 06:39 AM
| | I have read the points.
But should the pass of time make change? Then, shouldn't the lines, surfaces, points change? | | | | Brown Belt
Join Date: Apr 2005 Posts: 152
15 | |
10-09-2005, 02:52 PM
| Hello Guille, Quote: |
But should the pass of time make change? Then, shouldn't the lines, surfaces, points change?
| Though geometric shapes may vary with time, as angles change, or distance increases or decreases........
These properties of basic geometry will not vary: (1) two points lie in a unique line; (2) three points not on the same line determine a plane; (3) two lines in a plane intersect in a point; (4) two planes intersect in a line; (5) three planes not containing the same line intersect in a point. Our species has evolved in a domain of expansion which is three dimensional... Mankind developed geometry to help describe his enviroment, using distance as the primary unit of measurement... However, within the domain of expansion, from which mankind has evolved, TIME is primary, distance is only the property of three dimensional time(D(t^3)/6). Within our expanding universe, we are three dimensional time beings, only capable of observing time pass as motion occurs. (1 day=spin) and (1 year=orbit) Therefore our perception of geometry has been interprited as (X,Y,Z,t)... Within our expanding universe, Euclidean space is (D(t^3)/6)... Within Euclidean space, None of the five properties of our geometry change.... Happy Thoughts........Q7  | | | | The Thinker
Join Date: Mar 2005 Posts: 3,278
48 | |
10-09-2005, 03:00 PM
| | Thanks for the help there, quanta. Now, do these 5 properties change in riemanian and gaussian geometries? And if so, where these two geometries developed to study what ould happen with the change of any of these properties? | | | | Brown Belt
Join Date: Apr 2005 Posts: 152
15 | |
10-09-2005, 03:30 PM
| | Guille,
Both of these types of geometry are considered Non-Euclidean in nature, but I believe the properties stated still hold.
I believe that Riemann was primarily concerned with complex variables and that Gauss was more concerned with differential geometry.
But it has been more than 27 years since I have studied these subjects, so I must recommend Antonio for further clarification of this subject matter.
Happy Thoughts......Q7
| | | | Raider of the lost time
Join Date: Nov 2003 Posts: 6,010
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10-09-2005, 03:57 PM
| | I am going to add some ideas concerning parallel displacement but first I have to make some sketches to demonstrate my points. Be back as soon as possible, hopefully with some clear drawings.
__________________
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: 6,010
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10-09-2005, 04:27 PM
| Line AB and CD are parallel. Triangle abc with length ab constant is shown at time 1 and at time 2. Note that sides ac and bc and the 3 corresponding angles are changed during the time transformation, the area of triangle abc remains the same, it is an invariance of time transformation. 
__________________
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 | |
10-09-2005, 04:31 PM
| | Can the area (or volume, in 3d) change? | | | | Raider of the lost time
Join Date: Nov 2003 Posts: 6,010
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10-09-2005, 04:35 PM
| Quote: |
Originally Posted by GUILLE Can the area (or volume, in 3d) change? | It does not matter what dimension the parallel lines are, as long as they remain parallel, their area and volume do not change. Non-Euclidean geometries do not have parallel lines.
__________________
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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