Theory of Everything - View Single Post

AntonioLao · 04-20-2005, 02:38 PM

i'm going to try answering these questions one at a time starting with Q1.

hyperbolic geometry is based on the idea that infinite numbers of parallel lines can be drawn on the surface of a hyperboloid (a saddle shape surface). There exists one and only one minimum distance between two points. In 2D, the equation is that of a hyperbola given by

$\frac{x^2}{a^2}-\frac{y^2}{b^2}=d^2$

where d is the minimum distance.

For Q2, the Pythagorean theorem is stated as follow

$a^2+b^2=c^2$

this theorem is true iff a right triangle is defined and Euclid fifth postulate is also true. The distances are calculated by trigonometric circular functions, which are also based on the existence of right triangles and that the sum of interior angles is always exactly 180 degrees.

For Q3:
The inflationary model asserts that extreme curvature and high accelerated expansion happens only during the very early epoch of the universe (this event looks like an inverted delta function). After this accelerated expansion phase, the universe coagulated into stars and galaxies and the global spacetime structure appears homogeneous and isotropic.

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AntonioLao Raider of the lost time Status: Offline Posts: 5,613 Thanks Given: 790 Thanked 180x in 174 Posts Join Date: Nov 2003 Rep Power: 80	04-20-2005, 02:38 PM i'm going to try answering these questions one at a time starting with Q1. hyperbolic geometry is based on the idea that infinite numbers of parallel lines can be drawn on the surface of a hyperboloid (a saddle shape surface). There exists one and only one minimum distance between two points. In 2D, the equation is that of a hyperbola given by $\frac{x^2}{a^2}-\frac{y^2}{b^2}=d^2$ where d is the minimum distance. For Q2, the Pythagorean theorem is stated as follow $a^2+b^2=c^2$ this theorem is true iff a right triangle is defined and Euclid fifth postulate is also true. The distances are calculated by trigonometric circular functions, which are also based on the existence of right triangles and that the sum of interior angles is always exactly 180 degrees. For Q3: The inflationary model asserts that extreme curvature and high accelerated expansion happens only during the very early epoch of the universe (this event looks like an inverted delta function). After this accelerated expansion phase, the universe coagulated into stars and galaxies and the global spacetime structure appears homogeneous and isotropic.