| empirical origin of geometry -
06-25-2006, 03:08 PM
Geometry as a branch of mathematics has its origin in the measurement of terrestrial objects, measuring their attributes of length, area, and volume. These are meaningful only if the concept of physical dimension is clearly defined. However, by the axiomatic process, it is generally agreed that length, area, and volume respectively represent first, second, and third physical dimension. The introduction of inertial coordinate systems or reference frames, in general, would not possess agreement even by convention regarding these measurements. Unless, the systems are Euclidean, satisfying the 5th parallel axiom. It must also satisfy the orthogonal principle of Pythagorean Theorem. His 2,600 plus years old theorem forever implicated the subtle connection between the first and second physical dimension of space-time. This is done through the existence of perfect squares and their sums, indicated by infinite number of Pythagorean triples. These are, for positive integers m and n such that m > n is m – n, 2mn, m + n.
Time independence: [∂E(g)]˛=[∂F(a)×∂r(a)]·[∂F(b)×∂r(b)] and Mass independence: ¶a(t)·¶r(t)=c˛
| 
Re: empirical origin of geometry -
06-25-2006, 03:51 PM
Linear Mode
