empirical origin of geometry

[AntonioLao]

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.

[harmonygirl]

Thank you Antonio!!!! I have been learning about so-called 'sacred geometry' for a little while now and while it is fascinating, i am unable to reconcile this in a harmonic way. I am VERY glad you started this thread. I am interested in hearing your views on the matter. Do you believe in 'sacred geometry'?

[Guille]

Antonio,

It's nice to know that you are continuing with your toe quest. I find interesting about this thread that geometry has an empirical origin but a non-empirical form, for it isn't real in any of it's axioms. Nothing is exact, nothing is plane, nothing is streight, nothing is point...

[AntonioLao]

Do you believe in 'sacred geometry'?

I do. I found some more here http://en.wikipedia.org/wiki/Sacred_geometry

but a non-empirical form

This has to do with the understanding of physical dimensionality.