important of Apollonius' legacy

[AntonioLao]

The conic sections, as contained in Apollonius' 8-volme treatise 'On Conics' (circa 225 B.C.), can be considered as the beginning of all math analyses between Euclid's less numeric geometry and Euler's more abstract topology.

Conics contributed to the mathematicalization of physical sciences was never been more obvious than when Kepler applied the ellipse to his 3 laws of planetary motion. Furthermore, these were discovered about the same time that Galileo started the revolution of empirical science. Kepler's measurements led to Newton's 3 laws of motions and the universal law of gravitation.

In our modern search for a final theory, it might be important to look back and in a more detailed analysis just why nature chooses the conics as paths of optimum time differential of all continuous and gradual changes.

[Guille]

Can you shortly explain Euler's and Euclid's topologies?

If I'm to include topology in my theory of the photogravitational effect, whcih should I include?

[AntonioLao]

Can you shortly explain Euler's and Euclid's topologies?

Euclid's geometry is static and rigid, not deformable. Euler's geometry is dynamic and deformable subjected to twisting, stretching, compressing but not cutting.

[Guille]

Euclid's geometry is static and rigid, not deformable. Euler's geometry is dynamic and deformable subjected to twisting, stretching, compressing but not cutting.

Why not cutting? Is there any other topology? And does any allow to cut? (or devide something in two?).

[AntonioLao]

In order to cut something, the cutter must be in a higher dimension than that which is to be cut. This might be wrong also. I'm 3D, but I dont think I can cut a 3D object into 2D.

[Guille]

In order to cut something, the cutter must be in a higher dimension than that which is to be cut. This might be wrong also. I'm 3D, but I dont think I can cut a 3D object into 2D.

You must note that what you think is not exactly what there is.

[mkirkpatrick]

Are not conics another word for vortexes,maybe this is part of his undiscovered legacy?




regards michael.

[sharon333]

That could be the trick.

[AntonioLao]

However topologists' tricks can transform any shape into any other shapes as long as they are all mathematically equivalent and whoever proved Poincare conjecture of topology wins a $1M prize.