Category Archives: Projective Geometry

On Gauss’s Mountain

Posted on March 26, 2006 by PlatoHagel

You must understand that any corrections necessary are appreciated. The geometrical process spoken too here must be understood in it’s historical development to undertand, how one can see differently. Euclidean geometry, elementary geometry of two and three dimensions (plane and … Continue reading →

Posted in Concepts, Earth, Euclid, Gauss, geometries, imagery, Interferometer, Non Euclidean, Projective Geometry, Riemann Hypothesis, VLBI | Tagged , , , , , , , , , , | 2 Comments

The Z Machine

Posted on March 10, 2006 by PlatoHagel

There is no branch of mathematics, however abstract, which may not some day be applied to phenomena of the real world.— Nikolai Lobachevsky Sandia’s Z machine exceeds two billion degrees Kelvin Z’s energies in these experiments raised several questions. First, … Continue reading →

Posted in Geometrics, geometries, Mathematics, Microstate Blackholes, Non Euclidean, Projective Geometry, sonofusion, Standard model, Strangelets | Tagged , , , , , , , , | Leave a comment

What First principle was– was it the geometry

Posted on December 1, 2005 by PlatoHagel

I thought I would contrast this quote of Dirac’s with the one of Feynman’s. You see the very idea of a constancy that spread through all Maxwell’s equations was a necessary one which allowed Einstein to move into positive and … Continue reading →

Posted in deduction, Dirac, Einstein, False Vacuum, General Relativity, geometries, Projective Geometry | Tagged , , , , , , | 7 Comments

Projective Geometries

Posted on October 7, 2005 by PlatoHagel

Action at a Distance Now ths statement might seem counterproductive to the ideas of projective geometry but please bear with me. In physics, action at a distance is the interaction of two objects which are separated in space with no … Continue reading →

Posted in Concepts, Dirac, Einstein, Entanglement, Euclid, geometries, Glast, Gluon, Gravity, John Venn, M Theory, Mathematics, Particles, Perfect Fluid, Phase Transitions, Photon, planck, Projective Geometry, Quantum Gravity, Quark Gluon PLasma, Smolin, Strange Matter, Symmetry, Symmetry Breaking, Venn | Tagged , , , , , , , , , , , , , , , , , , , , , , , , | 1 Comment

Point–> Line–>Plane <—> Point<– String<– Brane

Posted on September 21, 2005 by PlatoHagel

Under the heading of Klein`s Ordering of the Geometries : A theorem which is valid for a geometry in this sequence is automatically valid for the ones that follow. The theorems of projective geometry are automatically valid theorems of Euclidean … Continue reading →

Posted in Brain, Dimension, geometries, Kaluza, Klein, Lisa Randall, Neurons, Non Euclidean, Particles, Projective Geometry, String Theory, Thomas Banchoff | Tagged , , , , , , , , , , , | 11 Comments

The Unity of Mathematics

Posted on May 11, 2005 by PlatoHagel

Alain Connes Where a dictionary proceeds in a circular manner, defning a word by reference to another, the basic concepts of mathematics are infinitely closer to an indecomposable element”, a kind of elementary particle” of thought with a minimal amount … Continue reading →

Posted in Bubbles, Concepts, Earth, Einstein, geometries, Gravity, Intuition, Kip Thorne, Klein, LIGO, Mathematics, Music, Projective Geometry, Sound, String Theory, Susskind, Toy Model | Tagged , , , , , , , , , , , , , , , , | Leave a comment

The Elastic Nature?

Posted on December 5, 2004 by PlatoHagel

As I have explained in a earlier link I am fascinated by the images of bubbles that were demonstrated through a way of thinking of the early universe to arise as Bubble Nucleation. These images all show the 2-, 3-, … Continue reading →

Posted in Bubbles, Einstein, Gauss, geometries, Particles, Projective Geometry | Tagged , , , , , | Leave a comment

Mapping Quark Confinement and The Energy

Posted on December 2, 2004 by PlatoHagel

As I moved through the thinking of those extra dimensions it became apparent to me that the conceptualization of that distance scale was a strange world indeed. How, if we had accept the move to non-euclidean views could we not … Continue reading →

Posted in Dimension, Einstein, Faraday, Gauss, geometries, Gravity, Kaluza, Klein, Non Euclidean, Photon, Projective Geometry, Quantum Gravity, Quark Confinement, Symmetry, Time Travel | Tagged , , , , , , , , , , , , , , | Leave a comment

No Royal Road to Geometry?

Posted on November 26, 2004 by PlatoHagel

All those who have written histories bring to this point their account of the development of this science. Not long after these men came Euclid, who brought together the Elements, systematizing many of the theorems of Eudoxus, perfecting many of … Continue reading →

Posted in Einstein, Euclid, Euler, General Relativity, geometries, Giovanni Girolamo Saccheri, Gravity, Loop Quantum, Mathematics, Music, Projective Geometry, Quantum Gravity, Summing over Histories | Tagged , , , , , , , , , , , , | Leave a comment