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The theory of relativity occurred to me by intuition, and music is the driving force behind this intuition.
- Albert Einstein
$$\cos x = \sum\limits_{n = 0}^\infty {\frac{{\left( { - 1} \right)^n x^{2n} }}{{\left( {2n} \right)!}}}$$

Geometry || Topology - the shape of things.

Sunday, 09 December 2012 12:47
There was this magnificent mathematical horse. You could teach it arithmetic which it learned with no difficulty, algebra was a breeze. It could even prove theorems in Euclidean Geometry, but when you tried to teach it Analytic Geometry, it would rear back on its hind legs, kick ferociously, neigh loudly, try to bite and generally resisted the subject.
The moral of this story is you can't put Descartes before the horse.

Geometry
Geometry and topology - Wikipedia


Voronoi

Interactive Voronoi and really you should visit the whole site. bl.ocks.org - mbostock


MuZuu - spiralsymetry
The Universe of Discourse : A draft of a short introduction to topology Short introduction to topology for people who don't really care about topology mjdominus/topology-doc


Euclid's Elements

Euclid's Elements - Wikipedia
Euclid's Elements (PDF)


Robinson Congruences and Twistors

On the Origins of Twistor Theory
Riemann sphere - Wikipedia -Riemann sphere can be visualized as the complex number plane wrapped around a sphere (by some form of stereographic projection.
locally it's sensible; it's the impossibility of the whole sketch.


4-Dimensional Rotations – Page4 | Space Symmetry Structure
AN INTRODUCTION TO TWISTORS (PDF) - twistor correspondence in 4-dimensions via a classical formula of Whittaker for harmonic functions in 3-space. Throughout our discussion we compare the Riemannian with the semi-Riemannian case.

Twistors and Feynman path integrals for light and forces | Quantum field theory
Gravitational Hopfions (PDF) - EM hopfion topologically nontrivial solution to the vacuum Maxwell eq. with cool properties.
Physics of Asymmetric Continuum: Extreme and Fracture Processes: Earthquake ... - Roman Teisseyre, Hiroyuki Nagahama, Eugeniusz Majewski - Google Books - this 104 dollar ebook talks about Penrose visualization of Ivor Robinson congruence based on geometrical construction designed to find solutions of Maxwell's freespace equations.

Orbiting the Moons of Pluto: Complex Solutions to the Einstein, Maxwell ... - Elizabeth A. Rauscher, Richard L. Amoroso - Google Books - $128 book with program to relate the twistor topology to the spinor space and specifically to the Dirac spinors. relationshop between twistor theory and the Dirac 'string trick'. give it the good ole Penrose spin
Soliton - Wikipedia

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Last Updated on Monday, 04 August 2014 22:44