Mandala

Jerzy Kocik

Mandala is a Tybetan concept of a diagram for meditation. It is a map of reality. It is believed that if you look at a mandala long enough, the inner meaning of the universe should emmerge.


These six diagrams are sort of mathematical mandalas. Each captures the core and essence of one of the formalisms of Lagrangian/Hamiltonian description of motion. The cube contains also Thermodynamics interpreted in terms of symplectic structure and electrodynamics added as a bonus.

The diagrams tell how bodies move, how light propagates, and what connects the two.

Enlarged version of the mandala cube

This is a seed page for Math 530, Fall 2009.

Places (for frequent visits):

The n-Category Café -- A group blog on math, physics and philosophy.
LANL Archives. Here is its Differential Geometry> front.
SIGMA (Symmetry, Integrability and Geometry) -- lots of articles .

Tools:

Learn LaTeX (google also for other recorces)
MikTeX --- the best version of TeX! Download it here.
Examples of what you may do with TikZ.
Cool fonts for TeX

Some books:

Mathematical Methods of Classical Mechanics by V. I. Arnold.
A Topological Picturebook by George Francis (of UIUC)
Foundations of Differentiable Manifolds and Lie Groups by Frank Warner
From Calculus to Cohomology: De Rham Cohomology and Characteristic Classes by Ib H. Madsen and Jxrgen Tornehave.
A Geometrical Picture Book by Burkard Polster (answer to the question on the "origin of patterns")
Remarks on the history of the notion of Lie differentiation by Andrzej Trautman (6 pages)
The Theory Of Lie Derivatives And Its Applications by Kentaro Yano (direct link to the pdf file, 321 pages)

Other:

Math and Imagination by by John Conway, Peter Doyle, Jane Gilman, and Bill Thurston.