File:One-form basis polar coordinates.svg

DescriptionOne-form basis polar coordinates.svg	English: This is a diagram for the Wikiversity:Special relativity and steps towards general relativity course. It uses 2D Euclidean w:polar coordinates to show that the basis one-forms, typically thought of as gradients, can vary in length depending on where they are located on a manifold. An associated background image to show the gradients is available at . See the technical comments below for a way to view these together.
Date	12 July 2011
Source	Own work
Author	Boud

The .svg version of the file is produced by

• the following .fig source code,
• several command line options: xfig -specialtext -latexfonts -startlatexFont default FILENAME.fig, and
• exporting to .svg format.

Other versions are produced with the same source code and xfig command line and appropriate export format(s). The background image File:Scalar fields theta quadrant.svg is best produced with the octave source code at File:Scalar fields theta quadrant.svg#octave_source_code and moved/copied to the local working directory. It is assumed to be called Scalar_fields_theta_quadrant.eps.

#FIG 3.2  Produced by xfig version 3.2.5b
Landscape
Center
Metric
A4      
100.00
Single
-2
1200 2
2 1 0 2 0 7 50 -1 -1 0.000 0 0 -1 0 0 2
	 4050 8100 4050 5400
2 1 0 2 0 7 50 -1 -1 0.000 0 0 -1 0 0 2
	 4050 8100 6750 8100
2 1 0 3 0 7 50 -1 -1 0.000 0 0 -1 1 0 2
	0 0 4.00 180.00 120.00
	 4379 7914 3284 6054
2 1 0 3 0 7 50 -1 -1 0.000 0 0 -1 1 0 2
	0 0 4.00 180.00 120.00
	 4391 7913 5726 7133
2 1 0 3 -1 7 50 -1 -1 0.000 0 0 -1 1 0 2
	0 0 4.00 180.00 120.00
	 5941 6906 5544 6250
2 1 0 3 -1 7 50 -1 -1 0.000 0 0 -1 1 0 2
	0 0 4.00 180.00 120.00
	 6021 6856 7356 6076
2 5 0 1 1 -1 90 -1 -1 0.000 0 0 -1 0 0 5
	0 Scalar_fields_theta_quadrant.eps
	 3581 5144 7205 5144 7205 8445 3581 8445 3581 5144
4 0 -1 50 -1 0 32 5.2883 2 495 3855 3193 6943 $\\tilde{e}^\\theta$\001
4 0 -1 50 -1 0 32 5.2883 2 495 3855 5710 6214 $\\tilde{e}^\\theta$\001
4 0 -1 50 -1 0 32 0.5236 2 495 2835 5215 7858 $\\tilde{e}^r$\001
4 0 -1 50 -1 0 32 0.5236 2 495 2835 6605 7013 $\\tilde{e}^r$\001
4 0 -1 50 -1 0 32 5.2883 2 510 5460 4666 5636 shallow $\\theta$ gradient\001
4 0 -1 50 -1 0 32 5.2883 2 510 4890 3256 5638 steep $\\theta$ gradient\001

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