Maths - How diagrams were generated

These graphs were drawn by an open source 3D program called Blender, the meshes were generated by a Blender python script as described on this page. The scripting mechanism for blender is described here.

euclidean metric

<BAG version="0.0.1">
<Reference>Cartesian</Reference>
<Coords min="-5.0" max="5.0" zero="-5.0" line="0.00999999977648" />
<Offset x="0.0" y="0.0" z="-5.0" />
<CamPos x="5.0" y="5.0" z="3.0" />
<CamDir x="-2.3900001049" y="2.96000003815" z="-1.11000001431" />
<Label>
multiply
</Label>
<complex in="0" out="1" />
<ParU Min="-2.0" Max="2.0">
16
</ParU>
<ParV Min="-2.0" Max="2.0">
24
</ParV>
<Surface m1="4" m2="5" m3="6" m4="7">
<fn1>
(u+v)/2
</fn1>
<fn2>
(u-v)/2
</fn2>
<fn3>
sqrt(u*u-v*v)
</fn3>
</Surface>
<Material Wireframe="0" Smooth="1" alpha="0.899999976158" emit="0.20000000298" glow="0.0">
<matCol r="0.5" g="0.0" b="0.0" />
</Material>
<Material Wireframe="1" Smooth="0" alpha="0.9" emit="0.2" glow="0.2">
<matCol r="0.0" g="0.0" b="0.0" />
</Material>
<Material Wireframe="0" Smooth="1" alpha="0.899999976158" emit="0.20000000298" glow="0.0">
<matCol r="0.0" g="0.5" b="0.0" />
</Material>
<Material Wireframe="1" Smooth="0" alpha="0.9" emit="0.4" glow="0.3">
<matCol r="0.0" g="0.0" b="0.0" />
</Material>
</BAG>

minkowski metric

<BAG version="0.0.1">
<Reference>Cartesian</Reference>
<Coords min="-5.0" max="5.0" zero="-5.0" line="0.00999999977648" />
<Offset x="0.0" y="0.0" z="-5.0" />
<CamPos x="5.0" y="5.0" z="3.0" />
<CamDir x="-2.3900001049" y="2.96000003815" z="-1.11000001431" />
<Label>
multiply
</Label>
<complex in="0" out="1" />
<ParU Min="-2.0" Max="2.0">
16
</ParU>
<ParV Min="-2.0" Max="2.0">
24
</ParV>
<Surface m1="4" m2="5" m3="6" m4="7">
<fn1>
(u+v)/2
</fn1>
<fn2>
(u-v)/2
</fn2>
<fn3>
sqrt(u*u-v*v)
</fn3>
<fn4>
1>abs(sqrt(u*u-v*v))
</fn4>
</Surface>
<Material Wireframe="0" Smooth="1" alpha="0.899999976158" emit="0.20000000298" glow="0.0">
<matCol r="0.5" g="0.0" b="0.0" />
</Material>
<Material Wireframe="1" Smooth="0" alpha="0.9" emit="0.2" glow="0.2">
<matCol r="0.0" g="0.0" b="0.0" />
</Material>
<Material Wireframe="0" Smooth="1" alpha="0.899999976158" emit="0.20000000298" glow="0.0">
<matCol r="0.0" g="0.5" b="0.0" />
</Material>
<Material Wireframe="1" Smooth="0" alpha="0.9" emit="0.4" glow="0.3">
<matCol r="0.0" g="0.0" b="0.0" />
</Material>
</BAG>



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see also:
Correspondence about this page

Book Shop - Further reading.

Where I can, I have put links to Amazon for books that are relevant to the subject, click on the appropriate country flag to get more details of the book or to buy it from them.

flag flag flag flag flag flag Roger Penrose - The Road to Reality: Partly a 'popular science' book as it tries to minimise the number of equations (Not that I'm complaining much his book 'Spinors and space-time' went over my head in the first few pages) it still has lots of interesting results that its difficult to find elsewhere.

 

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