Maths - 3D Clifford Algebra - Calculator Correction from Paolo

By: deleva (deleva) - 2007-05-30 03:05
https://www.euclideanspace.com/maths/algebra/clifford/d3/arithmetic/index.htm#calc 
 
The calculator does not seem to perform correctly a simple geometric product ab where a and b are orthogonal(which should be numerically equivalent to an outer product a ^ b and to a cross product a x b).  
 
The calculator gives ab = - a x b.  
 
However, every book and web page that I have seen agree that (a x b) * e123 = a ^ b, which means that  
the coefficients c1 c2 c3 of a x b = c are the same as  
the coefficients d23 d31 d12 of a ^ b = d 
 
because 
e1 * e123 = e23 
e2 * e123 = e31 
e3 * e123 = e12 
 
Do you agree? 
 
Paolo 




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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 Clifford Algebra to Geometric Calculus: A Unified Language for Mathematics and Physics (Fundamental Theories of Physics). This book is intended for mathematicians and physicists rather than programmers, it is very theoretical. It covers the algebra and calculus of multivectors of any dimension and is not specific to 3D modelling.

 

flag flag flag flag flag flag New Foundations for Classical Mechanics (Fundamental Theories of Physics). This is very good on the geometric interpretation of this algebra. It has lots of insights into the mechanics of solid bodies. I still cant work out if the position, velocity, etc. of solid bodies can be represented by a 3D multivector or if 4 or 5D multivectors are required to represent translation and rotation.

 

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