# Maths - 3D Clifford Algebra - Calculator Correction from Paolo

 Geometric product calculator 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

 RE: Geometric product calculator By: Martin Baker (martinbaker ) - 2007-06-15 01:34 Paolo,    Yes I agree, I tried it myself and got,  e1 * e2 = -e12  I'll correct it to agree with the multiplication table on the same page:  e1 * e2 = e12    Thanks very much for pointing this out I'll correct it as soon as I can.    Cheers,    Martin

 RE: Geometric product calculator By: Martin Baker (martinbaker ) - 2007-06-18 11:03 Paolo,    I've fixed it, it took me a while as some of the 'a' and 'b' operands were reversed, both in the javascript and some of the web page content.    Hopefully its all correct now, I've tested it as much as I can, but if anyone else would like to try it please let me know what you find.    Thanks again for letting me know about this.    Martin

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.      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.      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.