A book has a beginning, middle, and end. The Encyclopedia does not have these features. As instructors and students thrive on measured content, my editing in Wikibooks is an effort to form a sequential presentation of many articles in the Encyclopedia to enhance the accessibility of these topics.
My Encyclopedia entry is w: User:Rgdboer.
My wikibook Associative Composition Algebra is about the binarion and quaternion algebras over R and C. The ideas of relative simultaneity and rapidity of motion are communicated with split binarions. Four-dimensional spacetime is a subspace of biquaternions, and the final chapter writes spacetime transformations as projectivities on the line over biquaternions.
Some resources for developing suitable exercises[edit | edit source]
The following sources, nominally about C, may contain statements using * that generalize to AC algebras:
- w: Constantin Caratheodory (1932) Conformal Representation, Cambridge Tracts in Mathematics and Mathematical Physics #28, Cambridge University Press.
- w: Andrew Forsyth (1910) "Plane curves invariant under homographic transformation", w: Quarterly Journal of Pure and Applied Mathematics 41: 113 to 127.
- Andrew Forsyth (1911) "Equations of plane geometry expressed by means of complex variables", Quarterly Journal of Pure and Applied Mathematics 42: 1 to 40.
- w: Frank Morley & F.V. Morley (1933) Inversive Geometry, (reprint 1954 by Chelsea Publishing)
- w: Hans Schwerdtfeger (1962) Geometry of Complex Numbers, w: University of Toronto Press.
- w: Isaak Yaglom (1968) Complex Numbers in Geometry, Eric Primrose translator, Academic Press.
- umlauts: ä ë ö ü
- French e's é è
- symbols ± √ → ∪ ≠
Acknowledgment[edit | edit source]
The wikibook Associative Composition Algebra would not have been possible without the coaching of some Encyclopedia editors. It did not happen overnight, and there were twists and turns. This review is but a synopsis of events that can be confirmed by clicking on History of any article. In August, October, and November 2004 I posted articles on Split-complex numbers, Tessarines and Biquaternions. An article on Hyperbolic angle was also posted that November. And in December the first Inversive Ring Geometry was posted. February 2005 saw Coquaternion posted, citing James Cockle (1851).
In June 2007 Coquaternion was moved to Split quaternion, and that began the shift from Cockle's terminology to that used with composition algebra. In November 2010 Tessarine was moved to Bicomplex number, completing the shift. And in February 2013, after encouragement from another editor, I moved Inversive ring geometry to Projective line over a ring, aligning with general usage. Thus the wikibook provides a gloss on articles in the Encyclopedia that developed over a decade of collaboration.
Chapters in other books[edit | edit source]
Inevitably, looking to upgrade the writing in this project, some topics have been tackled: