# Rgdboer

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 exercisesEdit

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.

## AcknowledgmentEdit

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 booksEdit

Inevitably, looking to upgrade the writing in this project, some topics have been tackled: