Grassmann Algebra - page header
Grassmann algebra is an algebra for Geometry
The simple algebraic entities of Grassmann algebra may be interpreted as points, lines, planes, vectors, bivectors and trivectors, and their multidimensional variants. This interpretation imbues the product operations of the algebra with a concomitant geometric significance. On this page we display a series of graphics from Volume 1, using the entities and operations as direct inputs to the drawing routines.

Constructing conics in space

This graphic shows the conic formed from two points, a line, and two planes according to an equation in which P is the variable point describing the conic. Note that since a conic is of second degree, the variable point P occurs twice in the product. The product itself involves both the exterior product operation for building entities, and the regressive product operation for intersecting them.
Fig 4.31: Constructing conics in space
Constructing conics in space
© John Browne 2012.

This page will have more examples added shortly.

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