What's the meaning of the unit bivector i? I'm reading the Oersted Medal Lecture by David Hestenes to improve my understanding of Geometric Algebra and its applications in Physics. I understand he does not start from a mathematical "clean slate", but I don't care for that. I want to understand what he's saying and what I can do with this geometric algebra.
On page 10 he introduces the unit bivector i. I understand (I think) what unit vectors are: multiply by a scalar and get a scaled directional line. But a bivector is a(n oriented) parallellogram (plane). So if I multiply the unit bivector i with a scalar, I get a scaled parallellogram?

The unit bivector represents the 2D subspaces.  In 2D Euclidean GA, there are 4 coordinates:


*

*1 scalar coordinate

*2 vector coordinates

*1 bivector coordinate


A "vector" is then (s, e1, e2, e1^e2).
The unit bivector is frequently drawn as a parallelogram, but that's just a visualization aid.  It conceptually more closely resembles a directed area where the sign indicates direction.
