[yiyus]

I do not agree with this. The simplest mathematical concepts can look very complicated when presented in a formal way.

Learning the geometric product in high school wouldn't be more difficult than learning the dot and cross products, and would make obvious difficult to grasp concepts as complex numbers and even quaternions.

There are historical reasons for which we do not learn this from another point of view, and in my opinion it is, indeed, a great tragedy. A tragedy that I hope will be remedied some day.

Disclaimer: I deal everyday with 3D rotations. Euler angles have been traditionally used in my field, but they present many problems. Everybody knows we could do better with quaternions, but very few people understand them. I have shown many people how to interpret what quaternions are from geometric algebra concepts and I have not yet found anybody who doesn't think it is much more approachable that way.

[auggierose]

I do not disagree with you! For example the book http://faculty.luther.edu/~macdonal/laga/ gives an elementary introduction to the subject.

I have learnt about geometric algebra just this year, and applied it to compute the graphics in an app I wrote for a customer. It was a real eye opener, concepts that I struggled with before were really simplified by using geometric algebra.

BUT: I would never have guessed the usefulness of it for me from this paper.

[zardo]

Second recommendation for laga.