Trigonometry made more "rational" I read an article the other day on "rational trigonometry" and decided to go exploring... and I feel as if a lightbulb has turned on. This seems like such a wonderful new technique to doing otherwise cumbersome problems, and I agree that it does feel like a more "rational approach" to the subject. I only wish this would have been available doing my university days, but am happy to see work being done to simplify what is often presented as a difficult and often cumbersome subject. Thank you to all mathematicians who make it their life's work to explore new and exciting paths... especially in the field of trigonemtry!
This silly "alternative" geometry which "rejects" the distance concept in favour of the squared distance (so that one avoids the square root) and other pointless substitutions has already been debated at PF somewhere, and is of no mathematical worth whatsoever.
Basically, the guy has rediscovered the notion of dot product and cross product, but has presented it in a more cumbersome form. And yes, dot products and cross products are very nice things indeed. (But I wouldn't eschew trigonometry completely in their favor!)
Well, if you really think of it, Maths is a subjects of playing with sympols with logic and rational...the matter is how human find out the links between these and they are really great! And I think every of us will be as great as them too!