NewRPL: Complex Numbers in Cartesian Form r[x,y] , ...

[The Shadow]

(03-18-2017 11:38 AM)Vtile Wrote:  Does the split-complex have any real world application or is it purely theoretical concept to study and derive further mathematical concepts. Interesting none the less.

They do! Just like complex numbers encode rotations, split-complex numbers encode Lagrange-style "boosts" - essentially accelerations in special relativity. There's even two null lines in the split-Argand plane corresponding to the speed of light.

They also are to hyperbolae what complex numbers are to circles. They basically describe 1+1 Minkowski spacetime. (To get up to 3+1 like our universe requires Clifford algebra.)

My interest in them is *mostly* mathematical, though.

Quote:What I have understood the quarternions are heavily used in 3D analyse and programming (or how you should describe it)?

Quaternions encode 3d (and 4d) rotations, and do so much better than most of the alternatives in computer programming.

Though again, my own interest in them is primarily mathematical. I'm fascinated by the Hurwitz integers, the quaternion equivalent of whole numbers. I've programmed my 50g to handle them, but it's a bit cumbersome. Still haven't managed to factor them automatically.