> vectors are nice though. > for example, in the book I had, some aspects of the topic were expressed in > terms of a mess of trigonometry which wouldn't really work correctly in 3D. > some of these topics were fairly simple/elegant-looking if expressed with > vectors. > > so, linear systems and vectors, probably could do fairly well I think. > > more so, linear systems and vectors would give students a model that they > could more easily use with or test on a computer.
The problem with vectors is that they are closed only under subtraction, addition, and scalar multiplication. As soon as you take the product of two vectors, you get a completely different object/type, namely quaternions in the 3D case and rotors in the general case. Vector algebra's widespread use is an artifact of the vector v. quaternion debate from the 19th century. It's not the most versatile tool and hides lots of structure and symmetries. Similar to the "gotos considered harmful" mantra, I would add "vector algebra considered harmful". wes _______________________________________________ fonc mailing list [email protected] http://vpri.org/mailman/listinfo/fonc
