[Edu-sig] python satacad: class 6

[Arthur]

> -----Original Message-----
> From: edu-sig-bounces at python.org [mailto:edu-sig-bounces at python.org] On
> Behalf Of Kirby Urner
> Sent: Saturday, February 19, 2005 6:26 PM
> To: edu-sig at python.org
> Subject: [Edu-sig] python satacad: class 6
> 
> Then we dove into vectors for awhile:  translation, rotation and scaling
> being the big 3 computer graphics transformations.  I started constructing
> a
> vector class, then switched to a fully developed one.  That led us back to
> POV-Ray and some pre-rendered polyhedra downloaded off the netlib library.

"""
Gentlemen! The course of lectures which I now begin will be an immediate
continuation of, and a supplement to, my course of last Winter. My purpose
now, as it was then, is to gather together all the mathematics that you
studied during your student years, insofar as this could e of interest for
the future teacher, and in particular, so show its bearing on the business
of school instruction.
"""
Felix Klein, Elementary Mathematics from and Advanced Standpoint, 1908

Klein being a Great Mind in mathematics at the dawn of modernity, who turned
his attention, intellect and energy to the problem of education at the
"school" level.  To  me, he is a great redactor of modern mathematical ideas
to his day, and in that sense in the spirit of Euclid.

And what Klein prescribes in the end sounds much like a primer on the
underlying mathematics and ideas which we now know as the fundamentals of
computer vector graphics.  Except that we tend to know these ideas, and
teach them, out of the their historical and intellectual context.

And there is an argument that one cannot truly understand modern
intellectual sensibility without some grasp of these ideas, at least in
their spirit. 

Klein also being instrumental in opening his University's math department to
women.

And apparently, in the eyes of his students, living up his essential ideal
as a teacher - 

"Never be dull"

Side-trip:

The quaternion:

http://mathworld.wolfram.com/Quaternion.html

Quaternions - mid-1800's idea extending the concepts of so-called imaginary
numbers to new dimensions, and becoming the basis for the development of
vector mathematics,  mathematical physics, and  - in some sense modernity -
itself.  And a fundamental tool in the mathematics of 3d computer graphics
and probably known most commonly now in that context - but too often - out
of its historical context, and without understanding of its historical
significance. 

So my short manifesto is only ratifying the importance of where I think
Kirby is already going and what he is already doing.  

Computer graphics, good.

Computer graphics with pretense, better.

Art