[FOM] Standard Language of Euclid

[A. Mani]

 On Sun, Sep 27, 2009 at 9:16 PM,  <joeshipman at aol.com> wrote:
 > plane of order 12). Am I correct in surmising that there is no question
 > that can be stated in the language of elementary algebra and geometry
 > which is currently regarded as both open and interesting?

In mathematical morphology too there are results suggesting that an algebraic 
theory is possible. The basic problem is to represent complex real life 
shapes (2D and 3D) by means of algebraic operations on sets of vectors 
representing elementary shapes (bounded figures or line segments). Operations 
like the 'Minkowski addition operation (\oplus)' [ A \oplus B ={a+b; a in A, b 
in B}] show plenty of potential in many situations, but much remains to be 
done.  Example: A square region  \oplus slash = a cube .   
Pijush Ghosh has co-authored a book on the state of the theory. Otherwise 
applied morphology is done with a choice of primitive shapes, some rules and 
'intuition'.

Best

A. Mani
  
-- 
A. Mani
http://www.logicamani.co.cc