Fundamental Theorem of Geometry

name         Bryan
status       educator
grade        9-12
location     OH

Question -   There is a Fundamental Theorem of Arithmetic, 
Fundamental Theorem of Algebra, Fundamental Theorem of Calculus, 
and several other "Fundamental Theorems," but why is there no 
Fundamental Theorem of Geometry?
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   Some theorem designated "The Fundamental Theorem of ....." is a 
bit arbitrary since any of the mathematical disciplines you refer 
to rests upon a number of definitions, theorems, etc. I suppose for 
example that the "Fundamental Theorem of Euclidean Geometry" is the 
parallel line theorem, since that distinguishes plane geometry from 
convex and concave geometries. And what distinguishes complex 
variable analysis from the analysis of ordered pairs of real 
numbers (x,y) is the rule(s) of multiplication. I think the bottom 
line is there is nothing "fundamental" about the "fundamental" 
theorems. It just means that those theorems are significant 
departures from some contrasting prior discipline.

Vince Calder
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