Fundamental Theorem of Geometry

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Fundamental Theorem of Geometry

Name: Bryan
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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?

Replies:

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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