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Curve (1)


Curves as
“Cuspidal Edges”


A curve is not a primitive element, or a result of incidence. What is it?

Firstly, a curve is not a line.

A line is extension—alone.
Thus a
curve is not a line, for curvature is not extension.
That's all of it. Formally, nothing more is needed.

If that fails to convince,
the following remarks should make the case.

No geometric element is part of any other,
for lines and points and planes do not have parts.
In other words, elements may neither be assembled, nor sundered.
(Primitive elements are truly a-tomic—they cannot be cut.)
So a line may not
be bent, kinked, folded or distorted,
cut, broken, chopped, split, fractured,
or chained.
I think it can be deduced that a curve is not a bent line!

Tangled strings and bent wires may be curved,
but they are not tangled or bent lines

string         paperclip

With a bent line out of the running, we move on to discover what a curve actually is.


Curves as


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