[FOM] Standard Language of Euclid
pratt at cs.stanford.edu
Fri Oct 2 17:13:03 EDT 2009
Andrej Bauer wrote:
> Geometrically speaking, we're trying to see how to interpolate a
> parametric cubic polynomial curve through vertices of a convex
> quadrilateral. It's probably a judgement call as to whether that's "an
> increase in complexity", but it sure sounds "simple" to me.
The additional requirement that the norm of the curve also be a cubic is
equivalent to the representability of a sixth-degree polynomial as the
square of a cubic one. This in turn is equivalent to requiring that its
six roots form three double roots.
Book I of Euclid is all about iterated quadratics. Cubics are beyond
the "standard language of Euclid."
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