🚀 go-pugleaf

jac@ds8.scri.fsu.edu (Jim Carr) writes:

> That said: so you know that Euclidean geometry applies when parallel lines 
> do not meet, and non-Euclidean geometries otherwise (such as when doing 
> land surveying on the surface of the earth, or doing general relativity).

Just nit-picking, but there are two kinds of non-Euclidean geometries:
one where there is no parallel to any given line through a point
outside of it (e.g., on an ellipsoid), and one where there is more
than one (e.g., on a hyperboloid).  So you know you're living in an
Euclidean world when there is one and only one parallel to a line
running through a given point outside of it.

Both geometries can be formalized in the way of Euclid (although with
different results, of course), and all three formal systems are
consistent and complete.  If anyone is interested, I can post more details.

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