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Degeneracy

A geometric figure in which some usually-distinct but otherwise identical elements "collapse" together, and become indistinguishable, is said to be "degenerate".

 

Consider a triangle, with lines x, y and z, and vertices X, Y and Z., all distinct.  This is the customary view.

distinct_triangle

We may degenerate it in three ways----

 

(1) by moving all the vertices into one, while leaving the lines distinct.

(2)  by moving all the lines into one, while leaving the vertices distinct.

(3) Finally, we may degenerate it completely, leaving neither lines nor vertices distinct.


Cases (1) and (2) might be termed "semi-degenerate".

Clearly, this could be done with any figure consisting of points and lines in a plane.  The implication is that actual, "apparent"  figure may contain degenerate, hidden configurations that are in some sense "active", in spite of being hidden.


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