[AndrewC]

Why, the angle formed by the four zero-length sides of my square, of course.

Nice try, but that doesn't wash.

The angle we are talking about is defined thus--

an·gle²   Pronunciation Key  (nggl)
n.

1. Mathematics.
   1. The figure formed by two lines diverging from a common point.

And not this one --

an·gle¹   Pronunciation Key  (nggl)
intr.v. an·gled, an·gling, an·gles

1. To fish with a hook and line.
2. To try to get something by indirect or artful means: angle for a promotion

[general_re]

1. The figure formed by two lines diverging from a common point.

A good illustration of the limits of general dictionaries in defining mathematical concepts. Consider triangles instead of squares for a moment. Given:

c² = a² + b² - 2abcos(X)

('X' only because I'm not sure everyone can see a theta in their browsers :^) )

What, then, is the value of the given angle 'X' when sides a, b, and c are all zero?