# What does non-degenerate mean?

The context is that f is a real-valued function on a plane such that for every non-degenerate square ABCD in the plane, f(A)+f(B)+f(C)+f(D)=0....

What does this word mean here? I've found that "in mathematics, a degenerate case is a limiting case in which an element of a class of objects is qualitatively different from the rest of the class and hence belongs to another, usually simpler, class" (Wikipedia), but it's still a little unclear to me. Can someone help explain this more simply?

Thanks! Much appreciated.

• A point is a square with side length 0; I'd guess the author intends to exclude that case. – Mose Wintner Mar 1 '16 at 20:23
• Or if A = B and C = D, we'd have a line segment. – DylanSp Mar 1 '16 at 20:26
• A line is also considered a degenerate rectangle (or square). I guess any rectangle with a zero side. – Luis Vera Mar 1 '16 at 20:26
• Ohh, gotcha, thank you so much. Seemed pretty insignificant, but definitely important. Thanks again. – Grant Stenger Mar 1 '16 at 20:26
• So in this context it means specifically that $A, B, C$ and $D$ are four distinct points. – Arthur Mar 1 '16 at 20:53