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→The Mathematics Behind It: starting de-jargonization, but there's really very little jargon to begin with, this was taught to non-majors in just this way
===Theorem===
===Theorem===
All sets discussed here are point sets in <math>\mathbb{R}^3 \ </math>.
All sets discussed here are point sets in three dimensional, flat (ie, normal, everyday) space. A point set is just that - a set of points.
A '''rigid motion''' of a set is a translation, rotation, or a composition of those two kinds of motion. A rigid motion of a set <math>A \ </math> is often written <math>g(A) \ </math>.
A '''rigid motion''' of a set is a movement of the whole set one one direction, or a rotation, or a composition of those two kinds of motion. That is to say, the set doesn't bend or get broken up. A rigid motion of a set <math>A \ </math> is often written <math>g(A) \ </math>.
Let <math>A, B \ </math> be sets. We say there is a '''rigid body equivalence''' <math>A \cong B \ </math> if <math>A \ </math> can be partitioned into finitely many sets <math>A_1, ..., A_n \ </math> and there are <math>n \ </math> rigid motions <math>g_1, ..., g_n \ </math> such that <math>g_1(A_1) \cup ... \cup g_n(A_n) = B \ </math>.
Let <math>A, B \ </math> be sets. We say there is a '''rigid body equivalence''' <math>A \cong B \ </math> if <math>A \ </math> can be partitioned into finitely many sets <math>A_1, ..., A_n \ </math> and there are <math>n \ </math> rigid motions <math>g_1, ..., g_n \ </math> such that <math>g_1(A_1) \cup ... \cup g_n(A_n) = B \ </math>.