Write 4–6 sentences explaining why it is important to have precise definitions in mathematics. Choose five terms, some from geometry and some from other
areas of mathematics, and give a precise definition of each. Then change each
of those definitions so that it still describes the term but not precisely enough to
avoid ambiguity. Formulate counterexamples, with sketches when feasible, that
show how things could satisfy the less precise definitions but not match the
intended terms.