 The proof works like this: Start at the top and work down, letting the little squares represent numbers, 1 + 2 + 3 + 4 + 5. The total number of squares in the picture is equal to this sum. Notice also that the numbers of squares is equal to a large square with sides of length 5 that is cut in half along the diagonal, i.e., 52/2, plus the shaded bits that were cut off by the diagonal cut, i.e., 5/2. It is plausible to claim that the diagram is a perfectly good proof of the theorem. One can “see” complete generality in the picture. Even though it only illustrates the theorem for n = 5, somehow we can see that it works for every number, all infinitely many of them. The diagram does not implicitly suggest a “rigorous” verbal or symbolic proof. The regular proof of this theorem is by mathematical induction, but the diagram does not correspond to an inductive proof at all, since the key element in an inductive proof is the passage from n to n + 1. The simple moral we could draw from the example is just this: We can in special cases correctly infer theorems from pictures, that is, from visualizable situations. There is an intuition and from this intuition we can grasp the truth of the theorem. (See Brown 1999 [2008].)