I've often been asked what it was that caused me to become interested in mathematics—and just when and how did it happen. This will be told in a later story. Here I will tell of a couple of foreshadowings of that wonderful event.

Some time in elementary school (I cannot now recall the precise grade) an excellent teacher introduced our class to the subject of geometrical areas. She first sketched on the board a rectangle 5 units long and 3 units wide. Then, drawing lines parallel to the sides of the rectangle through the unit divisions of those sides, she divided the rectangle into an array of small unit squares. How many of these squares were there? Well, there were 3 rows of 5 unit squares apiece, giving a total of 3 × 5 = 15 unit squares in all. Thus the area of the rectangle in unit squares is given by the product of its two dimensions. Clearly the same would be true of any other rectangle having integral dimensions. Though at this stage, she said, it would be too difficult to prove that in any case, whether the sides are integral or not, the area of a rectangle is given by the product of its two dimensions, we will assume that this is indeed the case.

Next she drew a parallelogram on the board as shown in Figure 11, and dropped perpendiculars from the two top opposite vertices.