Suppose you had the parabola at your disposal. Here is a neat way of using it to multiply two positive numbers a and b. I saw this at the Wild About Math blog.
Locate the points and on the parabola . Then the line joining these two points has y-intercept ab. 🙂
Why is this true? Try to figure it out for yourself before reading on.
One way of seeing it is in observing that the y-intercept will be a weighted sum of the heights and . Given the points’ distances from the y axis are a and b, the weights are in the ratio b:a and since they sum to 1, they must be b/(a+b) and a/(a+b). Hence the y-intercept is