I’ve just learned about a fairly useless, yet utterly beguiling method for performing multiplication, and I’d like to share it!
Suppose you have two numbers you wish to multiply, call them a and b. Your first instinct is probably to write one under the other and start writing down partial products, or to reach for a calculator. But wait—there’s another way! All you need is a pencil, a ruler, and a Very Large sheet of graph paper. The first step is to draw the parabola which is the graph of (actually, this step is optional). Now, find the points on the parabola corresponding to and . In other words, plot the points and . So, for example, if we wanted to multiply 4 by 9, we would plot the points and . Now, use the ruler to connect the two points with a straight line, and look to see where it crosses the y-axis—and voila! You have your product.
Pretty amazing, huh? I have some questions for you:
- Can you explain why this works? Hint: you’ll need to dust off your knowledge on finding slopes and equations of lines (unless it isn’t dusty).
- Does it still work even if a and b have different signs?
- What about if a and/or b are equal to zero?
The ancient Greeks (who did all their arithmetic and algebra using geometry) would be proud.
This multiplication method comes courtesy of Sol Lederman at Wild About Math. Fans of The Math Less Traveled might want to check out Sol’s blog; he’s got some interesting posts on various math topics and math teaching.