I read lots of Math books and I've run into many many interesting Math "things" in my travels but here's something very clever I've never encountered before. Let's say you want to multiply 5 by 8. Do the following:
- Plot the graph of y=x^2.
- Draw a line that crosses the parabola where x = -5 and where x = 8 on the parabola. (Ignore the fact that x = -5 and not +5 at the left intersection point; this calculator does not do signed arithmetic!)
- Note the value of y where the line crosses the y-axis.
- The value of y is 40 and indeed 5 x 8 = 40.
Can you figure out why this trick works? Never mind that it's much more work to plot the graphs and determine where the line crosses the y-axis than it is to do the arithmetic in the first place!
This clever exploration, plus a number of other nice explorations for high school students come from the book Mathematics: A Human Endeavor by Harold Jacobs.