My friend Paul sent me the link to this fun time-waster called Balldroppings.
It’s simple: balls drop from a hole on the upper-left corner of your screen. By clicking and dragging with your mouse you can draw lines on the screen—barriers for the balls to bounce off of. When a ball hits a line, it sounds a note. Several lines will play a tune as they’re hit. I tried to adjust the length of the lines to change the pitch of the notes, but it doesn’t work that way. I had supposed that by lengthening the line you could lower the pitch, just like in real life.
Which reminded me that the Greek mathematician, Pythagoras, came up with that idea: if you pluck a string it will produce a note. If you halve that string and pluck it, the note produced will be one octave up on the scale. Halve it again and pluck it, the note goes up another octave. So he developed the scale we’re familiar with today, Do-re-mi-fa-so-la-ti-do by using fractions.
How do I know this? you may ask. I come by this information the hard way. I watched it in a cartoon.
Disney’s Donald in Mathmagic Land is one of my favorite cartoon shorts, and a great teaching tool. I used to show it to my students when I taught life drawing at Pittsburgh Technical Institute. For a time, the life drawing class was under threat of being dropped from the curriculum because it wasn’t apparent what value drawing the human form had for graphic designers. The value is: proportion. If you spend some time drawing human beings, you will acquire a sense of how long an arm is in relation to the size of a foot, how far down on the face the eyes should be, &c, &c. Even if you never again need to draw a person after you graduate from art school, you’ll still need to see different elements of a design in relationship to each other.
Pythagoras theorized that all beautiful proportions are so because they follow mathematical laws. His perfect ratio of one thing to another was 1:1.61—the Golden Mean. Go here to see a diagram of how to arrive at a rectangle using this ratio.
In a brilliant sequence, Donald Duck and we are shown examples from nature and classical art & architecture using Pythagoras’ Golden Mean.
Today in Europe, that ratio is used in standard paper sizes.
Rob Richards captured some of the fantastic background artwork for Donald in Mathmagic Land over at his blog, Animation Backgrounds.
The cartoon is available in DVD (I should update my videocassette) and of course I highly recommend it. Not only will you gain an appreciation of the relationship between mathematics and beauty, you’ll learn how to cheat at pool.