Aspect ratio is a way of describing how fat or skinny a rectangle is, regardless of its size. Geometric objects that are identical are called congruent, and objects that have the same shape, but are different sizes are called similar. Rectangles that are similar have the same aspect ratio.
For example, you can have large televisions, and small telivisions, but their screens are the same shape. Those screens are similar. HDTV, however, has a different shape.
The aspect ratio of a rectangle is simply its width divided by its height. if you make the rectangle twice as high, and twice as wide, the doubling part cancels out and it still has the same aspect ratio. A regular telivision has an aspect ratio of 4:3, or 1.333~. An HDTV telivision has an aspect ratio of 16:9, or 1.777~.
What happens if you rotate a rectangle 90 degrees? Is it still the same rectangle? Does it still have the same aspect ratio? What is the relationship between the two different aspect ratios?
What happens when the aspect ratio is 1? Is there a special name for this kind of rectangle?
The diagram above has two rectangles. (A solid blue one, and an outlined pink one). One is taller than it is wide, the other will be wider than it is tall. Do they have the same aspect ratio? (hint: think about what would happen if you rotated one of them.)
Try moving the red dot until the space between the two rectangles is a perfect square. Can you make a larger square? Smaller? What are the aspect ratios?
A golden rectangle is a rectangle shaped so that if you stick a square onto the long side of it, it forms a rectangle with the same aspect ratio as you started off with. By moving the dot to create a square between the two rectangles, you've created a golden rectangle. Artists have long considered the golden rectangle to be a perfect shape. How does the number you got for the ratios on your golden rectangle compare to the ratios for tv screens and HDTV? Which do you think is better? Which type is closer to a golden rectangle?
Compare the ratios you found here with the ratios from the Fibonacci Sequence and the Golden Triangle pages. When you're done with those, you may wonder where that golden ratio comes from, anyway?.