calebmitchell wrote:Okay...I didn't want to show off my ignorance yet again by being the first person to ask the question, but I'll bite: what's a golden ratio?
The golden ratio is the 'perfect proportion'; aesthetically, it 'looks right' (if you think of a generic rectangle, it's likely to look 'best' when it's at golden ratio proportions), and mathematically, it can be described as (1+sqrt(5))/2. What makes it so perfect? It can also be defined abstractly for two given lengths with a>b such that a/b = (a+b)/a.
There are lots of fun 'tricks' about the golden ratio:
Numerically, the ratio of each number in the Fibonacci sequence to the previous number will, in the limit, approach the golden ratio. For more math fun about Fibonacci numbers, click here.
In the shirt, there's a rectangle drawn to the golden ratio proportions: and then inside of it, there's another, smaller, rectangle drawn to golden ratio proportions. And so and and so forth. The spiral that the artist drew that connects the corners of these golden ratio rectangles is known as the Fibonacci spiral - so named because of the relationship between the Fibonacci sequence and the golden ratio.
For what it's worth, while the ratio is indeed beautiful and it does occur in many parts of nature -- it's not in many of the things we typically associate with it. For example, as a substitute for the Fibonacci spiral, many people in the past have attempted to use the Nautilus shell as an example of the golden ratio in nature. While it's close, it doesn't actually follow the golden ratio. For more on this, and other old myths about the golden ratio, check out this letter to the Mathematical Association of America.