The golden ratio should not need any introduction to those who have studied math and design in school. Some designers apply these mathematical concepts to come up with more visually appealing works. This infographic from companyfolders.com covers a few golden ratio facts:

What Is The Golden Ratio? What You Need to Know and How To Use It

The Mathematics of Beauty The Fibonacci Sequence is a sequence of numbers where each number is the sum of the previous two—i.e., 0, 1, 1, 2, 3, 5, 8, 13, 21, 34…and so on to infinity. The ratio of one number to the next is approximately 1.61803, which is called “phi”, or the Golden Ratio. It’s not a magical mathematical equation of the universe, but it definitely reflects natural, aesthetically beautiful patterns.

Math/Art/Science: Golden Ratio for Kids, from Artchoo (Maybe I would have understood this better in school if I had seen this comparison in my math class. Definitely.)

If you divide a line into two parts so that the longer part divided by the smaller part is also equal to the whole length divided by the longer part then you will have the golden ratio.

Great info on golden ratio and fibonacci numbers

Paul Gisbrecht: Human Reification or Ernst Neufert's definition of SPACE!! love him and his work!

"Another simple tool for web design linked to the golden ratio is Fibonacci numbers. A Fibonacci sequence begins with 0 and 1. The previous two numbers are added together to produce the next number in the sequence: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34… and so on."

The Mathematics of Beauty. The Fibonacci Sequence is a sequence of numbers where each number is the sum of the previous two—i.e., 0, 1, 1, 2, 3, 5, 8, 13, 21, 34…and so on to infinity. The ratio of one number to the next is approximately 1.61803, which is called “phi”, or the Golden Ratio. It’s not a magical mathematical equation of the universe, but it definitely reflects natural, aesthetically beautiful patterns.

The Golden Ratio in action - Shelley Esaak; Licensed to About.com

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