Golden Ratio

The golden ratio has been important in art and architecture at least since Greek times. Many of its appearances in nature are exaggerated but never-the-less it is important in aesthetic design.

• • The golden ratio from wiki. As you can see it connects to many things in geometry and can be obtained in many ways mathematically.

  • Continued fractions are interesting in general, and it's amazing that its kind of the simplest continues fraction which is the golden ratio.

  • Understand the connection to Fibonacci numbers and the Fibonacci spiral (see the images on the wiki page).

  • Check out also this fun video from the amazing Vi Hart (by the way her father George Hart is a mathematician and artists/sculptor. He was involved in a course at Aalto University and produced some pieces which are on display)

  • There are many thing here to expand on and understand, both mathematically and in terms of history, art and architecture.

  • And don't forget that the Fibonacci numbers also can be extracted from Pascal's triangle.