The Golden Rectangle and the Neuschwanstein Castle

Successive Golden Rectangles dividing a Golden Rectangle into squares (Neuschwanstein Castle).

A golden rectangle is a rectangle whose side lengths are in the golden ratio, one-to-phi, that is, approximately 1:1.618. A distinctive feature of this shape is that when a square section is removed, the remainder is another golden rectangle, that is, with the same proportions as the first. Square removal can be repeated infinitely, which leads to an approximation of the golden or Fibonacci spiral.

Fibonacci numbers (0,1,1,2,3,5,8,13,21,34...) are a sequence of numbers named after Leonardo of Pisa, known as Fibonacci. The first number of the sequence is 0, the second number is 1, and each subsequent number is equal to the sum of the previous two numbers of the sequence itself.

Neuschwanstein Castle is a 19th-century Bavarian palace on a rugged hill near Hohenschwangau and Füssen in southwest Bavaria, Germany. The palace was commissioned by Ludwig II of Bavaria as a retreat and as an homage to Richard Wagner, the King's inspiring muse. Although public photography of the interior is not permitted, it is the most photographed building in Germany and is one of the country's most popular tourist destinations.