# Golden Rectangle

The Golden Rectangle is said to be one of the most visually satisfying of all geometric forms. The Golden Ratio is implicitly defined in Euclid's Elements in Book IV dates about 300BC. It is used long before that by Egyptians to build pyramids.

How to draw a golden rectangle?

Start off by drawing a square.

Divide the square in the middle.

Draw a line from the middle bottom point to the opposite corner.

Now, draw a circle making the diagonal line the radius. In other words, the diagonal line will be the radius of your circle.

Extend the rectangle along the baseline until you reach the end of the radius.

Congratulations! You have a golden rectangle.

The ratio 1:1.618 is called the "golden ratio" (sometimes known as the Divine Proportion).

**Golden Rectangle in Action**

If you examine some of the aspect ratios, they are closely related to the golden ratio. For example,

- 35mm film has an aspect ratio of 36:24, which is 1:1.5 - close enough to 1:1.618
- HDTV aspect ratio is 16:9, which gives us 1:1.77
- Most wide screen's have an aspect ratio of 1:1.66. Maybe that's why movies look better on movie theatres.

**Parthenon**, built around 440BC.

Music: **Beethoven**

In an interesting little article in Mathematics Teaching volume 84 in 1978, Derek Haylock writes about The Golden Section in Beethoven's Fifth on pages 56-57. He finds that the famous opening "motto" appears not only in the first and last bars (bar 601 before the Coda) but also exactly at the golden mean point 0·618 of the way through the symphony (bar 372) and also at the start of the recapitulation which is phi or 0·382 of the way through the piece!

Composition in Red, Yellow and Blue’ 1926 by Piet Mondriaan

Asked if he always painted squares, his reply was: "Squares? I see no squares in my pictures."