The Golden Rectangle and Grand Canyon

Successive Golden Rectangles dividing a Golden Rectangle into squares (Grand Canyon).

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.

The Grand Canyon is a steep-sided gorge carved by the Colorado River in the U.S. state of Arizona, and parts of Nevada. It is largely contained within the Grand Canyon National Park — one of the first national parks in the United States. President Theodore Roosevelt was a major proponent of preservation of the Grand Canyon area, and visited on numerous occasions to hunt and enjoy the scenery.

Longstanding scientific consensus has been that the canyon was created by the Colorado River over a period of six million years, but research released in 2008 suggests a much longer 17 million year time span. The canyon is 277 miles (446 km) long, ranges in width from 4 to 18 miles (6.4 to 29 km) and attains a depth of more than a mile (1.6 km). Nearly two billion years of the Earth's history have been exposed as the Colorado River and its tributaries cut their channels through layer after layer of rock while the Colorado Plateau was uplifted.