Popular Woodworking 2003-12 № 138, страница 74

HISTORY OF THE GOLDEN SECTION

Secret societies, Leonardo da Vinci, nautilus seashells, mating rabbits and pineapples: The golden section's history and reach is as fascinating as it is debated. Briefly, here's what we know:

Pythagoras, a Greek mathematician, born about 570 B.C., discovered the golden section (also called the divine proportion, golden ratio and golden mean). He founded and was head of a strict and secret philosophical and religious school in southern Italy. The pentagram, a geometric representation of the golden section, symbolized the Pythagoreans' brotherhood and they called it "Health."

Many credit Athenian architect Phidias with pioneering the use of the golden ratio when helping design the Parthenon. From Phidias we get the Greek letter Phi (©). Today, Phi stands for the irrational number used in the golden section, 1.61803333...

Later, Leonardo of Pisa (who called himself Fibonacci) introduced a math problem in his book "Liber Abaci," published in 1202: A pair of rabbits are put in a field where they can't escape and they

can't die. Suppose at the age of one month the female can produce another pair of rabbits (always one male and one female) and she continues to do so each month for an entire year. As each new female rabbit becomes 1-month old, she, too, produces another pair. How many pairs of rabbits will there be in a year? The solution, which involves a series of numbers (1,1,2,3, 5,8,13, 21,...), is now called the Fibonacci series.

The ratio between two adjacent Fibonacci numbers after three is 1:1.168 - the golden ratio. Today, many say this relationship can be found in art (Mona Lisa), architecture (Notre Dame), population growth, nature (sunflowers), music (scales), the stock market, the human face (Audrey Hepburn), the cosmos and even theology.

For information, check out Mario Livio's "The Golden Ratio" (Broadway Books) and visit:

• www.mcs.surrey.ac.uk/Personal/ R.Knott/Fibonacci

• jimloy.com/geometry/golden.htm

• goldennumber.net

- Kara Gebhart

Drawer 2 = height of drawer 1 (hidden by desktop) + divider

Drawer 3 = height of drawer 2 + divider

Drawer 4 = height of drawer 3 + divider

The drawers shown in this desk are an excellent example of arithmetic progression, and the feet are golden rectangles.

The rectangular gallery is divided into smaller rectangles to create the door, pigeonholes, and drawers.The gallery features several golden rectangles.

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