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While the Golden Ratio appears in many geometrical figures, the easiest to visualize is a special kind of a rectangle that has the following unusual and unique property: Given this kind of rectange, cut off a square with sides equal to the smaller of the 2 sides of the rectange. You're left with a smaller rectangle. This smaller triangle has the same proportions as the original larger one. You can cut off another square from this one, and you'll be left with a still smaller rectangle of the same proportions. You can continue this as often as you like and you'll always be left with a rectange of sides in the same "Golden Ratio". This is one of the many remarkable properties of the Golden Ratio. Try it out, doodle some rectangles and find out what proportions it needs to have for this to work.

The Golden Ratio has the mathematical value of 1/2(1+Sqrt(5)), or about 1 in 1.618. Like a rectange of sides 1 and 1.618. See wiki article.

2007-01-17 10:34:27 · answer #1 · answered by Scythian1950 7 · 0 0

Take a line segment such as a 1 metre pole. Now position a dot on the pole about 2/3 of the way along it. The dot divides the pole into a big bit and a small bit. Now move the dot until the length of the pole divided by the length of the big bit is the same as the length of the big bit divided by the length of the small bit.

The pole is now divided by the dot in the golden ratio. If you do the calculations, you'll find that the pole is 1.618 times the big bit and the big bit is 1.618 times the small bit.

2007-01-17 18:35:42 · answer #2 · answered by Gnomon 6 · 0 0

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