Monday, March 17, 2014

Golden ratio caliper

The golden ratio is the ratio between two numbers, a and b, that together are a solution of the equation a/b = (a+b)/a. This ratio is equal to one plus the square root of five, all divided by two, an irrational number roughly equal to 1.61803. The golden ratio is also the ratio between subsequent terms of the Fibonacci sequence (as the length of the sequence approaches infinity, it shows up in geometrical divisions of certain isosceles triangles, a five-pointed star, a regular triangle inscribed in a circle, and other geometric shapes. These shapes play a role in art and architecture. For instance, the golden rectangle has sides where the long side is 1.61803 times longer than the short side, and this featured, for instance, in the construction of the Parthenon. A golden ratio caliper, such as this working LEGO version by Amida Na, can be expanded and contracted, but the ratio of the distances between the points, and also the ratio between the longer of those distances and the distance between the outer points, always equals the golden ratio.

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