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golden section

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Golden Section

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Mathematical relationship between three points, A, B, C, in a straight line, in which the ratio AC:BC equals the ratio BC:AB (about 8:13 or 1:1.618). The area of a rectangle produced by the whole line and one of the segments is equal to the square drawn on the other segment. A golden rectangle has sides in the golden mean. Considered a visually satisfying ratio, it was first constructed by the Greek mathematician Euclid and used in art and architecture, where it was given almost mystical significance by some Renaissance theorists.

The golden section was used extensively by certain painters, above all Piero della Francesca, who had an architectural background. In Vincent van Gogh's picture Mother and Child the Madonna's face fits perfectly into a golden rectangle.

In mathematics, the ratio of consecutive Fibonacci numbers tends to the golden ratio.

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