If we set the length to be and to represent the length of, then In Definition 3 of Book VI of Euclid’s Elements we can read: A straight line is said to have been cut in extreme and mean ratio when, as the whole line is to the greater segment, so is the greater to the less. Plato in his Timaeus, considered the golden section to be the most binding of all mathematical relationships and the key to the physics of the cosmos. A rectangle whose sides had this proportion was called the Golden Rectangle. The ancient Greeks believed that the proportion is the most pleasing, and therefore all of their sculpture 1, architecture elements, etc.

The first known approximate decimal expansion of the (inverse) golden ratio as 'about 0.6180340' was given in 1597 by M.Maestlin (1550-1631) in a letter to J.Kepler (1571-1630).

Note that the reciprocal called golden ratio conjugate (or also silver ratio) has minimal polynomial. Thus the Golden ratio is an algebraic number of order 2. To compute the golden ration with higher precision go to. Martin Ohm (1792-1872), a younger brother of physicist Georg Ohm, is believed to be the first to use the term golden ratio ). It is also known as the golden mean, the golden section and divine proportion or ratio (this name appears for the first time in the 1500's and was used till the 19th century. Main Index Mathematical Analysis Mathematical Constants GoldenRatio Your web-browser does not support JavaScript

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