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Old 07-03-2012, 06:55 AM   #44
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Re: aenima- problem 8

Michael Maestlin, first to publish a decimal approximation of the golden ratio, in 1597.
The first known approximation of the (inverse) golden ratio by a decimal fraction, stated as "about 0.6180340," was written in 1597 by Michael Maestlin of the University of Tübingen in a letter to his former student Johannes Kepler.[14]
Since the twentieth century, the golden ratio has been represented by the Greek letter Φ or φ (phi, after Phidias, a sculptor who is said to have employed it) or less commonly by τ (tau, the first letter of the ancient Greek root τομή—meaning cut).[2][15]
[edit]Timeline
Timeline according to Priya Hemenway.[16]
Phidias (490–430 BC) made the Parthenon statues that seem to embody the golden ratio.
Plato (427–347 BC), in his Timaeus, describes five possible regular solids (the Platonic solids: the tetrahedron, cube, octahedron, dodecahedron, and icosahedron), some of which are related to the golden ratio.[17]
Euclid (c. 325–c. 265 BC), in his Elements, gave the first recorded definition of the golden ratio, which he called, as translated into English, "extreme and mean ratio" (Greek: ἄκρος καὶ μέσος λόγος).[5]
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