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A proportion is a mathematical statement expressing equality of two ratios. [1] [2]: =: a and d are called extremes, b and c are called means. Proportion can be written as =, where ratios are expressed as fractions.
Other scholars question whether the golden ratio was known to or used by Greek artists and architects as a principle of aesthetic proportion. [11] Building the Acropolis is calculated to have been started around 600 BC, but the works said to exhibit the golden ratio proportions were created from 468 BC to 430 BC.
The golden ratio was called the extreme and mean ratio by Euclid, [2] and the divine proportion by Luca Pacioli; [3] and also goes by other names. [ b ] Mathematicians have studied the golden ratio's properties since antiquity.
The Canon applies the basic mathematical concepts of Greek geometry, such as the ratio, proportion, and symmetria (Greek for "harmonious proportions") and turns it into a system capable of describing the human form through a series of continuous geometric progressions. [4]
The proportions of the golden rectangle have been observed as early as the Babylonian Tablet of Shamash (c. 888–855 BC), [4] though Mario Livio calls any knowledge of the golden ratio before the Ancient Greeks "doubtful". [5]
It is a typical Greek sculpture depicting the beauty of the male body. "Polykleitos sought to capture the ideal proportions of the human figure in his statues and developed a set of aesthetic principles governing these proportions that was known as the Canon or 'Rule'. [7] He created the system based on mathematical ratios.
Pythagoras with a tablet of ratios, detail from The School of Athens by Raphael (1509) Greek mathematics allegedly began with Thales of Miletus (c. 624–548 BC). Very little is known about his life, although it is generally agreed that he was one of the Seven Wise Men of Greece.
The term "mean" (Ancient Greek μεσότης, mesótēs) appears in the Neopythagorean arithmetic handbooks in connection with the term "proportion" (Ancient Greek ἀναλογία, analogía). [ citation needed ]