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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.
Divina proportione (15th century Italian for Divine proportion), later also called De divina proportione (converting the Italian title into a Latin one) is a book on mathematics written by Luca Pacioli and illustrated by Leonardo da Vinci, completed by February 9th, 1498 [1] in Milan and first printed in 1509. [2]
It has been suggested that the ideal human figure has its navel at the golden ratio (, about 1.618), dividing the body in the ratio of 0.618 to 0.382 (soles of feet to navel:navel to top of head) (1 ⁄ is -1, about 0.618) and Leonardo da Vinci's Vitruvian Man is cited as evidence. [23]
These page proportions based on the golden ratio, are usually described through its convergents such as 2:3, 3:5, 5:8, 8:13, 13:21, 21:34, etc. Tschichold says that common ratios for page proportion used in book design include as 2:3, 1: √ 3, and the golden ratio. The image with circular arcs depicts the proportions in a medieval manuscript ...
Some commentators have speculated that Leonardo incorporated the golden ratio in the drawing, possibly due to his illustrations of Luca Pacioli's Divina proportione, largely plagiarized from Piero della Francesca, [22] [n 3] concerning the ratio.
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A root rectangle is a rectangle in which the ratio of the longer side to the shorter is the square root of an integer, such as √ 2, √ 3, etc. [2] The root-2 rectangle (ACDK in Fig. 10) is constructed by extending two opposite sides of a square to the length of the square's diagonal.
The golden ratio (phi) represented as a line divided into two segments a and b, such that the entire line is to the longer a segment as the a segment is to the shorter b segment. Date: 23 March 2007: Source: Image:Golden ratio line.png: Author: Traced by Stannered: Other versions: Derivative works of this file: Golden ratio line percentages.svg