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The golden ratio φ and its negative reciprocal −φ −1 are the two roots of the quadratic polynomial x 2 − x − 1. The golden ratio's negative −φ and reciprocal φ −1 are the two roots of the quadratic polynomial x 2 + x − 1. The golden ratio is also an algebraic number and even an algebraic integer.
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 Dutch art historian Carel Blotkamp hypothesizes that this painting is one of Mondrian's first to use a modular or grid-like system. [3] Later X-ray photography corroborates this, revealing that Mondrian sketched an underlying grid pattern of uniform rectangles based on the golden ratio. [4]
The British actor’s eye, eyebrow, nose, lips, chin, jaw, and facial shape measurements were found to be 93.04% aligned with the Golden Ratio, an equation used by the ancient Greeks to measure ...
In geometry, a golden rectangle is a rectangle with side lengths in golden ratio +:, or :, with approximately equal to 1.618 or 89/55. Golden rectangles exhibit a special form of self-similarity: if a square is added to the long side, or removed from the short side, the result is a golden rectangle as well.
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There is some debate on the extent to which works exhibited at the 1912 Salon de la Section d'Or employed the golden ratio, or not. Despite a general interest in mathematical harmony, whether the paintings featured in the celebrated Salon de la Section d'Or exhibition used the golden ratio itself in their compositions is difficult to determine.
The golden ratio budget echoes the more widely known 50-30-20 budget that recommends spending 50% of your income on needs, 30% on wants and 20% on savings and debt. The “needs” category covers ...