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Golden Ratio: Golden Ratio, Golden Ratio Base, List of Works Designed With the Golden Ratio, Pentagram, Proportion, Golden Section Search
Paperback. Books LLC 2010-05-05.
ISBN 9781155555096
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Förlagets beskrivning
Purchase includes free access to book updates online and a free trial membership in the publisher's book club where you can select from more than a million books without charge. Chapters: Golden Ratio, Golden Ratio Base, List of Works Designed With the Golden Ratio, Pentagram, Proportion, Golden Section Search, Golden Spiral, Golden Rectangle, Jay Hambidge, Golden Angle, Golden Triangle, Golomb Sequence, Lute of Pythagoras, Mark Barr. Excerpt: The golden angle is the angle subtended by the smaller (red) arc when two arcs that make up a circle are in the golden ratio In geometry , the golden angle is the smaller of the two angles created by sectioning the circumference of a circle according to the golden section ; that is, into two arcs such that the ratio of the length of the larger arc to the length of the smaller arc is the same as the ratio of the full circumference to the length of the larger arc. Algebraically, let c be the circumference of a circle , divided into a longer arc of length a and a smaller arc of length b such that and The golden angle is then the angle subtended by the smaller arc of length b . It measures approximately 137.51°, or about 2.399963 radians . The name comes from the golden angle's connection to the golden ratio ; the exact value of the golden angle is or where the equivalences follow from well-known algebraic properties of the golden ratio. Derivation The golden ratio is equal to = a / b given the conditions above. Let be the fraction of the circumference subtended by the golden angle, or equivalently, the golden angle divided by the angular measurement of the circle. But since it follows that This is equivalent to saying that golden angles can fit in a circle. The fraction of a circle occupied by the golden angle is therefore: The golden angle g can therefore be numerically approximated in degrees as: or in radians as: Golden angle in nature The angle between successive florets in some flowers is the golden angle. The golden ang
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Golden Ratio: Golden Ratio, Golden Ratio Base, List of Works Designed With the Golden Ratio, Pentagram, Proportion, Golden Section Search
Bokrecensioner » Golden Ratio: Golden Ratio, Golden Ratio Base, List of Works Designed With the Golden Ratio, Pentagram, Proportion, Golden Section Search
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