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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.
An LG 19-inch LCD monitor with an aspect ratio of 16:10. 16:10 (1.6:1), also known as the equivalent 8:5, is an aspect ratio commonly used for computer displays and tablet computers. It is equal to 8/5, close to the golden ratio (), which is approximately 1.618. Video editing applications are commonly designed to allow editing of 16:9 content ...
As an example, 8:5, 16:10, 1.6:1, 8 ⁄ 5 and 1.6 are all ways of representing the same aspect ratio. In objects of more than two dimensions, such as hyperrectangles , the aspect ratio can still be defined as the ratio of the longest side to the shortest side.
Sometimes this ratio is rounded to 1.67:1. From the late 1980s to the early 2000s, Walt Disney Feature Animation's CAPS program animated their features in the 1. 6:1 ratio (a compromise between the 1.85:1 theatrical ratio and the 1.33:1 ratio used for home video); this format is also used by the Nintendo 3DS's top screen. 1.75:1 = 7:4
Since the conversion factor 1.609344 for miles to kilometers is close to the golden ratio, the decomposition of distance in miles into a sum of Fibonacci numbers becomes nearly the kilometer sum when the Fibonacci numbers are replaced by their successors. This method amounts to a radix 2 number register in golden ratio base φ being shifted. To ...
This aspect ratio was chosen as the geometric mean between 4:3 and 2.35:1, an average of the various aspect ratios used in film. [3] While 16:9 is well-suited for modern HDTV broadcasts , older 4:3 video has to be either padded with bars on the left and right side (pillarboxed), cropped or stretched, while movies shot with wider aspect ratios ...
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.
In the following quote, an "apertal ratio" of "1 ⁄ 24" is calculated as the ratio of 6 inches (150 mm) to 1 ⁄ 4 inch (6.4 mm), corresponding to an f /24 f-stop: In every lens there is, corresponding to a given apertal ratio (that is, the ratio of the diameter of the stop to the focal length), a certain distance of a near object from it ...