Search results
Results from the WOW.Com Content Network
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.
A golden rectangle—that is, a rectangle with an aspect ratio of —may be cut into a square and a smaller rectangle with the same aspect ratio. The golden ratio has been used to analyze the proportions of natural objects and artificial systems such as financial markets , in some cases based on dubious fits to data. [ 8 ]
The root-3 rectangle is also called sixton, [6] and its short and longer sides are proportionally equivalent to the side and diameter of a hexagon. [7] Since 2 is the square root of 4, the root-4 rectangle has a proportion 1:2, which means that it is equivalent to two squares side-by-side. [7] The root-5 rectangle is related to the golden ratio ...
For example, a golden spiral can be approximated by first starting with a rectangle for which the ratio between its length and width is the golden ratio. This rectangle can then be partitioned into a square and a similar rectangle and this rectangle can then be split in the same way. After continuing this process for an arbitrary number of ...
In mathematics, the supergolden ratio is a geometrical proportion close to 85/58. Its true value is the real solution of the equation x 3 = x 2 + 1. The name supergolden ratio results from analogy with the golden ratio, the positive solution of the equation x 2 = x + 1. A triangle with side lengths ψ, 1, and 1 ∕ ψ has an angle of exactly ...
A "side-based" right triangle is one in which the lengths of the sides form ratios of whole numbers, such as 3 : 4 : 5, or of other special numbers such as the golden ratio. Knowing the relationships of the angles or ratios of sides of these special right triangles allows one to quickly calculate various lengths in geometric problems without ...
Calculate an interior point and its functional value F 2. The two interval lengths are in the ratio c : r or r : c where r = φ − 1; and c = 1 − r, with φ being the golden ratio. Using the triplet, determine if convergence criteria are fulfilled. If they are, estimate the X at the minimum from that triplet and return.
The term "bronze ratio" (=) (Cf. Golden Age and Olympic Medals) and even metals such as copper (=) and nickel (=) are occasionally found in the literature. [ 2 ] [ 3 ] In terms of algebraic number theory , the metallic means are exactly the real quadratic integers that are greater than 1 {\displaystyle 1} and have − 1 {\displaystyle -1} as ...