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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]
In geometry, a golden rectangle is a rectangle whose side lengths are in the golden ratio, : +, which is : (the Greek letter phi), where is approximately 1.618.. Golden rectangles exhibit a special form of self-similarity: All rectangles created by adding a square to a side, or removing a square from an end, of a golden rectangle are golden rectangles as well.
A supersilver rectangle contains two scaled ... Continued fraction (linear) ... The 14 odd composite numbers below 10 8 to pass the test are n = 3 2, 5 2, 5 3, 315 ...
Algebraic form. Continued fraction. The square root of 5 is the positive real number that, when multiplied by itself, gives the prime number 5. It is more precisely called the principal square root of 5, to distinguish it from the negative number with the same property. This number appears in the fractional expression for the golden ratio.
For example, the aspect ratio of a rectangle is the ratio of its longer side to its shorter side—the ratio of width to height, [1] [2] when the rectangle is oriented as a "landscape". The aspect ratio is most often expressed as two integer numbers separated by a colon (x:y), less commonly as a simple or decimal fraction. The values x and y do ...
A dynamic rectangle is a right-angled, four-sided figure (a rectangle) with dynamic symmetry which, in this case, means that aspect ratio (width divided by height) is a distinguished value in dynamic symmetry, a proportioning system and natural design methodology described in Jay Hambidge 's books. These dynamic rectangles begin with a square ...
A special right triangle is a right triangle with some regular feature that makes calculations on the triangle easier, or for which simple formulas exist. For example, a right triangle may have angles that form simple relationships, such as 45°–45°–90°. This is called an "angle-based" right triangle. A "side-based" right triangle is one ...
He wrote that "as 5 is to 8 so is 8 to 13, ... The convergents of the continued fraction for ... rectangle). For example, there are F 5+1 = F 6 = 8 ways one can climb ...
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