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A golden rectangle with sides ab placed adjacent to a square with sides of length a produces a similar golden rectangle. 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 ...
Aspect ratio. The aspect ratio of a geometric shape is the ratio of its sizes in different dimensions. 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 ...
Four-dimensional space ( 4D) is the mathematical extension of the concept of three-dimensional space (3D). Three-dimensional space is the simplest possible abstraction of the observation that one needs only three numbers, called dimensions, to describe the sizes or locations of objects in the everyday world.
The only non-rectangular or non-square national flag. Also the only flag with a decimal ratio below 1 (i.e. taller than it is wide). While the red inner part has a ratio of exactly 4:3 (0.75), [66] the complete flag has an irrational aspect ratio of approximately 1.21901:1 due to the blue border. [Note 3] [67] Netherlands: 2:3 (1.5)
In those cases, the characteristic length is the diameter of the pipe or, in case of non-circular tubes, its hydraulic diameter : Where is the cross-sectional area of the pipe and is its wetted perimeter. It is defined such that it reduces to a circular diameter of D for circular pipes. For flow through a square duct with a side length of a ...
A golden rectangle with long side a + b and short side a can be divided into two pieces: a similar golden rectangle (shaded red, right) with long side a and short side b and a square (shaded blue, left) with sides of length a. This illustrates the relationship a + b / a = a / b = φ.
For example, it is possible to pack 147 rectangles of size (137,95) in a rectangle of size (1600,1230). Packing different rectangles in a rectangle : The problem of packing multiple rectangles of varying widths and heights in an enclosing rectangle of minimum area (but with no boundaries on the enclosing rectangle's width or height) has an ...
Euclidean distance. In mathematics, the Euclidean distance between two points in Euclidean space is the length of the line segment between them. It can be calculated from the Cartesian coordinates of the points using the Pythagorean theorem, and therefore is occasionally called the Pythagorean distance . These names come from the ancient Greek ...