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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 ...
The elements of a polytope can be considered according to either their own dimensionality or how many dimensions "down" they are from the body.
Dynamic symmetry is a proportioning system and natural design methodology described in Hambidge's books. The system uses dynamic rectangles, including root rectangles based on ratios such as √ 2, √ 3, √ 5, the golden ratio (φ = 1.618...), its square root (√ φ = 1.272...), and its square (φ 2 = 2.618....), and the silver ratio (=).
A building's surface detailing, inside and outside, often includes decorative moulding, and these often contain ogee-shaped profiles—consisting (from low to high) of a concave arc flowing into a convex arc, with vertical ends; if the lower curve is convex and higher one concave, this is known as a Roman ogee, although frequently the terms are used interchangeably and for a variety of other ...
The basic quantities describing a sphere (meaning a 2-sphere, a 2-dimensional surface inside 3-dimensional space) will be denoted by the following variables r {\displaystyle r} is the radius, C = 2 π r {\displaystyle C=2\pi r} is the circumference (the length of any one of its great circles ),
Technically, it should be called the principal square root of 2, to distinguish it from the negative number with the same property. Geometrically, the square root of 2 is the length of a diagonal across a square with sides of one unit of length; this follows from the Pythagorean theorem. It was probably the first number known to be irrational. [1]
The simplest rectilinear polygon is an axis-aligned rectangle - a rectangle with 2 sides parallel to the x axis and 2 sides parallel to the y axis. See also: Minimum bounding rectangle . A golygon is a rectilinear polygon whose side lengths in sequence are consecutive integers.
For rectangles with a 3:2 ratio (as in 35mm film in still photography), it happens that the rabatment lines are exactly matched to the rule of thirds lines. [8] In a horizontally-aligned rectangle, there is one implied square for the left side and one for the right; for a vertically-aligned rectangle, there are upper and lower squares. [1]