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An identity matrix of any size, or any multiple of it is a diagonal matrix called a scalar matrix, for example, []. In geometry , a diagonal matrix may be used as a scaling matrix , since matrix multiplication with it results in changing scale (size) and possibly also shape ; only a scalar matrix results in uniform change in scale.
A root-phi rectangle divides into a pair of Kepler triangles (right triangles with edge lengths in geometric progression). The root-φ rectangle is a dynamic rectangle but not a root rectangle. Its diagonal equals φ times the length of the shorter side. If a root-φ rectangle is divided by a diagonal, the result is two congruent Kepler triangles.
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.
The identity matrix I n of size n is the n-by-n matrix in which all the elements on the main diagonal are equal to 1 and all other elements are equal to 0, for example, = [], = [], = [] It is a square matrix of order n, and also a special kind of diagonal matrix.
A rectangle is a rectilinear polygon: its sides meet at right angles. A rectangle in the plane can be defined by five independent degrees of freedom consisting, for example, of three for position (comprising two of translation and one of rotation), one for shape (aspect ratio), and one for overall size (area).
The diagonals of a square are equal and bisect each other, meeting at 90°. The diagonal of a square bisects its internal angle, forming adjacent angles of 45°. All four sides of a square are equal. Opposite sides of a square are parallel. A square has Schläfli symbol {4}. A truncated square, t{4}, is an octagon, {8}.
For n > 2, the number of diagonals is (); i.e., 0, 2, 5, 9, ..., for a triangle, square, pentagon, hexagon, ... . The diagonals divide the polygon into 1, 4, 11, 24, ... pieces OEIS : A007678 . For a regular n -gon inscribed in a unit-radius circle, the product of the distances from a given vertex to all other vertices (including adjacent ...
Rectangle – A parallelogram with four angles of equal size (right angles). Rhombus – A parallelogram with four sides of equal length. Any parallelogram that is neither a rectangle nor a rhombus was traditionally called a rhomboid but this term is not used in modern mathematics. [1]