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A square has two diagonals of equal length, which intersect at the center of the square. The ratio of a diagonal to a side is 2 ≈ 1.414. {\displaystyle {\sqrt {2}}\approx 1.414.} A regular pentagon has five diagonals all of the same length.
The external angle of a square is equal to 90°. [4] The diagonals of a square are equal and bisect each other, meeting at 90°. [5] The diagonals of a square bisect its internal angles, forming adjacent angles of 45°. [6] All four sides of a square are equal. [7] Opposite sides of a square are parallel. [8]
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 fraction 99 / 70 (≈ 1.4142857) is sometimes used as a good rational approximation with a reasonably small denominator.
For a square matrix, the diagonal (or main diagonal or principal diagonal) is the diagonal line of entries running from the top-left corner to the bottom-right corner. [1] [2] [3] For a matrix with row index specified by and column index specified by , these would be entries with =.
If a 2 x 2 real matrix has zero trace, its square is a diagonal matrix. The trace of a 2 × 2 complex matrix is used to classify Möbius transformations. First, the matrix is normalized to make its determinant equal to one. Then, if the square of the trace is 4, the corresponding transformation is parabolic.
A square diagonal matrix is a symmetric matrix, so this can also be called a symmetric diagonal matrix. The following matrix is square diagonal matrix: [] If the entries are real numbers or complex numbers, then it is a normal matrix as well. In the remainder of this article we will consider only square diagonal matrices, and refer to them ...
where the lengths of the diagonals are p and q and the angle between them is θ. [15] In the case of an orthodiagonal quadrilateral (e.g. rhombus, square, and kite), this formula reduces to = since θ is 90°. The area can be also expressed in terms of bimedians as [16] = ,
The hemidiagon (1:½ √ 5) longer side is half the one of the root-5 rectangle and is produced by projecting the diagonal of half a square until it is perpendicular with the origin. Besides the square and the double square, the only other static rectangle included in the list is the hemiolion , which is produced by projecting 90° or 180 ...