Chirality (mathematics)
In geometry, a figure is chiral (and said to have chirality) if it is not identical to its mirror image, or, more precisely, if it cannot be mapped to its mirror image by rotations and translations alone. An object that is not chiral is said to be ''achiral''. A chiral object and its mirror image are said to be enantiomorphs. The word ''chirality'' is derived from the Greek (cheir), the hand, the most familiar chiral object; the word ''enantiomorph'' stems from the Greek (enantios) 'opposite' + (morphe) 'form'. Examples Some chiral three-dimensional objects, such as the helix, can be assigned a right or left handedness, according to the right-hand rule. Many other familiar objects exhibit the same chiral symmetry of the human body, such as gloves and shoes. Right shoes differ from left shoes only by being mirror images of each other. In contrast thin gloves may not be considered chiral if you can wear them inside-out. The J, L, S and Z-shaped ''tetrominoes'' of the popula ...
[...More Info...]       [...Related Items...]     OR:     [Wikipedia]   [Google]   [Baidu]  

Orthogonal Matrix
In linear algebra, an orthogonal matrix, or orthonormal matrix, is a real square matrix whose columns and rows are orthonormal vectors. One way to express this is Q^\mathrm Q = Q Q^\mathrm = I, where is the transpose of and is the identity matrix. This leads to the equivalent characterization: a matrix is orthogonal if its transpose is equal to its inverse: Q^\mathrm=Q^, where is the inverse of . An orthogonal matrix is necessarily invertible (with inverse ), unitary (), where is the Hermitian adjoint ( conjugate transpose) of , and therefore normal () over the real numbers. The determinant of any orthogonal matrix is either +1 or −1. As a linear transformation, an orthogonal matrix preserves the inner product of vectors, and therefore acts as an isometry of Euclidean space, such as a rotation, reflection or rotoreflection. In other words, it is a unitary transformation. The set of orthogonal matrices, under multiplication, forms the group , known as the orthogo ...
[...More Info...]       [...Related Items...]     OR:     [Wikipedia]   [Google]   [Baidu]  

Mirror Plane Of Symmetry
A mirror image (in a plane mirror) is a reflected duplication of an object that appears almost identical, but is reversed in the direction perpendicular to the mirror surface. As an optical effect it results from reflection off from substances such as a mirror or water. It is also a concept in geometry and can be used as a conceptualization process for 3-D structures. In geometry and geometrical optics In two dimensions In geometry, the mirror image of an object or two-dimensional figure is the virtual image formed by reflection in a plane mirror; it is of the same size as the original object, yet different, unless the object or figure has reflection symmetry (also known as a P-symmetry). Two-dimensional mirror images can be seen in the reflections of mirrors or other reflecting surfaces, or on a printed surface seen inside-out. If we first look at an object that is effectively two-dimensional (such as the writing on a card) and then turn the card to face a mirror, the obj ...
[...More Info...]       [...Related Items...]     OR:     [Wikipedia]   [Google]   [Baidu]  

Glide Reflection
In 2-dimensional geometry, a glide reflection (or transflection) is a symmetry operation that consists of a reflection over a line and then translation along that line, combined into a single operation. The intermediate step between reflection and translation can look different from the starting configuration, so objects with glide symmetry are in general, not symmetrical under reflection alone. In group theory, the ''glide plane'' is classified as a type of opposite isometry of the Euclidean plane. A single glide is represented as frieze group p11g. A glide reflection can be seen as a limiting rotoreflection, where the rotation becomes a translation. It can also be given a Schoenflies notation as S2∞, Coxeter notation as ��+,2+ and orbifold notation as ∞×. Description The combination of a reflection in a line and a translation in a perpendicular direction is a reflection in a parallel line. However, a glide reflection cannot be reduced like that. Thus the effect of ...
[...More Info...]       [...Related Items...]     OR:     [Wikipedia]   [Google]   [Baidu]  

Frieze Group
In mathematics, a frieze or frieze pattern is a two-dimensional design that repeats in one direction. Such patterns occur frequently in architecture and decorative art. Frieze patterns can be classified into seven types according to their symmetries. The set of symmetry, symmetries of a frieze pattern is called a frieze group. Frieze groups are two-dimensional line groups, having repetition in only one direction. They are related to the more complex wallpaper groups, which classify patterns that are repetitive in two directions, and crystallographic groups, which classify patterns that are repetitive in three directions. General Formally, a frieze group is a class of infinite discrete symmetry groups of patterns on a strip (infinitely wide rectangle), hence a class of groups of isometries of the plane, or of a strip. A symmetry group of a frieze group necessarily contains translations and may contain glide reflections, reflections along the long axis of the strip, reflections a ...
[...More Info...]       [...Related Items...]     OR:     [Wikipedia]   [Google]   [Baidu]  

Krok 6 Mirrored
Krok or KROK or variant thereof, may refer to: People * Duke Krok, the father of Libuše in Czech legend * Matthew Krok (b. 1983), Australian child actor * Morris Krok (1931–2005), South African writer Other uses * Krok, Wisconsin, an unincorporated community in the United States * KROK (FM), a radio station (95.7 FM) licensed to South Fort Polk, Louisiana, United States * KROK International Animated Films Festival, a Russian / Ukrainian film festival * 3102 Krok, an asteroid See also * * KROC (other) * Kroc (surname) * Krock (other) * KROQ-FM KROQ-FM (106.7 MHz) is a commercial radio station licensed to Pasadena, California, serving Greater Los Angeles. Owned by Audacy, Inc., it broadcasts an alternative rock format known as "The World Famous KROQ" (pronounced "kay-rock"). The st ...

Krok 6
Krok or KROK or variant thereof, may refer to: People * Duke Krok, the father of Libuše in Czech legend * Matthew Krok (b. 1983), Australian child actor * Morris Krok (1931–2005), South African writer Other uses * Krok, Wisconsin, an unincorporated community in the United States * KROK (FM), a radio station (95.7 FM) licensed to South Fort Polk, Louisiana, United States * KROK International Animated Films Festival, a Russian / Ukrainian film festival * 3102 Krok, an asteroid See also * * KROC (other) * Kroc (surname) * Krock (other) * KROQ-FM KROQ-FM (106.7 MHz) is a commercial radio station licensed to Pasadena, California, serving Greater Los Angeles. Owned by Audacy, Inc., it broadcasts an alternative rock format known as "The World Famous KROQ" (pronounced "kay-rock"). The st ...

Isosceles Triangle
In geometry, an isosceles triangle () is a triangle that has two sides of equal length. Sometimes it is specified as having ''exactly'' two sides of equal length, and sometimes as having ''at least'' two sides of equal length, the latter version thus including the equilateral triangle as a special case. Examples of isosceles triangles include the isosceles right triangle, the golden triangle, and the faces of bipyramids and certain Catalan solids. The mathematical study of isosceles triangles dates back to ancient Egyptian mathematics and Babylonian mathematics. Isosceles triangles have been used as decoration from even earlier times, and appear frequently in architecture and design, for instance in the pediments and gables of buildings. The two equal sides are called the legs and the third side is called the base of the triangle. The other dimensions of the triangle, such as its height, area, and perimeter, can be calculated by simple formulas from the lengths of the legs ...
[...More Info...]       [...Related Items...]     OR:     [Wikipedia]   [Google]   [Baidu]  

Equilateral Triangle
In geometry, an equilateral triangle is a triangle in which all three sides have the same length. In the familiar Euclidean geometry, an equilateral triangle is also equiangular; that is, all three internal angles are also congruent to each other and are each 60°. It is also a regular polygon, so it is also referred to as a regular triangle. Principal properties Denoting the common length of the sides of the equilateral triangle as a, we can determine using the Pythagorean theorem that: *The area is A=\frac a^2, *The perimeter is p=3a\,\! *The radius of the circumscribed circle is R = \frac *The radius of the inscribed circle is r=\frac a or r=\frac *The geometric center of the triangle is the center of the circumscribed and inscribed circles *The altitude (height) from any side is h=\frac a Denoting the radius of the circumscribed circle as ''R'', we can determine using trigonometry that: *The area of the triangle is \mathrm=\fracR^2 Many of these quantities have simple ...
[...More Info...]       [...Related Items...]     OR:     [Wikipedia]   [Google]   [Baidu]  

Triangle
A triangle is a polygon with three edges and three vertices. It is one of the basic shapes in geometry. A triangle with vertices ''A'', ''B'', and ''C'' is denoted \triangle ABC. In Euclidean geometry, any three points, when non- collinear, determine a unique triangle and simultaneously, a unique plane (i.e. a two-dimensional Euclidean space). In other words, there is only one plane that contains that triangle, and every triangle is contained in some plane. If the entire geometry is only the Euclidean plane, there is only one plane and all triangles are contained in it; however, in higher-dimensional Euclidean spaces, this is no longer true. This article is about triangles in Euclidean geometry, and in particular, the Euclidean plane, except where otherwise noted. Types of triangle The terminology for categorizing triangles is more than two thousand years old, having been defined on the very first page of Euclid's Elements. The names used for modern classification are ...
[...More Info...]       [...Related Items...]     OR:     [Wikipedia]   [Google]   [Baidu]  

Axis Of Symmetry
Axial symmetry is symmetry around an axis; an object is axially symmetric if its appearance is unchanged if rotated around an axis."Axial symmetry"

American Meteorological Society

glossary of meteorology. Retrieved 2010-04-08. For example, a baseball bat without trademark or other design, or a plain white tea saucer, looks the same if it is rotated by any angle about the line passing lengthwise through its center, so it is axially symmetric. Axial symmetry can also be
[...More Info...]       [...Related Items...]     OR:     [Wikipedia]   [Google]   [Baidu]