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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 Rotation (mathematics), rotations and Translation (geometry), 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 wiktionary:inside ou ... [...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 th ... [...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 specular reflection off from surfaces of lustrous materials, especially a mirror or water. It is also a concept in geometry and can be used as a conceptualization process for 3D 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 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Glide Reflection
In geometry, a glide reflection or transflection is a geometric transformation that consists of a reflection across a hyperplane and a translation ("glide") in a direction parallel to that hyperplane, combined into a single transformation. Because the distances between points are not changed under glide reflection, it is a motion or isometry. When the context is the two-dimensional Euclidean plane, the hyperplane of reflection is a straight line called the ''glide line'' or ''glide axis''. When the context is three-dimensional space, the hyperplane of reflection is a plane called the ''glide plane''. The displacement vector of the translation is called the ''glide vector''. When some geometrical object or configuration appears unchanged by a transformation, it is said to have symmetry, and the transformation is called a symmetry operation. ''Glide-reflection symmetry'' is seen in frieze groups (patterns which repeat in one dimension, often used in decorative borders), wallpa ... [...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. The term is derived from friezes in architecture and decorative arts, where such repeating patterns are often used. 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. History Mathematical friezes have their origins in the formulas for the '' pentagramma mirificum'' found by Carl Friedrich Gauss in 1843 and Harold Scott MacDonald Coxeter's study of symmetries in the mid-20th century. Frieze patterns were formally introduced by Coxeter in 1971. In the 1970s to 1980s, frieze patte ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Krok 6 Mirrored
Krok or KROK or variants thereof, may refer to: People and legendary figures * Duke Krok, the father of Libuše in Czech legend * Matthew Krok (born 1983), Australian child actor * Morris Krok (1931–2005), South African writer * Zygmunt Solorz-Żak (born Zygmunt Józef Krok in 1956), Polish businessman and media tycoon Places * Krok, Wisconsin, an unincorporated community in the United States * Krok Island, Kemp Land, Antarctica * Krok Fjord, Princess Elizabeth Land, Antarctica * Krok Lake, Princess Elizabeth Land, Antarctica * 3102 Krok, an asteroid Other uses * The Harvard Krokodiloes or the Kroks, Harvard's oldest a cappella group * KROK International Animated Films Festival, a Russian / Ukrainian film festival * KROK (FM), a radio station licensed to South Fort Polk, Louisiana, United States See also * * KROC (other) * Kroc (surname) * Krock (other) * KROQ-FM KROQ-FM (106.7 MHz) is a commercial radio station licensed to Pasadena, Califo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Isosceles Triangle
In geometry, an isosceles triangle () is a triangle that has two Edge (geometry), sides of equal length and two angles of equal measure. 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 (mathematics), 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 (geometry), ''base'' of the triangle. The other dimensions of the triangle, such ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Equilateral Triangle
An equilateral triangle is a triangle in which all three sides have the same length, and all three angles are equal. Because of these properties, the equilateral triangle is a regular polygon, occasionally known as the regular triangle. It is the special case of an isosceles triangle by modern definition, creating more special properties. The equilateral triangle can be found in various tilings, and in polyhedrons such as the deltahedron and antiprism. It appears in real life in popular culture, architecture, and the study of stereochemistry resembling the molecular known as the trigonal planar molecular geometry. Properties An equilateral triangle is a triangle that has three equal sides. It is a special case of an isosceles triangle in the modern definition, stating that an isosceles triangle is defined at least as having two equal sides. Based on the modern definition, this leads to an equilateral triangle in which one of the three sides may be considered its base. Th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Triangle
A triangle is a polygon with three corners and three sides, one of the basic shapes in geometry. The corners, also called ''vertices'', are zero-dimensional points while the sides connecting them, also called ''edges'', are one-dimensional line segments. A triangle has three internal angles, each one bounded by a pair of adjacent edges; the sum of angles of a triangle always equals a straight angle (180 degrees or π radians). The triangle is a plane figure and its interior is a planar region. Sometimes an arbitrary edge is chosen to be the ''base'', in which case the opposite vertex is called the ''apex''; the shortest segment between the base and apex is the ''height''. The area of a triangle equals one-half the product of height and base length. In Euclidean geometry, any two points determine a unique line segment situated within a unique straight line, and any three points that do not all lie on the same straight line determine a unique triangle situated w ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Axis Of Symmetry
An axis (: axes) may refer to: Mathematics *A specific line (often a directed line) that plays an important role in some contexts. In particular: ** Coordinate axis of a coordinate system *** ''x''-axis, ''y''-axis, ''z''-axis, common names for the coordinate axes of a Cartesian coordinate system ** Axis of rotation ** Axis of symmetry ** Axis of a conic section Politics *Axis powers of World War II, 1936–1945. * Axis of evil (first used in 2002), U.S. President George W. Bush's description of Iran, Iraq, and North Korea *Axis of Resistance (first used in 2002), the Shia alliance of Iran, Syria, and Hezbollah * Axis of Upheaval (first used in 2024), foreign policy neologism of the Anti-western collaboration between Russia, China, Iran, and North Korea * Jakarta-Pyongyang-Peking Axis, diplomatic alignment and alliance between Indonesia, China, and North Korea during Sukarno's Presidency *Political spectrum, sometimes called an axis Science *Axis (anatomy), the second cerv ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
