Geometrically, the swastika can be regarded as an irregular icosagon or 20-sided polygon. The arms are of varying width and are often rectilinear (but need not be). However, the proportions of the Nazi swastika were fixed: they were based on a 5x5 grid.[7] Characteristic is the 90° rotational symmetry (that is, the symmetry of the cyclic group C4h) and chirality, hence the absence of reflectional symmetry, and the existence o ...

See also:

Swastika, Swastika - Overview, Swastika - Etymology and alternative names, Swastika - History, Swastika - Comet/bird hypothesis, Swastika - Early Hinduism, Swastika - Adoption of the swastika in the West, Swastika - Geometry and symbolism, Swastika - Sauwastika, Swastika - Art and architecture, Swastika - Religion and mythology, Swastika - Hinduism, Swastika - Buddhism, Swastika - Jainism, Swastika - The Abrahamic religions, Swastika - Other Asian traditions, Swastika - Native American traditions, Swastika - Pre-Christian European traditions, Swastika - Early 20th century, Swastika - Britain, Swastika - North America, Swastika - Russia, Swastika - Poland, Swastika - Finland, Swastika - Sweden, Swastika - Latvia, Swastika - Icelandic, Swastika - Ireland, Swastika - Nazi Germany, Swastika - Taboo in Western countries, Swastika - Popular culture and media, Swastika - Notes

Read more here: » Swastika: Encyclopedia II - Swastika - Geometry and symbolism

See also:

Swastika, Swastika - Overview, Swastika - Etymology and alternative names, Swastika - History, Swastika - Adoption of the swastika in the West, Swastika - Geometry and symbolism, Swastika - Sauwastika, Swastika - Art and architecture, Swastika - Religion and mythology, Swastika - Hinduism, Swastika - Buddhism, Swastika - Jainism, Swastika - The Abrahamic religions, Swastika - Other Asian traditions, Swastika - Native American traditions, Swastika - Pre-Christian European traditions, Swastika - Early 20th century, Swastika - Britain, Swastika - North America, Swastika - Russia, Swastika - Poland, Swastika - Finland, Swastika - Sweden, Swastika - Latvia, Swastika - Icelandic, Swastika - Ireland, Swastika - Nazi Germany, Swastika - Taboo in Western countries, Swastika - Popular culture and media, Swastika - Notes

Read more here: » Swastika: Encyclopedia II - Swastika - Geometry and symbolism

Geometrically, the swastika can be regarded as an irregular icosagon or 20-sided polygon. The arms are of varying width and are often rectilinear (but need not be). However, the proportions of the Nazi swastika were fixed: they were based on a 5x5 grid.[6] Characteristic is the 90° rotational symmetry (that is, the symmetry of the cyclic group C4h) and chirality, hence the absence of reflectional symmetry, and the existence o ...

See also:

Swastika, Swastika - Overview, Swastika - Etymology and alternative names, Swastika - History, Swastika - Adoption of the swastika in the West, Swastika - Geometry and symbolism, Swastika - Sauwastika, Swastika - Art and architecture, Swastika - Religion and mythology, Swastika - Hinduism, Swastika - Buddhism, Swastika - Jainism, Swastika - The Abrahamic religions, Swastika - Other Asian traditions, Swastika - Native American traditions, Swastika - Pre-Christian European traditions, Swastika - Asatru, Swastika - Early 20th century, Swastika - Europe, Swastika - North America, Swastika - Nazi Germany, Swastika - Taboo in Western countries, Swastika - Apperance in Media

Read more here: » Swastika: Encyclopedia II - Swastika - Geometry and symbolism

The swastika (from Sanskrit svastika) is an equilateral cross with its arms bent at right angles either left-facing (卍) or right-facing (卐). It is traditionally oriented so that a main line is horizontal, though it is occasionally rotated at forty-five degrees, and the Hindu version is often decorated with a dot in each quadrant. ...

Including:

Swastika - Overview Swastika - Etymology and alternative names Swastika - History
Swastika - Adoption of the swastika in the West
Swastika - Geometry and symbolism
Swastika - Sauwastika
Swastika - Art and architecture Swastika - Religion and mythology
Swastika - Hinduism Swastika - Buddhism Swastika - Jainism Swastika - The Abrahamic religions Swastika - Other Asian traditions Swastika - Native American traditions Swastika - Pre-Christian European traditions Swastika - Asatru
Swastika - Early 20th century
Swastika - Europe Swastika - North America
Swastika - Nazi Germany Swastika - Taboo in Western countries Swastika - Apperance in Media

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Sacred Geometry: YANTRAS - What is a Yantra?

All ancient cultures had sacred geometric designs representative of their Gods, which had a mantra (or sacred sound vibration) that corresponded to it. The Indians, Egyptians, Jews, Chinese, and Mayans all had systems of "planetary yantras" used to combat malefic influences. Yantra is the ultimate "symbology". In the Vedic culture we find much power and energy said to be held within sacred geometric symbols. They are to be found throughout sacred scriptures, carved in stone, hidden within paintings and in temples.

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Geometry (Greek γεωμετρία; geo = earth, metria = measure) arose as the field of knowledge dealing with spatial relationships. It was one of the two fields of pre-modern mathematics, the other being the study of numbers. In modern times, geometric concepts have been generalized to a high level of abstraction and complexity, and have been subjected to the methods of calculus and abstract algebra, so that many modern branches of the field are barely recognizable as the descendants of early geometry. (See areas of mathemat ...

Including:

Geometry - The earliest geometry Geometry - The Greek period c. 600 B.C. – 600 A.D.
Geometry - Thales and Pythagoras Geometry - Plato Geometry - Euclid Geometry - Archimedes Geometry - After Archimedes
Geometry - The Middle Ages Renaissance and Reformation Geometry - The 17th and early 18th centuries Geometry - The late 18th and 19th centuries
Geometry - Non-Euclidean geometry Geometry - Introduction of mathematical rigor Geometry - Analysis situs or topology
Geometry - The 20th century

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Sacred geometry is geometry that is sacred to the observer or discoverer of the geometry. This meaning is sometimes described as being the language of the God of the religion of the people who discovered or used it. Sacred geometry can be described as attributing a religious or cultural value to the graphical representation of the mathematical relationships and the design of the man-made objects that sy ...

Including:

Sacred geometry - External link

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In computer science, computational geometry is the study of algorithms to solve problems stated in terms of geometry. Some purely geometrical problems arise out of the study of computational geometric algorithms, and the study of such problems is also considered to be part of computational geometry. The main driving force for the development of computational geometry as a discipline was progress in computer graphics, computer-aided design and manufacturing (CAD/CAM), but man ...

Including:

Computational geometry - Combinatorial computational geometry
Computational geometry - Problems
Computational geometry - Numerical geometry Computational geometry - Books

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Analytic geometry, also called coordinate geometry and earlier referred to as Cartesian geometry, is the study of geometry using the principles of algebra. Usually the Cartesian coordinate system is applied to manipulate equations for planes, lines, curves, and circles, often in two and sometimes in three dimensions of measurement. As taught in school books, analytic geometry can be explained more simply: it is concerned with defining geometrical shapes in a numerical way, and extracting numerical information from that r ...

Including:

Analytic geometry - Important themes of analytical geometry Analytic geometry - Example Analytic geometry - Other uses

Read more here: » Analytic geometry: Encyclopedia - Analytic geometry

In geometry, two shapes are called congruent if one can be transformed into the other by an isometry, i.e. a combination of translations, rotations and reflections. Note: This article is about congruences in geometry. For notions of congruence in algebra, see congruence relation. Congruence geometry - Definition of congruence in analytic geometry. In a Euclidean system, congruence is fundamental; it's the counterpart of an equals sign in numerical analysis. In analytic geometry, congru ...

Including:

Congruence geometry - Definition of congruence in analytic geometry Congruence geometry - Congruence of triangles

Read more here: » Congruence geometry: Encyclopedia - Congruence geometry

In mathematics, inversive geometry is the geometry of circles and the set of transformations that map all circles into circles, where by a circle one may also mean a line (a circle with infinite radius). Inversive geometry - Circle inversion. Inversive geometry - Inverse of a point. In the plane, the inverse of a point P in respect to a circle of center O and radius R is a point P' such that P and P' are on the same ray goi ...

Including:

Inversive geometry - Circle inversion
Inversive geometry - Inverse of a point Inversive geometry - Properties Inversive geometry - Application
Inversive geometry - The Erlangen program Inversive geometry - Duality of inversive geometry and hyperbolic geometry Inversive geometry - Computer program Inversive geometry - External link

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Algebraic geometry is a branch of mathematics which, as the name suggests, combines abstract algebra, especially commutative algebra, with geometry. It can be seen as the study of solution sets of systems of algebraic equations. When there is more than one variable, geometric considerations enter and are important to understand the phenomenon. One can say that the subject starts where equation solving leaves off, and it becomes at least as important to understand the totality of solutions of a system of equations as to find som ...

Including:

Algebraic geometry - Zeroes of simultaneous polynomials Algebraic geometry - Affine varieties Algebraic geometry - Regular functions Algebraic geometry - The category of affine varieties Algebraic geometry - Projective space Algebraic geometry - The modern viewpoint Algebraic geometry - Notes and history

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A chord of a curve is a geometric line segment whose endpoints both lie on the curve. A secant or a secant line is the line extension of a chord. Chord geometry - Chords of a circle. Among properties of chords of a circle are the following: Chords are equidistant from the center if and only if their lengths are equal. A chord's perpendicular bisector passes the center. If the line extensions (secant lines) of chords AB and CD intersect at a point P, then ...

Including:

Chord geometry - Chords of a circle Chord geometry - Chords in Trigonometry

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Area is a quantity expressing the size of a figure in the Euclidean plane or on a 2-dimensional surface. Points and lines have zero area. Depending on the particular definition taken, a figure may have infinite area, for example the entire Euclidean plane. In three dimensions, the analog of area is called a volume. Area geometry - How to define area. Although area seems to be one of the basic notions in geometry, it is not at all easy to define even in the Euclidean plane. Most textbooks avoid defining an a ...

Including:

Area geometry - How to define area Area geometry - Formulae
Area geometry - Areas of 2-dimensional figures Area geometry - Surface area of 3-dimensional figures

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Ackermann steering geometry is a geometric arrangement of linkages in the steering of a car or other vehicle designed to solve the problem of wheels on the inside and outside of a turn needing to trace out circles of different radii. This engineering solution is attributable to Langensperger in 1816, but was patented by arrangement in London, in 1817, by Rudolph Ackermann, whose name stuck to it. The same idea was a ...

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Bookshelf Symbol 7 is a typeface which comes packaged with Microsoft Office 2003. In 2004, Microsoft released a critical update (Knowledge Base Article 833407) to remove two swastikas and a Star of David from this typeface, presumably after complaints from users who took the swastikas as support for Nazism. ...

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Swastika is a very important solar symbol. Solar symbol - Symbolism. It has several mystical symbolisms. There are "positive" and "negative" swastikas. Solar symbol - Usage. Buddhist Emblem Jain Emblem Manji Nazi Emblem. Solar symbol - More Information. For more information on Swastika, see Swastika and: [1]; [2]; [3] (the most commonly used); ...

See also:

Solar symbol, Solar symbol - ⊙ Circle with a point at its centre, Solar symbol - Symbolism, Solar symbol - Usage, Solar symbol - More Information, Solar symbol - Swastika, Solar symbol - Symbolism, Solar symbol - Usage, Solar symbol - More Information

Read more here: » Solar symbol: Encyclopedia II - Solar symbol - Swastika

There is heuristic value to studying descriptive geometry. It promotes visualization and spatial analytical abilities. It promotes intuitive ability to recognize the direction of viewing for best presenting a geometric problem for solution. Representative examples: Descriptive geometry - The direction to best view:. Two skew lines (pipes, perhaps) in general positions in order to determine the location of their shortest connector (common perpendicular). Two skew lines (pipes) in general posi ...

See also:

Descriptive geometry, Descriptive geometry - Protocols, Descriptive geometry - Heuristics, Descriptive geometry - The direction to best view:, Descriptive geometry - General solutions

Read more here: » Descriptive geometry: Encyclopedia II - Descriptive geometry - Heuristics

This branch is also known as geometric modelling, computer-aided geometric design (CAGD), and may be often found under the keyword curves and surfaces. Core problems are curve and surface modelling and representation. The most important instruments here are parametric curves and parametric surfaces, such as Bezier curves, spline curves and surfaces. An important non-parametric approach is the level set method. First (and still most important) application areas are shipbuilding, aircraft, and automoti ...

See also:

Computational geometry, Computational geometry - Combinatorial computational geometry, Computational geometry - Problems, Computational geometry - Numerical geometry, Computational geometry - Books

Read more here: » Computational geometry: Encyclopedia II - Computational geometry - Numerical geometry

General solutions are a class of solutions within descriptive geometry that contain all possible solutions to a problem. The general solution is represented by a single, three-dimensional object, usually a cone, the directions of the elements of which are the desired direction of viewing (projection) for any of an infinite number of solution views. For example: To find the general solution such that two, unequal length, skew lines in general positions (say, rockets in flight?) appear: Equal length Equal length an ...

See also:

Descriptive geometry, Descriptive geometry - Protocols, Descriptive geometry - Heuristics, Descriptive geometry - The direction to best view:, Descriptive geometry - General solutions

Read more here: » Descriptive geometry: Encyclopedia II - Descriptive geometry - General solutions