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Hyperbolic Spiral
A hyperbolic spiral is a plane curve, which can be described in polar coordinates by the equation :r=\frac of a hyperbola. Because it can be generated by a circle inversion of an Archimedean spiral, it is called Reciprocal spiral, too.. Pierre Varignon first studied the curve in 1704. Later Johann Bernoulli and Roger Cotes worked on the curve as well. The hyperbolic spiral has a pitch angle that increases with distance from its center, unlike the logarithmic spiral (in which the angle is constant) or Archimedean spiral (in which it decreases with distance). For this reason, it has been used to model the shapes of spiral galaxies, which in some cases similarly have an increasing pitch angle. However, this model does not provide a good fit to the shapes of all spiral galaxies. In cartesian coordinates the hyperbolic spiral with the polar equation :r=\frac a \varphi ,\quad \varphi \ne 0 can be represented in Cartesian coordinates by :x = a \frac \varphi, \qquad y = a \frac \var ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Polar Coordinate System
In mathematics, the polar coordinate system is a two-dimensional coordinate system in which each point on a plane is determined by a distance from a reference point and an angle from a reference direction. The reference point (analogous to the origin of a Cartesian coordinate system) is called the ''pole'', and the ray from the pole in the reference direction is the ''polar axis''. The distance from the pole is called the ''radial coordinate'', ''radial distance'' or simply ''radius'', and the angle is called the ''angular coordinate'', ''polar angle'', or ''azimuth''. Angles in polar notation are generally expressed in either degrees or radians (2 rad being equal to 360°). Grégoire de Saint-Vincent and Bonaventura Cavalieri independently introduced the concepts in the mid-17th century, though the actual term "polar coordinates" has been attributed to Gregorio Fontana in the 18th century. The initial motivation for the introduction of the polar system was the study of circula ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Jakob Philipp Kulik
Jakob Philipp Kulik (1793–1863) was an Austrian mathematician known for his construction of a massive factor tables. Biography Kulik was born in Lemberg, which was part of the Austrian empire, and is now Lviv located in Ukraine. Kulik's factor tables In 1825, Kulik mentioned a table of factors up to 30 million, but this table does no longer seem to exist. It is also not clear if it had really been completed. From about 1825 until 1863 Kulik produced a factor table of numbers up to 100330200 (except for numbers divisible by 2, 3, or 5). This table basically had the same format as the table to 30 million and it is therefore most likely that the work on the "Magnus canon divisorum" spanned from the mid-1820s to Kulik's death, at which time the tables were still unfinished. These tables fill eight volumes totaling 4212 pages, and are kept in the archives of the Academy of Sciences in Vienna. Volume II of the 8-volume set has been lost. Works *Jakob Philipp Kulik: De pha ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Friedrich Grelle
Friedrich may refer to: Names *Friedrich (surname), people with the surname ''Friedrich'' *Friedrich (given name), people with the given name ''Friedrich'' Other *Friedrich (board game), a board game about Frederick the Great and the Seven Years' War * ''Friedrich'' (novel), a novel about anti-semitism written by Hans Peter Richter *Friedrich Air Conditioning, a company manufacturing air conditioning and purifying products *, a German cargo ship in service 1941-45 See also *Friedrichs (other) *Frederick (other) *Nikolaus Friedreich Nikolaus Friedreich (1 July 1825 in Würzburg – 6 July 1882 in Heidelberg) was a German pathologist and neurologist, and a third generation physician in the Friedreich family. His father was psychiatrist Johann Baptist Friedreich (1796–1862) ... {{disambig ja:フリードリヒ ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Circle Inversion
A circle is a shape consisting of all points in a plane that are at a given distance from a given point, the centre. Equivalently, it is the curve traced out by a point that moves in a plane so that its distance from a given point is constant. The distance between any point of the circle and the centre is called the radius. Usually, the radius is required to be a positive number. A circle with r=0 (a single point) is a degenerate case. This article is about circles in Euclidean geometry, and, in particular, the Euclidean plane, except where otherwise noted. Specifically, a circle is a simple closed curve that divides the plane into two regions: an interior and an exterior. In everyday use, the term "circle" may be used interchangeably to refer to either the boundary of the figure, or to the whole figure including its interior; in strict technical usage, the circle is only the boundary and the whole figure is called a '' disc''. A circle may also be defined as a special kin ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Osculating Circle
In differential geometry of curves, the osculating circle of a sufficiently smooth plane curve at a given point ''p'' on the curve has been traditionally defined as the circle passing through ''p'' and a pair of additional points on the curve infinitesimally close to ''p''. Its center lies on the inner normal line, and its curvature defines the curvature of the given curve at that point. This circle, which is the one among all tangent circles at the given point that approaches the curve most tightly, was named ''circulus osculans'' (Latin for "kissing circle") by Leibniz. The center and radius of the osculating circle at a given point are called center of curvature and radius of curvature of the curve at that point. A geometric construction was described by Isaac Newton in his '' Principia'': Nontechnical description Imagine a car moving along a curved road on a vast flat plane. Suddenly, at one point along the road, the steering wheel locks in its present position. Thereaf ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Circle Inversion
A circle is a shape consisting of all points in a plane that are at a given distance from a given point, the centre. Equivalently, it is the curve traced out by a point that moves in a plane so that its distance from a given point is constant. The distance between any point of the circle and the centre is called the radius. Usually, the radius is required to be a positive number. A circle with r=0 (a single point) is a degenerate case. This article is about circles in Euclidean geometry, and, in particular, the Euclidean plane, except where otherwise noted. Specifically, a circle is a simple closed curve that divides the plane into two regions: an interior and an exterior. In everyday use, the term "circle" may be used interchangeably to refer to either the boundary of the figure, or to the whole figure including its interior; in strict technical usage, the circle is only the boundary and the whole figure is called a '' disc''. A circle may also be defined as a special kin ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Spiral Galaxy
Spiral galaxies form a class of galaxy originally described by Edwin Hubble in his 1936 work ''The Realm of the Nebulae''Alt URL pp. 124–151) and, as such, form part of the . Most spiral galaxies consist of a flat, rotating containing s, gas and dust, and a central concentration of stars known as the |
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