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Poncelet–Steiner Theorem
In the branch of mathematics known as Euclidean geometry, the Poncelet–Steiner theorem is one of several results concerning compass and straightedge constructions having additional restrictions imposed on the traditional rules. This result states that whatever can be constructed by straightedge and compass together can be constructed by straightedge alone, provided that a single circle and its centre are given. This theorem is related to the rusty compass equivalence. : ''Any Euclidean construction, insofar as the given and required elements are points (or lines), if it can be completed with both the compass and the straightedge together, may be completed with the straightedge alone provided that no fewer than one circle with its center exist in the plane.'' Though a compass can make constructions significantly easier, it is implied that there is no functional purpose of the compass once the first circle has been drawn. All constructions remain possible, though it is naturally ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Steiner Construction Of A Parallel To A Diameter , the professional wrestling "tag team" of real-life brothers Rick and Scott Steiner
{{disambiguation, geo ...
Steiner may refer to: Felix Steiner, German Waffen SS-commander Surname *Steiner (surname) Other uses *Steiner, Michigan, a village in the United States * Steiner, Mississippi * Steiner Studios, film and television production studio in New York City * Steiner's theorem, used to determine the mass moment of inertia around an axis. Also known as parallel axis theorem See also * Poncelet–Steiner theorem *Steiner point (other) * Steiner surface *Steiner system, a type of block design *Steiner tree *Waldorf education, also called Steiner education *The Steiner Brothers The Steiner Brothers are an American professional wrestling tag team consisting of brothers Robert "Rick Steiner" Rechsteiner and Scott "Scott Steiner" Rechsteiner. The brothers wrestled as amateurs at the University of Michigan. The team ma ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Niccolò Fontana Tartaglia
Niccolò Fontana Tartaglia (; 1499/1500 – 13 December 1557) was an Italian mathematician, engineer (designing fortifications), a surveyor (of topography, seeking the best means of defense or offense) and a bookkeeper from the then Republic of Venice. He published many books, including the first Italian translations of Archimedes and Euclid, and an acclaimed compilation of mathematics. Tartaglia was the first to apply mathematics to the investigation of the paths of cannonballs, known as ballistics, in his ''Nova Scientia'' (''A New Science'', 1537); his work was later partially validated and partially superseded by Galileo's studies on falling bodies. He also published a treatise on retrieving sunken ships. Personal life Niccolò Fontana was born in Brescia, the son of Michele Fontana, a dispatch rider who travelled to neighbouring towns to deliver mail. In 1506, Michele was murdered by robbers, and Niccolò, his two siblings, and his mother were left impoverished. Niccol� ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Other Types Of Restricted Construction
Other often refers to: * Other (philosophy), a concept in psychology and philosophy Other or The Other may also refer to: Film and television * ''The Other'' (1913 film), a German silent film directed by Max Mack * ''The Other'' (1930 film), a German film directed by Robert Wiene * ''The Other'' (1972 film), an American film directed by Robert Mulligan * ''The Other'' (1999 film), a French-Egyptian film directed by Youssef Chahine * ''The Other'' (2007 film), an Argentine-French-German film by Ariel Rotter * The Other (''Doctor Who''), a fictional character in ''Doctor Who'' * The Other (Marvel Cinematic Universe), a fictional character in the Marvel Cinematic Universe Literature * '' Other: British and Irish Poetry since 1970'', a 1999 poetry anthology * ''The Other'' (Applegate novel), a 2000 ''Animorphs'' novel by K.A. Applegate * ''The Other'' (Tryon novel), a 1971 horror novel by Tom Tryon * "The Other" (short story), a 1972 short story by Jorge Luis Borges * ''The ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Concentric
In geometry, two or more objects are said to be concentric, coaxal, or coaxial when they share the same center or axis. Circles, regular polygons and regular polyhedra, and spheres may be concentric to one another (sharing the same center point), as may cylinders (sharing the same central axis). Geometric properties In the Euclidean plane, two circles that are concentric necessarily have different radii from each other.. However, circles in three-dimensional space may be concentric, and have the same radius as each other, but nevertheless be different circles. For example, two different meridians of a terrestrial globe are concentric with each other and with the globe of the earth (approximated as a sphere). More generally, every two great circles on a sphere are concentric with each other and with the sphere. By Euler's theorem in geometry on the distance between the circumcenter and incenter of a triangle, two concentric circles (with that distance being zero) are ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
One To One Correspondence
In mathematics, a bijection, also known as a bijective function, one-to-one correspondence, or invertible function, is a function between the elements of two sets, where each element of one set is paired with exactly one element of the other set, and each element of the other set is paired with exactly one element of the first set. There are no unpaired elements. In mathematical terms, a bijective function is a one-to-one (injective) and onto (surjective) mapping of a set ''X'' to a set ''Y''. The term ''one-to-one correspondence'' must not be confused with ''one-to-one function'' (an injective function; see figures). A bijection from the set ''X'' to the set ''Y'' has an inverse function from ''Y'' to ''X''. If ''X'' and ''Y'' are finite sets, then the existence of a bijection means they have the same number of elements. For infinite sets, the picture is more complicated, leading to the concept of cardinal number—a way to distinguish the various sizes of infinite sets. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Focus (geometry)
In geometry, focuses or foci (), singular focus, are special points with reference to which any of a variety of curves is constructed. For example, one or two foci can be used in defining conic sections, the four types of which are the circle, ellipse, parabola, and hyperbola. In addition, two foci are used to define the Cassini oval and the Cartesian oval, and more than two foci are used in defining an ''n''-ellipse. Conic sections Defining conics in terms of two foci An ellipse can be defined as the locus of points for which the sum of the distances to two given foci is constant. A circle is the special case of an ellipse in which the two foci coincide with each other. Thus, a circle can be more simply defined as the locus of points each of which is a fixed distance from a single given focus. A circle can also be defined as the circle of Apollonius, in terms of two different foci, as the locus of points having a fixed ratio of distances to the two foci. A parabola i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Eccentricity (mathematics)
In mathematics, the eccentricity of a conic section is a non-negative real number that uniquely characterizes its shape. More formally two conic sections are similar if and only if they have the same eccentricity. One can think of the eccentricity as a measure of how much a conic section deviates from being circular. In particular: * The eccentricity of a circle is zero. * The eccentricity of an ellipse which is not a circle is greater than zero but less than 1. * The eccentricity of a parabola is 1. * The eccentricity of a hyperbola is greater than 1. * The eccentricity of a pair of lines is \infty Definitions Any conic section can be defined as the locus of points whose distances to a point (the focus) and a line (the directrix) are in a constant ratio. That ratio is called the eccentricity, commonly denoted as . The eccentricity can also be defined in terms of the intersection of a plane and a double-napped cone associated with the conic section. If the cone is orient ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Steiner Conic
The Steiner conic or more precisely Steiner's generation of a conic, named after the Swiss mathematician Jakob Steiner, is an alternative method to define a non-degenerate projective conic section in a projective plane over a field. The usual definition of a conic uses a quadratic form (see Quadric (projective geometry)). Another alternative definition of a conic uses a ''hyperbolic polarity''. It is due to '' K. G. C. von Staudt'' and sometimes called a von Staudt conic. The disadvantage of von Staudt's definition is that it only works when the underlying field has odd characteristic (i.e., Char\ne2). Definition of a Steiner conic *Given two pencils B(U),B(V) of lines at two points U,V (all lines containing U and V resp.) and a projective but not perspective mapping \pi of B(U) onto B(V). Then the intersection points of corresponding lines form a non-degenerate projective conic section (figure 1) A ''perspective'' mapping \pi of a pencil B(U) onto a pencil B(V) is a bijec ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Projective Transformations
In projective geometry, a homography is an isomorphism of projective spaces, induced by an isomorphism of the vector spaces from which the projective spaces derive. It is a bijection that maps lines to lines, and thus a collineation. In general, some collineations are not homographies, but the fundamental theorem of projective geometry asserts that is not so in the case of real projective spaces of dimension at least two. Synonyms include projectivity, projective transformation, and projective collineation. Historically, homographies (and projective spaces) have been introduced to study perspective and projections in Euclidean geometry, and the term ''homography'', which, etymologically, roughly means "similar drawing", dates from this time. At the end of the 19th century, formal definitions of projective spaces were introduced, which differed from extending Euclidean or affine spaces by adding points at infinity. The term "projective transformation" originated in these abst ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Proof Of Impossibility
In mathematics, a proof of impossibility is a proof that demonstrates that a particular problem cannot be solved as described in the claim, or that a particular set of problems cannot be solved in general. Such a case is also known as a negative proof, proof of an impossibility theorem, or negative result. Because they show that something cannot be done, proofs of impossibility can be the resolutions to decades or centuries of work attempting to find a solution. Proving that something is impossible is usually much harder than the opposite task, as it is often necessary to develop a proof that works in general, rather than to just show a particular example. Impossibility theorems are usually expressible as negative existential propositions or universal propositions in logic. The irrationality of the square root of 2 is one of the oldest proofs of impossibility. It shows that it is impossible to express the square root of 2 as a ratio of two integers. Another consequential proof o ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Jakob Steiner
Jakob Steiner (18 March 1796 – 1 April 1863) was a Swiss mathematician who worked primarily in geometry. Life Steiner was born in the village of Utzenstorf, Canton of Bern. At 18, he became a pupil of Heinrich Pestalozzi and afterwards studied at Heidelberg. Then, he went to Berlin, earning a livelihood there, as in Heidelberg, by tutoring. Here he became acquainted with A. L. Crelle, who, encouraged by his ability and by that of Niels Henrik Abel, then also staying at Berlin, founded his famous '' Journal'' (1826). After Steiner's publication (1832) of his ''Systematische Entwickelungen'' he received, through Carl Gustav Jacob Jacobi, who was then professor at Königsberg University, and earned an honorary degree there; and through the influence of Jacobi and of the brothers Alexander and Wilhelm von Humboldt a new chair of geometry was founded for him at Berlin (1834). This he occupied until his death in Bern on 1 April 1863. He was described by Thomas Hirst as fol ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
