HOME  TheInfoList.com 
Brianchon Theorem In geometry, Brianchon's theorem Brianchon's theorem is a theorem stating that when a hexagon is circumscribed around a conic section, its principal diagonals (those connecting opposite vertices) meet in a single point. It is named after Charles Julien Brianchon (1783–1864).Contents1 Formal statement 2 Connection to Pascal's theorem 3 In the affine plane 4 Proof 5 See also 6 ReferencesFormal statement[edit] Let ABCDEF be a hexagon formed by six tangent lines of a conic section. Then lines AD, BE, CF (extended diagonals each connecting opposite vertices) intersect at a single point.[1]:p. 218[2] Connection to Pascal's theorem[edit] The polar reciprocal and projective dual of this theorem give Pascal's theorem. In the affine plane[edit] Brianchon's theorem Brianchon's theorem is true in both the affine plane and the real projective plane [...More...]  "Brianchon Theorem" on: Wikipedia Yahoo Parouse 

Geometry Geometry Geometry (from the Ancient Greek: γεωμετρία; geo "earth", metron "measurement") is a branch of mathematics concerned with questions of shape, size, relative position of figures, and the properties of space. A mathematician who works in the field of geometry is called a geometer. Geometry Geometry arose independently in a number of early cultures as a practical way for dealing with lengths, areas, and volumes [...More...]  "Geometry" on: Wikipedia Yahoo Parouse 

Real Projective Plane In mathematics, the real projective plane is an example of a compact nonorientable twodimensional manifold; in other words, a onesided surface. It cannot be embedded in standard threedimensional space without intersecting itself. It has basic applications to geometry, since the common construction of the real projective plane is as the space of lines in R3 passing through the origin. The plane is also often described topologically, in terms of a construction based on the Möbius strip: if one could glue the (single) edge of the Möbius strip Möbius strip to itself in the correct direction, one would obtain the projective plane [...More...]  "Real Projective Plane" on: Wikipedia Yahoo Parouse 

Special Special Special or specials may refer to:Contents1 Music 2 Film and television 3 Other uses 4 See alsoMusic[edit] Special Special (album), a 1992 [...More...]  "Special" on: Wikipedia Yahoo Parouse 

International Standard Book Number "ISBN" redirects here. For other uses, see ISBN (other).International Standard Book Book NumberA 13digit ISBN, 9783161484100, as represented by an EAN13 bar codeAcronym ISBNIntroduced 1970; 48 years ago (1970)Managing organisation International ISBN AgencyNo. of digits 13 (formerly 10)Check digit Weighted sumExample 9783161484100Website www.isbninternational.orgThe International Standard Book Book Number (ISBN) is a unique[a][b] numeric commercial book identifier. Publishers purchase ISBNs from an affiliate of the International ISBN Agency.[1] An ISBN is assigned to each edition and variation (except reprintings) of a book. For example, an ebook, a paperback and a hardcover edition of the same book would each have a different ISBN. The ISBN is 13 digits long if assigned on or after 1 January 2007, and 10 digits long if assigned before 2007 [...More...]  "International Standard Book Number" on: Wikipedia Yahoo Parouse 

H. S. M. Coxeter Harold Scott MacDonald "Donald" Coxeter, FRS, FRSC, CC (February 9, 1907 – March 31, 2003)[2] was a Britishborn Canadian geometer. Coxeter is regarded as one of the greatest geometers of the 20th century. He was born in London London but spent most of his adult life in Canada. He was always called Donald, from his third name MacDonald.[3] He was most noted for his work on regular polytopes and higherdimensional geometries [...More...]  "H. S. M. Coxeter" on: Wikipedia Yahoo Parouse 

Seven Circles Theorem In geometry, the seven circles theorem is a theorem about a certain arrangement of seven circles in the Euclidean plane. Specifically, given a chain of six circles all tangent to a seventh circle and each tangent to its two neighbors, the three lines drawn between opposite pairs of the points of tangency on the seventh circle all pass through the same point. Though elementary in nature, this theorem was not discovered until 1974 (by Evelyn, MoneyCoutts, and Tyrrell). See also[edit]Brianchon's theoremReferences[edit]Cundy, H. Martyn (1978). "The sevencircles theorem". The Mathematical Gazette. 62 (421): 200–203. JSTOR 3616692. Evelyn, C. J. A.; MoneyCoutts, G. B.; Tyrrell, J. A. (1974). The Seven Circles Theorem and Other New Theorems. London: Stacey International. ISBN 9780950330402. Wells, D. (1991). The Penguin Dictionary of Curious and Interesting Geometry. New York: Penguin Books [...More...]  "Seven Circles Theorem" on: Wikipedia Yahoo Parouse 

Radical Axis The radical axis (or power line) of two circles is the locus of points at which tangents drawn to both circles have the same length. The radical axis is always a straight line and always perpendicular to the line connecting the centers of the circles, albeit closer to the circumference of the larger circle. If the circles intersect, the radical axis is the line passing through the intersection points; similarly, if the circles are tangent, the radical axis is simply the common tangent. For any point P on the radical axis, there is a unique circle centered on P that intersects both circles at right angles (orthogonally); conversely, the center of any circle that cuts both circles orthogonally must lie on the radical axis [...More...]  "Radical Axis" on: Wikipedia Yahoo Parouse 

Line At Infinity In geometry and topology, the line at infinity is a projective line that is added to the real (affine) plane in order to give closure to, and remove the exceptional cases from, the incidence properties of the resulting projective plane. The line at infinity is also called the ideal line.[1]Contents1 Geometric formulation 2 Topological perspective 3 History 4 See also 5 ReferencesGeometric formulation[edit] In projective geometry, any pair of lines always intersects at some point, but parallel lines do not intersect in the real plane. The line at infinity is added to the real plane. This completes the plane, because now parallel lines intersect at a point which lies on the line at infinity. Also, if any pair of lines intersect at a point on the line at infinity, then the pair of lines are parallel. Every line intersects the line at infinity at some point [...More...]  "Line At Infinity" on: Wikipedia Yahoo Parouse 

Parabola In mathematics, a parabola is a plane curve which is mirrorsymmetrical and is approximately Ushaped. It fits any of several superficially different mathematical descriptions, which can all be proved to define exactly the same curves.Part of a parabola (blue), with various features (other colours). The complete parabola has no endpoints. In this orientation, it extends infinitely to the left, right, and upward.One description of a parabola involves a point (the focus) and a line (the directrix). The focus does not lie on the directrix. The parabola is the locus of points in that plane that are equidistant from both the directrix and the focus. Another description of a parabola is as a conic section, created from the intersection of a right circular conical surface and a plane which is parallel to another plane that is tangential to the conical surface.[a] A third description is algebraic [...More...]  "Parabola" on: Wikipedia Yahoo Parouse 

Projective Plane In mathematics, a projective plane is a geometric structure that extends the concept of a plane. In the ordinary Euclidean plane, two lines typically intersect in a single point, but there are some pairs of lines (namely, parallel lines) that do not intersect. A projective plane can be thought of as an ordinary plane equipped with additional "points at infinity" where parallel lines intersect. Thus any two distinct lines in a projective plane intersect in one and only one point. Renaissance artists, in developing the techniques of drawing in perspective, laid the groundwork for this mathematical topic. The archetypical example is the real projective plane, also known as the extended Euclidean plane.[1] This example, in slightly different guises, is important in algebraic geometry, topology and projective geometry where it may be denoted variously by PG(2, R), RP2, or P2(R), among other notations [...More...]  "Projective Plane" on: Wikipedia Yahoo Parouse 

Euclidean Plane Twodimensional space Twodimensional space or bidimensional space is a geometric setting in which two values (called parameters) are required to determine the position of an element (i.e., point). In Mathematics, it is commonly represented by the symbol ℝ2. For a generalization of the concept, see dimension. Twodimensional space Twodimensional space can be seen as a projection of the physical universe onto a plane [...More...]  "Euclidean Plane" on: Wikipedia Yahoo Parouse 

Hexagon In geometry, a hexagon (from Greek ἕξ hex, "six" and γωνία, gonía, "corner, angle") is a sixsided polygon or 6gon [...More...]  "Hexagon" on: Wikipedia Yahoo Parouse 

Pascal's Theorem In projective geometry, Pascal's theorem Pascal's theorem (also known as the hexagrammum mysticum theorem) states that if six arbitrary points are chosen on a conic (i.e., ellipse, parabola or hyperbola) and joined by line segments in any order to form a hexagon, then the three pairs of opposite sides of the hexagon (extended if necessary) meet in three points which lie on a straight line, called the Pascal line of the hexagon. The theorem is also valid in the Euclidean plane, but the statement needs to be adjusted to deal with the special cases when opposite sides are [...More...]  "Pascal's Theorem" on: Wikipedia Yahoo Parouse 

Projective Dual In geometry, a striking feature of projective planes is the symmetry of the roles played by points and lines in the definitions and theorems, and (plane) duality is the formalization of this concept. There are two approaches to the subject of duality, one through language (§ Principle of Duality) and the other a more functional approach through special mappings. These are completely equivalent and either treatment has as its starting point the axiomatic version of the geometries under consideration. In the functional approach there is a map between related geometries that is called a duality. Such a map can be constructed in many ways [...More...]  "Projective Dual" on: Wikipedia Yahoo Parouse 

Polar Reciprocation In geometry, the pole and polar are respectively a point and a line that have a unique reciprocal relationship with respect to a given conic section [...More...]  "Polar Reciprocation" on: Wikipedia Yahoo Parouse 