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Dandelin Spheres
In geometry, the Dandelin spheres are one or two spheres that are tangent both to a plane and to a cone that intersects the plane. The intersection of the cone and the plane is a conic section, and the point at which either sphere touches the plane is a focus of the conic section, so the Dandelin spheres are also sometimes called focal spheres.Taylor, Charles. ''An Introduction to the Ancient and Modern Geometry of Conics''page 196 ("focal spheres") (Deighton, Bell and co., 1881). The Dandelin spheres were discovered in 1822. They are named in honor of the French mathematician [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Locus (mathematics)
In geometry, a locus (plural: ''loci'') (Latin word for "place", "location") is a set (mathematics), set of all Point (geometry), points (commonly, a line (geometry), line, a line segment, a curve (mathematics), curve or a Surface (topology), surface), whose location satisfies or is determined by one or more specified conditions.. The set of the points that satisfy some property is often called the ''locus of a point'' satisfying this property. The use of the singular in this formulation is a witness that, until the end of the 19th century, mathematicians did not consider infinite sets. Instead of viewing lines and curves as sets of points, they viewed them as places where a point may be ''located'' or may move. History and philosophy Until the beginning of the 20th century, a geometrical shape (for example a curve) was not considered as an infinite set of points; rather, it was considered as an entity on which a point may be located or on which it moves. Thus a circle (mathemat ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Conic Sections
A conic section, conic or a quadratic curve is a curve obtained from a Conical surface, cone's surface intersecting a plane (mathematics), plane. The three types of conic section are the hyperbola, the parabola, and the ellipse; the circle is a special case of the ellipse, though it was sometimes considered a fourth type. The Greek mathematics, ancient Greek mathematicians studied conic sections, culminating around 200 BC with Apollonius of Perga's systematic work on their properties. The conic sections in the Euclidean plane have various distinguishing properties, many of which can be used as alternative definitions. One such property defines a non-circular conic to be the set (mathematics), set of those points whose distances to some particular point, called a ''Focus (geometry), focus'', and some particular line, called a ''directrix'', are in a fixed ratio, called the ''Eccentricity (mathematics), eccentricity''. The type of conic is determined by the value of the ec ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Greg Egan
Greg Egan (born 20 August 1961) is an Australian science fiction writer and mathematician, best known for his works of hard science fiction. Egan has won multiple awards including the John W. Campbell Memorial Award, the Hugo Award, and the Locus Award. Life and work Egan holds a Bachelor of Science degree in mathematics from the University of Western Australia. He published his first work in 1983. He specialises in hard science fiction stories with mathematical and quantum ontology themes, including the nature of consciousness. Other themes include genetics, simulated reality, posthumanism, mind uploading, sexuality, artificial intelligence, and the superiority of rational naturalism to religion. He often deals with complex technical material, like new physics and epistemology. He is a Hugo Award winner (with eight other works shortlisted for the Hugos) and has also won the John W. Campbell Memorial Award for Best Science Fiction Novel. His early stories feature strong ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Kepler's Laws Of Planetary Motion
In astronomy, Kepler's laws of planetary motion, published by Johannes Kepler in 1609 (except the third law, which was fully published in 1619), describe the orbits of planets around the Sun. These laws replaced circular orbits and epicycles in the heliocentric theory of Nicolaus Copernicus with elliptical orbits and explained how planetary velocities vary. The three laws state that: # The orbit of a planet is an ellipse with the Sun at one of the two foci. # A line segment joining a planet and the Sun sweeps out equal areas during equal intervals of time. # The square of a planet's orbital period is proportional to the cube of the length of the semi-major axis of its orbit. The elliptical orbits of planets were indicated by calculations of the orbit of Mars. From this, Kepler inferred that other bodies in the Solar System, including those farther away from the Sun, also have elliptical orbits. The second law establishes that when a planet is closer to the Sun, it travels fa ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hugh Hamilton (bishop)
Hugh Hamilton (26 March 1729 – 1 December 1805) was a mathematician, natural philosopher (scientist) and professor at Trinity College Dublin, and later a Church of Ireland bishop, Bishop of Clonfert and Kilmacduagh and then Bishop of Ossory. Life He was born at Knock, near Balrothery in County Dublin (now Fingal), on 26 March 1729, the eldest son of Alexander (died 1768) and Isabella Hamilton. His father was a solicitor and politician who represented the Killyleagh constituency in the Irish House of Commons from 1739 to 1759. Alexander's great-grandfather Hugh Hamilton migrated from Scotland to County Down in the early 17th century. The Scottish architect James Hamilton of Finnart was an ancestor. Isabella Hamilton was born Isabella Maxwell, the daughter of Robert Maxwell of Finnebrogue, Downpatrick. Hugh's siblings included George Hamilton, Baron of the Court of Exchequer (Ireland) and Charles, father of the wealthy Canadian lumber merchant and politician George Hamilto ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Pappus Of Alexandria
Pappus of Alexandria (; ; AD) was a Greek mathematics, Greek mathematician of late antiquity known for his ''Synagoge'' (Συναγωγή) or ''Collection'' (), and for Pappus's hexagon theorem in projective geometry. Almost nothing is known about his life except for what can be found in his own writings, many of which are lost. Pappus apparently lived in Alexandria, where he worked as a Mathematics education, mathematics teacher to higher level students, one of whom was named Hermodorus.Pierre Dedron, J. Itard (1959) ''Mathematics And Mathematicians'', Vol. 1, p. 149 (trans. Judith V. Field) (Transworld Student Library, 1974) The ''Collection'', his best-known work, is a compendium of mathematics in eight volumes, the bulk of which survives. It covers a wide range of topics that were part of the ancient mathematics curriculum, including geometry, astronomy, and mechanics. Pappus was active in a period generally considered one of stagnation in mathematical studies, where, to s ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cylinder (geometry)
A cylinder () has traditionally been a three-dimensional solid, one of the most basic of curvilinear geometric shapes. In elementary geometry, it is considered a prism with a circle as its base. A cylinder may also be defined as an infinite curvilinear surface in various modern branches of geometry and topology. The shift in the basic meaning—solid versus surface (as in a solid ball versus sphere surface)—has created some ambiguity with terminology. The two concepts may be distinguished by referring to solid cylinders and cylindrical surfaces. In the literature the unadorned term "cylinder" could refer to either of these or to an even more specialized object, the '' right circular cylinder''. Types The definitions and results in this section are taken from the 1913 text ''Plane and Solid Geometry'' by George A. Wentworth and David Eugene Smith . A ' is a surface consisting of all the points on all the lines which are parallel to a given line and which pass through ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Apex (geometry)
In geometry, an apex (: apices) is the vertex which is in some sense the "highest" of the figure to which it belongs. The term is typically used to refer to the vertex opposite from some " base". The word is derived from the Latin for 'summit, peak, tip, top, extreme end'. The term apex may be used in different contexts: * In an isosceles triangle, the apex is the vertex where the two sides of equal length meet, opposite the unequal third side. * In a pyramid or cone In geometry, a cone is a three-dimensional figure that tapers smoothly from a flat base (typically a circle) to a point not contained in the base, called the '' apex'' or '' vertex''. A cone is formed by a set of line segments, half-lines ..., the apex is the vertex at the "top" (opposite the base). In a pyramid, the vertex is the point that is part of all the lateral faces, or where all the lateral edges meet. References Parts of a triangle Polyhedra {{elementary-geometry-stub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Parabola
In mathematics, a parabola is a plane curve which is Reflection symmetry, mirror-symmetrical and is approximately U-shaped. It fits several superficially different Mathematics, mathematical descriptions, which can all be proved to define exactly the same curves. One description of a parabola involves a Point (geometry), point (the Focus (geometry), focus) and a Line (geometry), line (the Directrix (conic section), directrix). The focus does not lie on the directrix. The parabola is the locus (mathematics), locus of points in that plane that are equidistant from 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 (geometry), plane Parallel (geometry), parallel to another plane that is tangential to the conical surface. The graph of a function, graph of a quadratic function y=ax^2+bx+ c (with a\neq 0 ) is a parabola with its axis parallel to the -axis. Conversely, every ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hyperbola
In mathematics, a hyperbola is a type of smooth function, smooth plane curve, curve lying in a plane, defined by its geometric properties or by equations for which it is the solution set. A hyperbola has two pieces, called connected component (topology), connected components or branches, that are mirror images of each other and resemble two infinite bow (weapon), bows. The hyperbola is one of the three kinds of conic section, formed by the intersection of a plane (mathematics), plane and a double cone (geometry), cone. (The other conic sections are the parabola and the ellipse. A circle is a special case of an ellipse.) If the plane intersects both halves of the double cone but does not pass through the apex of the cones, then the conic is a hyperbola. Besides being a conic section, a hyperbola can arise as the locus (mathematics), locus of points whose difference of distances to two fixed focus (geometry), foci is constant, as a curve for each point of which the rays to two fix ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
