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A cylinder (from Greek κύλινδρος – kulindros, "roller, tumbler") has traditionally been a threedimensional solid, one of the most basic of curvilinear geometric shapes. It is the idealized version of a solid physical tin can having lids on top and bottom. This traditional view is still used in elementary treatments of geometry, but the advanced mathematical viewpoint has shifted to the infinite curvilinear surface and this is how a cylinder is now defined in various modern branches of geometry and topology. The shift in the basic meaning (solid versus surface) has created some ambiguity with terminology. It is generally hoped that context makes the meaning clear [...More Info...] [...Related Items...] 

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. 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 third description is algebraic [...More Info...] [...Related Items...] 

Cavalieri's Principle
In geometry, Cavalieri's principle, a modern implementation of the method of indivisibles, named after Bonaventura Cavalieri, is as follows: Today Cavalieri's principle is seen as an early step towards integral calculus, and while it is used in some forms, such as its generalization in Fubini's theorem, results using Cavalieri's principle can often be shown more directly via integration [...More Info...] [...Related Items...] 

Semimajor And Semiminor Axes
In geometry, the major axis of an ellipse is its longest diameter: a line segment that runs through the center and both foci, with ends at the widest points of the perimeter. The semimajor axis is one half of the major axis, and thus runs from the centre, through a focus, and to the perimeter [...More Info...] [...Related Items...] 

Cylindrical Coordinates
A cylindrical coordinate system is a threedimensional coordinate system that specifies point positions by the distance from a chosen reference axis, the direction from the axis relative to a chosen reference direction, and the distance from a chosen reference plane perpendicular to the axis. The latter distance is given as a positive or negative number depending on which side of the reference plane faces the point. The origin of the system is the point where all three coordinates can be given as zero [...More Info...] [...Related Items...] 

Diameter
In geometry, a diameter of a circle is any straight line segment that passes through the center of the circle and whose endpoints lie on the circle. It can also be defined as the longest chord of the circle. Both definitions are also valid for the diameter of a sphere. In more modern usage, the length of a diameter is also called the diameter [...More Info...] [...Related Items...] 

Annulus (mathematics)
In mathematics, an annulus (the Latin word for "little ring" is anulus/annulus, with plural anuli/annuli) is a ringshaped object, a region bounded by two concentric circles. The adjectival form is annular (as in annular eclipse). The open annulus is topologically equivalent to both the open cylinder S1> × (0,1) and the punctured plane [...More Info...] [...Related Items...] 

On The Sphere And Cylinder
On the Sphere and Cylinder (Greek: Περὶ σφαίρας καὶ κυλίνδρου) is a work that was published by Archimedes in two volumes c [...More Info...] [...Related Items...] 

Archimedes
Archimedes of Syracuse (/ˌɑːrkɪˈmiːdiːz/; Greek: Ἀρχιμήδης; c. 287 – c. 212 BC) was a Greek mathematician, physicist, engineer, inventor, and astronomer. Although few details of his life are known, he is regarded as one of the leading scientists in classical antiquity [...More Info...] [...Related Items...] 

Sphere
A sphere (from Greek σφαῖρα — sphaira, "globe, ball") is a perfectly round geometrical object in threedimensional space that is the surface of a completely round ball (viz., analogous to a circular object in two dimensions). Like a circle, which geometrically is an object in twodimensional space, a sphere is defined mathematically as the set of points that are all at the same distance r from a given point, but in threedimensional space. This distance r is the radius of the ball, and the given point is the center of the mathematical ball. These are also referred to as the radius and center of the sphere, respectively [...More Info...] [...Related Items...] 

Circumscribe
In geometry, the circumscribed circle or circumcircle of a polygon is a circle which passes through all the vertices of the polygon. The center of this circle is called the circumcenter and its radius is called the circumradius. A polygon which has a circumscribed circle is called a cyclic polygon (sometimes a concyclic polygon, because the vertices are concyclic). All regular simple polygons, all isosceles trapezoids, all triangles and all rectangles are cyclic. A related notion is the one of a minimum bounding circle, which is the smallest circle that completely contains the polygon within it [...More Info...] [...Related Items...] 

Ruled Surface
In geometry, a surface S is ruled (also called a scroll) if through every point of S there is a straight line that lies on S. Examples include the plane, the curved surface of a cylinder or cone, a conical surface with elliptical directrix, the right conoid, the helicoid, and the tangent developable of a smooth curve in space. A ruled surface can be described as the set of points swept by a moving straight line. For example, a cone is formed by keeping one point of a line fixed whilst moving another point along a circle. A surface is doubly ruled if through every one of its points there are two distinct lines that lie on the surface. The hyperbolic paraboloid and the hyperboloid of one sheet are doubly ruled surfaces [...More Info...] [...Related Items...] 

Hyperbola
In mathematics, a hyperbola (plural hyperbolas or hyperbolae) is a type of smooth 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 components or branches, that are mirror images of each other and resemble two infinite bows. The hyperbola is one of the three kinds of conic section, formed by the intersection of a plane and a double cone. (The other conic sections are the parabola and the ellipse [...More Info...] [...Related Items...] 

Semimajor Axis
In geometry, the major axis of an ellipse is its longest diameter: a line segment that runs through the center and both foci, with ends at the widest points of the perimeter. The semimajor axis is one half of the major axis, and thus runs from the centre, through a focus, and to the perimeter [...More Info...] [...Related Items...] 

Quadric Surface
In mathematics, a quadric or quadric surface (quadric hypersurface in higher dimensions), is a generalization of conic sections (ellipses, parabolas, and hyperbolas). It is a hypersurface (of dimension D) in a (D + 1)dimensional space, and it is defined as the zero set of an irreducible polynomial of degree two in D + 1 variables (D=1 in the case of conic sections) [...More Info...] [...Related Items...] 