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A cylinder (from Ancient Greek κύλινδρος (kúlindros) 'roller, tumbler') [1] 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 right circular cylinder is a cylinder whose generatrices are perpendicular to the bases. Thus, in a right circular cylinder, the generatrix and the height have the same measurements. [ 1 ] It is also less often called a cylinder of revolution, because it can be obtained by rotating a rectangle of sides r {\displaystyle r} and g {\displaystyle ...
Steinmetz solid (intersection of two cylinders) In geometry, a Steinmetz solid is the solid body obtained as the intersection of two or three cylinders of equal radius at right angles. Each of the curves of the intersection of two cylinders is an ellipse. The intersection of two cylinders is called a bicylinder.
Line-cylinder intersection is the calculation of any points of intersection, given an analytic geometry description of a line and a cylinder in 3d space. An arbitrary line and cylinder may have no intersection at all.
For simple objects with geometric symmetry, one can often determine the moment of inertia in an exact closed-form expression. Typically this occurs when the mass density is constant, but in some cases the density can vary throughout the object as well. In general, it may not be straightforward to symbolically express the moment of inertia of ...
A two-dimensional orthographic projection at the left with a three-dimensional one at the right depicting a capsule. A capsule (from Latin capsula, "small box or chest"), or stadium of revolution, is a basic three-dimensional geometric shape consisting of a cylinder with hemispherical ends. [1]
Stereographic projection of the duocylinder's ridge (see below), as a flat torus.The ridge is rotating about the xw-plane.. The duocylinder, also called the double cylinder or the bidisc, is a geometric object embedded in 4-dimensional Euclidean space, defined as the Cartesian product of two disks of respective radii r 1 and r 2:
In differential geometry, the Gaussian curvature or Gauss curvature Κ of a smooth surface in three-dimensional space at a point is the product of the principal curvatures, κ 1 and κ 2, at the given point: =.