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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.
For example, a circle swept along a straight axis would define a cylinder (see Figure). A rectangle swept along a straight axis would define a "brick" (see Figure). Four dimensions with contrastive values (i.e., mutually exclusive values) define the current set of geons (see Figure): Shape of cross section: round vs. straight.
The recognition-by-components theory suggests that there are fewer than 36 geons which are combined to create the objects we see in day-to-day life. [3] For example, when looking at a mug we break it down into two components – "cylinder" and "handle". This also works for more complex objects, which in turn are made up of a larger number of geons.
In mathematics, non-Euclidean geometry consists of two geometries based on axioms closely related to those that specify Euclidean geometry.As Euclidean geometry lies at the intersection of metric geometry and affine geometry, non-Euclidean geometry arises by either replacing the parallel postulate with an alternative, or relaxing the metric requirement.
Geometric objects with a well-defined axis include circles (any line through the center), spheres, cylinders, [2] conic sections, and surfaces of revolution. Concentric objects are often part of the broad category of whorled patterns, which also includes spirals (a curve which emanates from a point, moving farther away as it revolves around the ...
Hence the point space of a locally compact connected Laguerre plane is homeomorphic to the cylinder or it is a -dimensional manifold, cf. [64] A large class of -dimensional examples, called ovoidal Laguerre planes, is given by the plane sections of a cylinder in real 3-space whose base is an oval in .
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A two-dimensional representation of the Klein bottle immersed in three-dimensional space. In mathematics, the Klein bottle (/ ˈ k l aɪ n /) is an example of a non-orientable surface; that is, informally, a one-sided surface which, if traveled upon, could be followed back to the point of origin while flipping the traveler upside down.