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It is similar to a cylinder in 3-space, which is the Cartesian product of a disk with a line segment. But unlike the cylinder, both hypersurfaces (of a regular duocylinder) are congruent. Its dual is a duospindle, constructed from two circles, one in the xy-plane and the other in the zw-plane.
Relatedly, when embedded into Euclidean space, the Möbius strip has only one side. A three-dimensional object that slides one time around the surface of the strip is not mirrored, but instead returns to the same point of the strip on what appears locally to be its other side, showing that both positions are really part of a single side.
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 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.
Ehrenfest considered an ideal Born-rigid cylinder that is made to rotate. Assuming that the cylinder does not expand or contract, its radius stays the same. But measuring rods laid out along the circumference should be Lorentz-contracted to a smaller value than at rest, by the usual factor γ. This leads to the paradox that the rigid measuring ...
In geometry, a disk (also spelled disc) [1] is the region in a plane bounded by a circle. A disk is said to be closed if it contains the circle that constitutes its boundary, and open if it does not. [2] For a radius, , an open disk is usually denoted as and a closed disk is ¯.
In the classical presentation of a three-set Venn diagram as three overlapping circles, the central region (representing elements belonging to all three sets) takes the shape of a Reuleaux triangle. [3] The same three circles form one of the standard drawings of the Borromean rings, three mutually linked rings that cannot, however, be realized ...
By Euler's theorem in geometry on the distance between the circumcenter and incenter of a triangle, two concentric circles (with that distance being zero) are the circumcircle and incircle of a triangle if and only if the radius of one is twice the radius of the other, in which case the triangle is equilateral. [5]: p. 198