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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.
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.
A disk the size of Earth, for example, would likely crack, heat up, liquefy, and re-form into a roughly spherical shape. On a disk strong enough to maintain its shape, gravity would not pull downward with respect to the surface, but would pull toward the center of the disk, [1] contrary to what is observed on level terrain (and which would ...
A right circular hollow cylinder (or cylindrical shell) is a three-dimensional region bounded by two right circular cylinders having the same axis and two parallel annular bases perpendicular to the cylinders' common axis, as in the diagram. Let the height be h, internal radius r, and external radius R.
Its curious shape is that of a cylinder [42] with a height one-third of its diameter. The flat top forms the inhabited world. Carlo Rovelli suggests that Anaximander took the idea of the Earth's shape as a floating disk from Thales, who had imagined the Earth floating in water, the "immense ocean from which everything is born and upon which the ...
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 ¯.
It is flat in the same sense that the surface of a cylinder is flat. In 3 dimensions, one can bend a flat sheet of paper into a cylinder without stretching the paper, but this cylinder cannot be bent into a torus without stretching the paper (unless some regularity and differentiability conditions are given up, see below).
Archimedes showed that the surface area of a sphere is exactly four times the area of a flat disk of the same radius, and the volume enclosed by the sphere is exactly 2/3 of the volume of a cylinder of the same height and radius. Most basic formulas for surface area can be obtained by cutting surfaces and flattening them out (see: developable ...