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In projective geometry, a cylinder is simply a cone whose apex (vertex) lies on the plane at infinity. If the cone is a quadratic cone, the plane at infinity (which passes through the vertex) can intersect the cone at two real lines, a single real line (actually a coincident pair of lines), or only at the vertex.
Vectors. Mathematically, a four-dimensional space is a space that needs four parameters to specify a point in it. For example, a general point might have position vector a, equal to. This can be written in terms of the four standard basis vectors (e1, e2, e3, e4), given by. so the general vector a is.
A zoetrope is a pre-film animation device that produces the illusion of motion, by displaying a sequence of drawings or photographs showing progressive phases of that motion. A zoetrope is a cylindrical variant of the phénakisticope, an apparatus suggested after the stroboscopic discs were introduced in 1833.
A Möbius strip made with paper and adhesive tape. In mathematics, a Möbius strip, Möbius band, or Möbius loop[a] is a surface that can be formed by attaching the ends of a strip of paper together with a half-twist. As a mathematical object, it was discovered by Johann Benedict Listing and August Ferdinand Möbius in 1858, but it had already ...
A welded steel pressure vessel constructed as a horizontal cylinder with domed ends. An access cover can be seen at one end, and a drain valve at the bottom centre. A pressure vessel is a container designed to hold gases or liquids at a pressure substantially different from the ambient pressure. Construction methods and materials may be chosen ...
Packing problems are a class of optimization problems in mathematics that involve attempting to pack objects together into containers. The goal is to either pack a single container as densely as possible or pack all objects using as few containers as possible. Many of these problems can be related to real-life packaging, storage and ...
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 Stanford torus interior (cutaway view) Interior view of a large scale O'Neill cylinder, showing alternating land and window stripes. A space settlement (also called a space habitat, spacestead, space city or space colony) is a settlement in outer space, sustaining more extensively habitation facilities in space than a general space station or spacecraft.