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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.
In three dimensions, ... People determine the minimum height h of a cylinder with given radius R that will pack n identical spheres of radius r ... For example, it is ...
MapReduce is a programming model and an associated implementation for processing and generating big data sets with a parallel and distributed algorithm on a cluster. [1] [2] [3]A MapReduce program is composed of a map procedure, which performs filtering and sorting (such as sorting students by first name into queues, one queue for each name), and a reduce method, which performs a summary ...
A solid figure is the region of 3D space bounded by a two-dimensional closed surface; for example, a solid ball consists of a sphere and its interior. Solid geometry deals with the measurements of volumes of various solids, including pyramids , prisms (and other polyhedrons ), cubes , cylinders , cones (and truncated cones ).
The generation of a bicylinder Calculating the volume of a bicylinder. A bicylinder generated by two cylinders with radius r has the volume =, and the surface area [1] [6] =.. The upper half of a bicylinder is the square case of a domical vault, a dome-shaped solid based on any convex polygon whose cross-sections are similar copies of the polygon, and analogous formulas calculating the volume ...
A 3D torus prim created in Second Life, an example of a parametric shape. A Parametric shape is a standardized two-dimensional or three-dimensional shape defined by a minimal set of parameters, such as an ellipse defined by two points at its foci, or three points at its center, vertex, and co-vertex.
In three dimensions the Böröczky bound is approximately 85.327613%, and is realized by the horosphere packing of the order-6 tetrahedral honeycomb with Schläfli symbol {3,3,6}. [30] In addition to this configuration at least three other horosphere packings are known to exist in hyperbolic 3-space that realize the density upper bound.
An example is a right circular cone. Circular symmetry in 3 dimensions has all pyramidal symmetry , C n v as subgroups. A double-cone , bicone , cylinder , toroid and spheroid have circular symmetry, and in addition have a bilateral symmetry perpendicular to the axis of system (or half cylindrical symmetry ).