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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 ...
In geometry, the napkin-ring problem involves finding the volume of a "band" of specified height around a sphere, i.e. the part that remains after a hole in the shape of a circular cylinder is drilled through the center of the sphere. It is a counterintuitive fact that this volume does not depend on the original sphere's radius but only on the ...
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 ...
Recreational mathematics planar boundary and area problem. The goat grazing problem is either of two related problems in recreational mathematics involving a tethered goat grazing a circular area: the interior grazing problem and the exterior grazing problem. The former involves grazing the interior of a circular area, and the latter, grazing ...
Line-cylinder intersection is the calculation of any points of intersection, given an analytic geometry description of a line and a cylinder in 3d space. An arbitrary line and cylinder may have no intersection at all. Or there may be one or two points of intersection. [1] Or a line may lie along the surface of a cylinder, parallel to its axis ...
e. In the mathematical field of geometric topology, the Poincaré conjecture (UK: / ˈpwæ̃kæreɪ /, [2] US: / ˌpwæ̃kɑːˈreɪ /, [3][4] French: [pwɛ̃kaʁe]) is a theorem about the characterization of the 3-sphere, which is the hypersphere that bounds the unit ball in four-dimensional space. Originally conjectured by Henri Poincaré in ...