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PR is the diameter of a circle centered on O; its radius AO is the arithmetic mean of a and b. Using the geometric mean theorem, triangle PGR's altitude GQ is the geometric mean. For any ratio a:b, AO ≥ GQ. A semicircle can be used to construct the arithmetic and geometric means of two lengths using straight-edge and compass.
The following is a list of centroids of various two-dimensional and three-dimensional objects. The centroid of an object in -dimensional space is the intersection of all hyperplanes that divide into two parts of equal moment about the hyperplane.
Sphericon animation STL model of a sphericon Animation of a rolling sphericon. In solid geometry, the sphericon is a solid that has a continuous developable surface with two congruent, semi-circular edges, and four vertices that define a square.
The 3D ACIS Modeler (ACIS) is a geometric modeling kernel developed by Spatial Corporation (formerly Spatial Technology), part of Dassault Systèmes.ACIS is used by many software developers in industries such as computer-aided design (CAD), computer-aided manufacturing (CAM), computer-aided engineering (CAE), architecture, engineering and construction (AEC), coordinate-measuring machine (CMM ...
The metric of the model on the half-plane, { , >}, is: = + ()where s measures the length along a (possibly curved) line. The straight lines in the hyperbolic plane (geodesics for this metric tensor, i.e., curves which minimize the distance) are represented in this model by circular arcs perpendicular to the x-axis (half-circles whose centers are on the x-axis) and straight vertical rays ...
The geometry in solid modeling is fully described in 3‑D space; objects can be viewed from any angle. Solid modeling (or solid modelling) is a consistent set of principles for mathematical and computer modeling of three-dimensional shapes .
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The prolate spheroid is generated by rotation about the z-axis of an ellipse with semi-major axis c and semi-minor axis a; therefore, e may again be identified as the eccentricity. (See ellipse.) [4] These formulas are identical in the sense that the formula for S oblate can be used to calculate the surface area of a prolate spheroid and vice ...
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