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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.
Diagram of the HOMO and LUMO of a molecule. Each circle represents an electron in an orbital; when light of a high enough frequency is absorbed by an electron in the HOMO, it jumps to the LUMO. 3D model of the highest occupied molecular orbital in CO 2 3D model of the lowest unoccupied molecular orbital in CO 2
Princeton shape-based 3D model search engine; Keenan's 3D Model Repository hosted by the Carnegie Mellon University; HeiCuBeDa Hilprecht – Heidelberg Cuneiform Benchmark Dataset for the Hilprecht Collection a collection of almost 2.000 cuneiform tablets for bulk-download acquired with a high-resolution 3D-scanner.
Textbooks on complex functions often mention two common models of hyperbolic geometry: the Poincaré half-plane model where the absolute is the real line on the complex plane, and the Poincaré disk model where the absolute is the unit circle in the complex plane. Hyperbolic motions can also be described on the hyperboloid model of hyperbolic ...
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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