Search results
Results from the WOW.Com Content Network
The congruence theorems side-angle-side (SAS) and side-side-side (SSS) also hold on a sphere; in addition, if two spherical triangles have an identical angle-angle-angle (AAA) sequence, they are congruent (unlike for plane triangles). [9] The plane-triangle congruence theorem angle-angle-side (AAS) does not hold for spherical triangles. [10]
Synthetic-aperture sonar (SAS) is a form of sonar in which sophisticated post-processing of sonar data is used in ways closely analogous to synthetic-aperture radar. Synthetic-aperture sonars combine a number of acoustic pings to form an image with much higher along-track resolution than conventional sonars.
Case 1: three sides given (SSS). The cosine rule may be used to give the angles A, B, and C but, to avoid ambiguities, the half angle formulae are preferred. Case 2: two sides and an included angle given (SAS). The cosine rule gives a and then we are back to Case 1. Case 3: two sides and an opposite angle given (SSA).
The hinge theorem holds in Euclidean spaces and more generally in simply connected non-positively curved space forms.. It can be also extended from plane Euclidean geometry to higher dimension Euclidean spaces (e.g., to tetrahedra and more generally to simplices), as has been done for orthocentric tetrahedra (i.e., tetrahedra in which altitudes are concurrent) [2] and more generally for ...
For example, the fact that any convergent sequence in a metric space is a Cauchy sequence is a direct consequence of the triangle inequality, because if we choose any x n and x m such that d(x n, x) < ε/2 and d(x m, x) < ε/2, where ε > 0 is given and arbitrary (as in the definition of a limit in a metric space), then by the triangle ...
Permission is granted to copy, distribute and/or modify this document under the terms of the GNU Free Documentation License, Version 1.2 or any later version published by the Free Software Foundation; with no Invariant Sections, no Front-Cover Texts, and no Back-Cover Texts.
SAS macros are pieces of code or variables that are coded once and referenced to perform repetitive tasks. [8] SAS data can be published in HTML, PDF, Excel, RTF and other formats using the Output Delivery System, which was first introduced in 2007. [9] SAS Enterprise Guide is SAS's point-and-click interface.
The centroid of a ring or a bowl, for example, lies in the object's central void. If the centroid is defined, it is a fixed point of all isometries in its symmetry group . In particular, the geometric centroid of an object lies in the intersection of all its hyperplanes of symmetry .