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Radius of curvature and center of curvature. In differential geometry, the radius of curvature, R, is the reciprocal of the curvature. For a curve, it equals the radius of the circular arc which best approximates the curve at that point. For surfaces, the radius of curvature is the radius of a circle that best fits a normal section or ...
CATIA (/ k ə ˈ t iː ə /, an acronym of computer-aided three-dimensional interactive application) is a multi-platform software suite for computer-aided design (CAD), computer-aided manufacturing (CAM), computer-aided engineering (CAE), 3D modeling and product lifecycle management (PLM), developed by the French company Dassault Systèmes.
In physics, circular motion is movement of an object along the circumference of a circle or rotation along a circular arc. It can be uniform, with a constant rate of rotation and constant tangential speed, or non-uniform with a changing rate of rotation. The rotation around a fixed axis of a three-dimensional body involves the circular motion ...
For curves embedded in 3D surfaces the offset may be taken along a geodesic. [25] Another way to generalize it is (even in 2D) to consider a variable distance, e.g. parametrized by another curve. [22] One can for example stroke (envelope) with an ellipse instead of circle [22] as it is possible for example in METAFONT. [26]
If the radii are equal, the radical axis is the line segment bisector of M 1, M 2. In any case the radical axis is a line perpendicular to ¯. On notations. The notation radical axis was used by the French mathematician M. Chasles as axe radical. [1] J.V. Poncelet used chorde ideale. [2]
Proposition one states: The area of any circle is equal to a right-angled triangle in which one of the sides about the right angle is equal to the radius, and the other to the circumference of the circle. Any circle with a circumference c and a radius r is equal in area with a right triangle with the two legs being c and r.
In the following equations, denotes the sagitta (the depth or height of the arc), equals the radius of the circle, and the length of the chord spanning the base of the arc. As 1 2 l {\displaystyle {\tfrac {1}{2}}l} and r − s {\displaystyle r-s} are two sides of a right triangle with r {\displaystyle r} as the hypotenuse , the Pythagorean ...
[1] [4] That is, if a given munitions design has a CEP of 100 m, when 100 munitions are targeted at the same point, an average of 50 will fall within a circle with a radius of 100 m about that point. There are associated concepts, such as the DRMS (distance root mean square), which is the square root of the average squared distance error, a ...