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For example: the involutes of a circle are parallel spirals (see diagram). And: [17] A parabola has as (two-sided) offsets rational curves of degree 6. A hyperbola or an ellipse has as (two-sided) offsets an algebraic curve of degree 8. A Bézier curve of degree n has as (two-sided) offsets algebraic curves of degree 4n − 2. In particular, a ...
Every circle on the axis that passes through the two foci of the coordinate system intersects the two circles orthogonally. A maximal collection of circles, all having centers on a given line and all pairs having the same radical axis, is known as a pencil of coaxal circles .
The radius and the azimuth are together called the polar coordinates, as they correspond to a two-dimensional polar coordinate system in the plane through the point, parallel to the reference plane. The third coordinate may be called the height or altitude (if the reference plane is considered horizontal), longitudinal position , [ 1 ] or axial ...
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.
Roundness is the measure of how closely the shape of an object approaches that of a mathematically perfect circle.Roundness applies in two dimensions, such as the cross sectional circles along a cylindrical object such as a shaft or a cylindrical roller for a bearing.
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 ...
The cycloid through the origin, generated by a circle of radius r rolling over the x-axis on the positive side (y ≥ 0), consists of the points (x, y), with = () = (), where t is a real parameter corresponding to the angle through which the rolling circle has rotated.
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.