Sentence examples for surface of revolution from inspiring English sources
noun
A surface formed when a given curve is revolved around a given axis. If the resulting surface is a closed one, it also defines a solid of revolution.
- A sphere is a surface of revolution of a circle around an axis which runs through the center of the circle.
In a right circular cone, the directrix is a circle, and the cone is a surface of revolution.
The surface of revolution generated when an upward-opening catenary is revolved around the horizontal axis is called a catenoid.
The locus of all the points Q is a surface of revolution about the lens axis known as the equivalent refracting locus of the lens.
The catenoid was discovered in 1744 by the Swiss mathematician Leonhard Euler and it is the only minimal surface, other than the plane, that can be obtained as a surface of revolution.
Pappus stated this result, along with a similar theorem concerning the area of a surface of revolution, in his Mathematical Collection, which contained many challenging geometric ideas and would be of great interest to mathematicians in later centuries.
Similarly, as shown by Eugenio Beltrami (1835 1900), who ended his teaching career in Saccheri's old post at Pavia, the geometry defined in the plane by the hypothesis of the acute angle fits perfectly a surface of revolution of constant negative curvature now called a pseudosphere (see figure)—again, provided that its geodesics are accepted as the straight lines of the geometry.
Compared to the existing 'direct' fitting methods, the proposed method has some distinctive advantages: it provides a natural means to parameterization, enables to recover exact NURBS geometry when the COP-data represent a true surface-of-revolution, and allows an easy point-membership classification for NURBS-bounded solid objects.
In our method, we decompose surfaces of revolution into a sequence of coaxial revolute quadrics and reduce the intersection problem for two surfaces of revolution to the intersection problem for two revolute quadrics.
Although both Descartes and Fermat suggested using three coordinates to study curves and surfaces in space, three-dimensional analytic geometry developed slowly until about 1730, when the Swiss mathematicians Leonhard Euler and Jakob Hermann and the French mathematician Alexis Clairaut produced general equations for cylinders, cones, and surfaces of revolution.
Kinematic surfaces form a general class of surfaces, including surfaces of revolution, helices, spirals, and more.
It is also demonstrated that they represent all the possible meshes parallel to surfaces of revolution.
