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A portion of the curve x = 2 + cos(z) rotated around the z-axis A torus as a square revolved around an axis parallel to one of its diagonals.. A surface of revolution is a surface in Euclidean space created by rotating a curve (the generatrix) one full revolution around an axis of rotation (normally not intersecting the generatrix, except at its endpoints). [1]
Rotating a curve. The surface formed is a surface of revolution; it encloses a solid of revolution. Solids of revolution (Matemateca Ime-Usp)In geometry, a solid of revolution is a solid figure obtained by rotating a plane figure around some straight line (the axis of revolution), which may not intersect the generatrix (except at its boundary).
The relation remains valid for a geodesic on an arbitrary surface of revolution. A statement of the general version of Clairaut's relation is: [1] Let γ be a geodesic on a surface of revolution S, let ρ be the distance of a point of S from the axis of rotation, and let ψ be the angle between γ and the meridian of S. Then ρ sin ψ is ...
Stretching a soap film between two parallel circular wire loops generates a catenoidal minimal surface of revolution. In mathematics, a minimal surface of revolution or minimum surface of revolution is a surface of revolution defined from two points in a half-plane, whose boundary is the axis of revolution of the surface.
The graph of a continuous function of two variables, defined over a connected open subset of R 2 is a topological surface. If the function is differentiable, the graph is a differentiable surface. A plane is both an algebraic surface and a differentiable surface. It is also a ruled surface and a surface of revolution.
In geometry, a catenoid is a type of surface, arising by rotating a catenary curve about an axis (a surface of revolution). [1] It is a minimal surface, meaning that it occupies the least area when bounded by a closed space. [2] It was formally described in 1744 by the mathematician Leonhard Euler.
The surface of revolution created by revolving a tractrix about its asymptote is a pseudosphere. The tractrix is a transcendental curve ; it cannot be defined by a polynomial equation. Practical application
Tractroid. The same surface can be also described as the result of revolving a tractrix about its asymptote.For this reason the pseudosphere is also called tractroid.As an example, the (half) pseudosphere (with radius 1) is the surface of revolution of the tractrix parametrized by [2]