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A secant plane is a plane containing a nontrivial
Tangents and Secants in Map Projections
Planes (geometry)
A secant plane is a plane containing a nontrivial section
Section, Sectioning, or Sectioned may refer to:
Arts, entertainment and media
* Section (music), a complete, but not independent, musical idea
* Section (typography), a subdivision, especially of a chapter, in books and documents
** Section sig ...
of a sphere
A sphere (from Ancient Greek, Greek , ) is a surface (mathematics), surface analogous to the circle, a curve. In solid geometry, a sphere is the Locus (mathematics), set of points that are all at the same distance from a given point in three ...
or an ellipsoid
An ellipsoid is a surface that can be obtained from a sphere by deforming it by means of directional Scaling (geometry), scalings, or more generally, of an affine transformation.
An ellipsoid is a quadric surface; that is, a Surface (mathemat ...
, or such a plane that a sphere is projected onto. Secant planes are similar to tangent planes, which contact the sphere's surface at a point, while secant planes contact the surface along curves.
The two-dimensional representations of secant planes are secant line
In geometry, a secant is a line (geometry), line that intersects a curve at a minimum of two distinct Point (geometry), points..
The word ''secant'' comes from the Latin word ''secare'', meaning ''to cut''. In the case of a circle, a secant inter ...
s, the lines that join two distinct points on a curve.
Applications
Secant planes are used inmap projection
In cartography, a map projection is any of a broad set of Transformation (function) , transformations employed to represent the curved two-dimensional Surface (mathematics), surface of a globe on a Plane (mathematics), plane. In a map projection, ...
s. The secant plane intersects a globe along a small circle with no distortion, forming a standard parallel which has true scale.
See also
*Circular section
In geometry, a circular section is a circle on a quadric surface (such as an ellipsoid or hyperboloid). It is a special plane (geometry), plane section of the quadric, as this circle is the intersection with the quadric of the plane containing the ...
* Circular segment
In geometry, a circular segment or disk segment (symbol: ) is a region of a disk which is "cut off" from the rest of the disk by a straight line. The complete line is known as a '' secant'', and the section inside the disk as a '' chord''.
More ...
* Spherical cap
In geometry, a spherical cap or spherical dome is a portion of a sphere or of a ball (mathematics), ball cut off by a plane (mathematics), plane. It is also a spherical segment of one base, i.e., bounded by a single plane. If the plane passes thr ...
* Tangent space
In mathematics, the tangent space of a manifold is a generalization of to curves in two-dimensional space and to surfaces in three-dimensional space in higher dimensions. In the context of physics the tangent space to a manifold at a point can be ...
References
{{ReflistExternal links
Tangents and Secants in Map Projections
Planes (geometry)