“stereographic projection”的概念、定义、习题解题方法及翻译-数学辞典

单词

stereographic projection

释义

stereographic projection

Suppose that a sphere, centre O, touches a plane at the point S, and let N be the opposite end of the diameter through S. If P is any point (except N) on the sphere, the line NP meets the plane in a corresponding point P′. Conversely, each point in the plane determines a point on the sphere, so there is a one-to-one correspondence between the points of the sphere (except N) and the points of the plane. This means of mapping sphere to plane is called stereographic projection. Circles not through N on the sphere's surface are mapped to circles in the plane; circles through N are mapped to straight lines. The mapping is conformal; that is, angles at which curves intersect are preserved by the projection.

Points near N are mapped to points with large modulus, and so it is natural to associate N with infinity in the extended complex plane. In this way we identify the extended complex plane with the Riemann sphere.

Stereographic projection

http://www.math.union.edu/~dpvc/math/4D/stereo-projection/welcome.html

• A full description of stereographic projection with two videos to illustrate how it looks.

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