Geometric transformation

A geometric transformation is any bijection of a set having some geometric structure to itself or another such set. Specifically, "A geometric transformation is a function whose domain and range are sets of points. Most often the domain and range of a geometric transformation are both R2 or both R3. Often geometric transformations are required to be 1-1 functions, so that they have inverses." [1] The study of geometry may be approached via the study of these transformations.[2]

Geometric transformations can be classified by the dimension of their operand sets (thus distinguishing between planar transformations and those of space, for example). They can also be classified according to the properties they preserve:

Each of these classes contains the previous one.[4]

Transformations of the same type form groups that may be sub-groups of other transformation groups.

See also


  1. Zalman Usiskin, Anthony L. Peressini, Elena Marchisotto – Mathematics for High School Teachers: An Advanced Perspective, page 84.
  2. Venema, Gerard A. (2006), Foundations of Geometry, Pearson Prentice Hall, p. 285, ISBN 9780131437005
  3. 1 2 Geometric transformation, p. 131, at Google Books
  4. 1 2 Leland Wilkinson, D. Wills, D. Rope, A. Norton, R. Dubbs – Geometric transformation, p. 182, at Google Books
  5. stevecheng (2013-03-13). "first fundamental form" (PDF). Retrieved 2014-10-01.
  6. Geometric transformation, p. 191, at Google Books Bruce E. Meserve – Fundamental Concepts of Geometry, page 191.]

Further reading

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