In mathematics, a conformal map is a function which preserves angles. In the most common case the function is between domains in the complex plane.
More formally, a map,
is called conformal (or angle-preserving) at u0 if it preserves oriented angles between curves through with respect to their orientation (i.e., not just the acute angle). Conformal maps preserve both angles and the shapes of infinitesimally small figures, but not necessarily their size.
The conformal property may be described in terms of the Jacobian derivative matrix of a coordinate transformation. If the Jacobian matrix of the transformation is everywhere a scalar times a rotation matrix, then the transformation is conformal.
Conformal maps can be defined between domains in higher dimensional Euclidean spaces, and more generally on a Riemannian or semi-Riemannian manifold.
Read more about Conformal Map: Complex Analysis, Riemannian Geometry, Higher-dimensional Euclidean Space, Uses, Alternative Angles
Famous quotes containing the word map:
“When I had mapped the pond ... I laid a rule on the map lengthwise, and then breadthwise, and found, to my surprise, that the line of greatest length intersected the line of greatest breadth exactly at the point of greatest depth.”
—Henry David Thoreau (1817–1862)