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Parabolic coordinates

Published online by Cambridge University Press:  21 June 2021

Steven J. Kilner and
David L. Farnsworth
Steven J. Kilner
Affiliation:
Department of Mathematics, 1000 East Henrietta Road, Monroe Community College, Rochester, NY 14623, USA e-mail: skilner@monroecc.edu
David L. Farnsworth
Affiliation:
School of Mathematical Sciences, 84 Lomb Memorial Drive, Rochester Institute of Technology, Rochester, NY 14623, USA e-mail: DLFSMA@rit.edu

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An important first step in understanding or solving a problem can be the selection of coordinates. Insight can be gained from finding invariants within a class of coordinate systems. For example, an important feature of rectangular coordinates is that the Euclidean distance between two points is an invariant of a change to another rectangular system by a rigid motion, which consists of translations, rotations and reflections. Indeed, the form of the distance function is an invariant. In calculus courses, students learn about polar coordinates, so that useful curves can be simply expressed and more easily studied.

Information

Type
Articles
Information
The Mathematical Gazette , Volume 105 , Issue 563 , July 2021, pp. 226 - 236
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Copyright
© Mathematical Association 2021

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