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Parabolic coordinates

Published online by Cambridge University Press:  21 June 2021

Steven J. Kilner
Department of Mathematics, 1000 East Henrietta Road, Monroe Community College, Rochester, NY14623, USA e-mail:
David L. Farnsworth
School of Mathematical Sciences, 84 Lomb Memorial Drive, Rochester Institute of Technology, Rochester, NY14623, USA e-mail:


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.

© Mathematical Association 2021

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