Hostname: page-component-586b7cd67f-l7hp2 Total loading time: 0 Render date: 2024-11-24T02:34:10.734Z Has data issue: false hasContentIssue false
  • English
  • Français

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, NY14623, USA e-mail: [email protected]
David L. Farnsworth
Affiliation:
School of Mathematical Sciences, 84 Lomb Memorial Drive, Rochester Institute of Technology, Rochester, NY14623, USA e-mail: [email protected]
Get access Rights & Permissions [Opens in a new window]

Extract

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.

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Bix, R. , Conics and cubics: A concrete introduction to algebraic curves (2nd edn.), Springer (2006).Google Scholar
Spain, B., Analytical conics, Dover (2007).Google Scholar
Akopyan, A. V and Zaslavsky, A. A., Geometry of conics, American Mathematical Society (2007).CrossRefGoogle Scholar
Zwillinger, D., editor, CRC standard mathematical tables and formulas (33rd edn.), CRC Press (2018).Google Scholar
Boyer, C. B., History of analytic geometry, Dover (2017).Google Scholar
Coolidge, J. L. , A history of the conic sections and quadratic surfaces, Dover (1968). Google Scholar
Askwith, E. H., The analytical geometry of the conic sections (2nd edn.), Sagwan Press (2015).Google Scholar
Salmon, G., A treatise on conic sections (6th edn.), Chelsea (1954).Google Scholar
Robinson, H. N., Conic sections and analytical geometry: Theoretically and practically illustrated, Ivison, Phinney & Company (1863), digitised photocopy by Bibliobazaar (2019).Google Scholar
Coffin, J. H. , Elements of conic sections and analytical geometry, Palala Press (2016). Google Scholar
Downs, J. W. , Practical conic sections: The geometric properties of ellipses, parabolas and hyperbolas, Dover (2003). Google Scholar
http://www.practicalstudent.com/subjects/tg/planefigures/parconrec.shtml Google Scholar
https://www.youtube.com/watch?v=_pDL1xz5SUo Google Scholar
https://www.youtube.com/watch?v=C5otn6WOGyk Google Scholar
https://www.youtube.com/watch?v=V4tkuTc_UNg Google Scholar
Glaeser, G., Stachel, H., and Odehnal, B. , The universe of conics: From the ancient Greeks to 21st century developments, Springer (2016). CrossRefGoogle Scholar