Hostname: page-component-78c5997874-94fs2 Total loading time: 0 Render date: 2024-11-11T04:20:51.622Z Has data issue: false hasContentIssue false
  • English
  • Français

Relating constructions and properties through duality

Published online by Cambridge University Press:  15 February 2024

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 Mathematics and Statistics, 84 Lomb Memorial Drive, Rochester Institute of Technology, Rochester, NY 14623 USA e-mail: dlfsma@rit.edu
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

Our goal is to find new constructions and properties of parabolas. Our strategy is to display the steps in a known construction or property, and then to take the dual of the steps in order to create a new construction or property.

Type
Articles
Information
The Mathematical Gazette , Volume 108 , Issue 571 , March 2024 , pp. 27 - 35
Check for updates
Copyright
© The Authors, 2024 Published by Cambridge University Press on behalf of The Mathematical Association

References

Demana, F., Waits, B. K., Foley, G. D. and Kennedy, D., Precalculus: functions and graphs (5th edn.), Pearson (2000).Google Scholar
Kilner, S. J. and Farnsworth, D. L., Tangent and supporting lines, envelopes, and dual curves (2021), available at http://arxiv.org/abs/2105.11951 Google Scholar
Kilner, S. J. and Farnsworth, D. L., Pairing theorems about parabolas through duality, Math. Gaz. 105 (November 2021) pp. 385-396.CrossRefGoogle Scholar
Halmos, P. R., Finite-dimensional vector spaces (2nd edn.), Dover (2017).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
Bix, R., Conics and cubics (2nd edn.), Springer (2006).Google Scholar
Coolidge, J. L., A history of the conic sections and quadratic surfaces, Dover (1968).Google Scholar
Briggs, W., Cochran, L. and Gillett, B., Calculus: early transcendental (2nd edn.), Pearson (2014). Google Scholar