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The most general
planar transformations that map parabolas into parabolas
Michael Bolt, Timothy Ferdinands and Landon Kavlie
Vol. 2 (2009), No. 1, 79–88
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Abstract |
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Consider the space of vertical parabolas in the plane interpreted generally to include nonvertical lines. It is proved that an injective map from a closed region bounded by one such parabola into the plane that maps vertical parabolas to other vertical parabolas must be the composition of a Laguerre transformation with a nonisotropic dilation. Here, a Laguerre transformation refers to a linear fractional or antilinear fractional transformation of the underlying dual plane. |
Keywords
dual number, Laguerre transformation, parabola
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Mathematical Subject Classification 2000
Primary: 51B15
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Milestones
Received: 5 September 2008
Accepted: 11 February 2009
Published: 18 March 2009
Communicated by Michael Dorff
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Authors |
| Michael Bolt | |
| Department of Mathematics and
Statistics Calvin College 1740 Knollcrest Circle SE Grand Rapids, Michigan 49546-4403 United States |
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| http://www.calvin.edu/~mdb7/ | |
| Timothy Ferdinands | |
| Department of Mathematics and
Statistics Calvin College 1740 Knollcrest Circle SE Grand Rapids, Michigan 49546-4403 United States |
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| Landon Kavlie | |
| Department of Mathematics and
Statistics 1740 Knollcrest Circle SE Calvin College Grand Rapids, Michigan 49546-4403 United States |
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