Vol. 8, No. 3, 2015

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Two-parameter taxicab trigonometric functions

Kelly Delp and Michael Filipski

Vol. 8 (2015), No. 3, 467–480

In this paper, we review some of the fundamental properties of the 1, or taxicab, metric on 2. We define and give explicit formulas for two-parameter sine and cosine functions for this metric space. We also determine the maximum of these functions, which is greater than 1.

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taxicab trigonometry, Minkowski geometry
Mathematical Subject Classification 2010
Primary: 51F99, 52A21
Received: 24 June 2013
Revised: 6 November 2013
Accepted: 7 November 2013
Published: 5 June 2015

Communicated by Frank Morgan
Kelly Delp
Department of Mathematics
Ithaca College
201 Muller Center
Ithaca, NY 14850
United States
Michael Filipski
Department of Mathematics
University at Buffalo
244 Mathematics Building
Buffalo, NY 14260
United States