Problem Statement I
Problem
Statement II
Solution to Original
Problem
Outline of Construction
of Ambiguous Tracks
Animations
and Examples
of Ambiguous Tracks
Geometry of Tire
Tracks
Part I of Solution:
Creating an Initial
Piece of Track
Part II of Solution
Extending the Track
References
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References
M. DoCarmo, Differential Geometry of Curves and Surfaces,
Prentic Hall, (1976)
S.R. Dunbar, R.J. Bosman, and S.E.M. Nooij, The track of a
bicycle back-tire, Mathematics Magazine, 74 (2001), 273-287.
C.H. Edwards and D.E. Penney, Calculus, with analytic geometry
and early transcendentals, 5th edition, Prentice Hall, 1998,
Section 12.6 pages 759-773.
D.L. Finn, Can a bicycle create a unicycle track?, College
Mathematics Journal.
A. Gray, Modern Differential Geometry of Curves and Surfaces,
CRC Press, 1993.
H.I. Freedman and S.D. Riemenschneider, Determining the path
of the rear wheels of a bus, SIAM Review, 25 (1983),
561-567.
Konhauser,Velleman, and Wagon, Which way did the bicycle go?
... and other intriguing mathematical mysteries, MAA, 1996.
J. Oprea, Differential Geometry and its Applications, Prentice
Hall, 1997.
J. Stewart, Calculus: Concepts and Contexts, 2nd Edition,
Brooks/Cole, 2001, Section 10.3, pages 717-725.
S. Tabachnikov, Tire track geometry: variations on a theme,
preprint.
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