Space curves that point almost everywhere
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- by J. B. Wilker PDF
- Trans. Amer. Math. Soc. 250 (1979), 263-274 Request permission
Abstract:
We construct a simple, closed, continuously differentiable curve $r: [0, 1] \to {E^d} (d \geqslant 3)$ whose tangent vector never points twice in the same direction of ${S^{d - 1}}$ yet sweeps out a set of directions equal to almost all of ${S^{d - 1}}$.References
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Additional Information
- © Copyright 1979 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 250 (1979), 263-274
- MSC: Primary 53A04
- DOI: https://doi.org/10.1090/S0002-9947-1979-0530055-9
- MathSciNet review: 530055