| 单词 | Curve of Constant Width |
| 释义 | Curve of Constant WidthCurves which, when rotated in a square, make contact with all four sides. The ``width'' of a closed convex curve isdefined as the distance between parallel lines bounding it (``supporting lines''). Every curve of constant width isconvex. Curves of constant width have the same ``width'' regardless of their orientation between the parallel lines. Infact, they also share the same Perimeter (Barbier's Theorem). Examples include the Circle (withlargest Area), and Reuleaux Triangle (with smallest Area) but there are an infinite number. A curve of constantwidth can be used in a special drill chuck to cut square ``Holes.'' A generalization gives solids of constant width. These do not have the same surface Area for a given width, but theirshadows are curves of constant width with the same width! See also Delta Curve, Kakeya Needle Problem, Reuleaux Triangle
Bogomolny, A. ``Shapes of Constant Width.'' http://www.cut-the-knot.com/do_you_know/cwidth.html. Böhm, J. ``Convex Bodies of Constant Width.'' Ch. 4 in Mathematical Models from the Collections of Universities and Museums (Ed. G. Fischer). Braunschweig, Germany: Vieweg, pp. 96-100, 1986. Fischer, G. (Ed.). Plates 98-102 in Mathematische Modelle/Mathematical Models, Bildband/Photograph Volume. Braunschweig, Germany: Vieweg, pp. 89 and 96, 1986. Gardner, M. Ch. 18 in The Unexpected Hanging and Other Mathematical Diversions. Chicago, IL: Chicago University Press, 1991. Goldberg, M. ``Circular-Arc Rotors in Regular Polygons.'' Amer. Math. Monthly 55, 393-402, 1948. Kelly, P. Convex Figures. New York: Harcourt Brace, 1995. Rademacher, H. and Toeplitz, O. The Enjoyment of Mathematics: Selections from Mathematics for the Amateur. Princeton, NJ: Princeton University Press, 1957. Yaglom, I. M. and Boltyanski, V. G. Convex Figures. New York: Holt, Rinehart, and Winston, 1961. |
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