Curve of constant width: Difference between revisions

Revision as of 21:06, 12 January 2021

Revision as of 22:12, 12 January 2021

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==Generalizations==

One way to generalize these concepts to three dimensions is through the [[surface of constant width|surfaces of constant width]]. The three-dimensional analog of a Reuleaux triangle, the [[Reuleaux tetrahedron]], does not have constant width, but minor modificationschanges ofto it, produce the [[Meissner bodies]], which do.{{r|gardner|mmo}} A different class of three-dimensional generalizations, the [[space curve]]s of constant width, are defined by the properties that each plane that crosses the curve perpendicularly intersects it at exactly one other point, where it is also perpendicular, and that all pairs of points intersected by perpendicular planes are the same distance apart.{{r|fujiwara|cieslak|teufel|wegner72}}

Curves and bodies of constant width have also been studied in [[non-Euclidean geometry]]{{r|leichtweiss}} and for non-Euclidean [[normed vector space]]s.{{r|eggleston}}