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单词 Curve of constant breadth
释义

Curve of constant breadth

中文百科

定宽曲线 Curve of constant width

(重定向自Curve of constant breadth)

定宽曲线英语:Curve of constant width),或称恒宽曲线,定义:平面上一凸形封闭曲线,不论如何转动,其宽度永远不变,则称之定宽曲线或恒宽曲线。这里所称的“宽度”是指平行线“夹住”某封闭曲线时,平行线间的距离,所谓"夹住"是指每个平行线与凸形封闭曲线相交至少一点且与凸形封闭曲线围起来的内部区域(interior)不相交。

或者可以说,将一个闭合曲线放在两条平行线中间,使之与这两平行线相切,则可以做到:无论这个闭合曲线如何运动,只要它仍与原平行线中的一条直线相切,就必与另一条直线线相切,那幺此闭合曲线为定宽曲线。

英语百科

Curve of constant width 定宽曲线

(重定向自Curve of constant breadth)
A Reuleaux triangle is a curve of constant width. The sides of the square are supporting lines: each touches the curve but does not intersect the interior. The Reuleaux triangle can be rotated whilst always touching each side of the square in a single point; this demonstrates that its width (separation between parallel supporting lines) is constant in all directions.
Construction diagram for generating a curve of constant width from a triangle
Rollers
A Δ-curve rotating in an equilateral triangle

In geometry, a curve of constant width is a convex planar shape whose width (defined as the perpendicular distance between two distinct parallel lines each having at least one point in common with the shape's boundary but none with the shape's interior) is the same regardless of the orientation of the curve.

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更新时间:2025/6/17 22:41:44