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- Curve_of_constant_width abstract "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.More generally, any compact convex planar body D has one pair of parallel supporting lines in any given direction. A supporting line is a line that has at least one point in common with the boundary of D but no points in common with the interior of D. The width of the body is defined as before. If the width of D is the same in all directions, the body is said to have constant width and its boundary is a curve of constant width; the planar body itself is called an orbiform.The width of a circle is constant: its diameter. On the other hand, the width of a square varies between the length of a side and that of a diagonal, in the ratio . Thus the question arises: if a given shape's width is constant in all directions, is it necessarily a circle? The surprising answer is that there are many non-circular shapes of constant width. A nontrivial example is the Reuleaux triangle. To construct this, take an equilateral triangle with vertices ABC and draw the arc BC on the circle centered at A, the arc CA on the circle centered at B, and the arc AB on the circle centered at C. The resulting figure is of constant width.The Reuleaux triangle lacks tangent continuity at three points, but constant-width curves can also be constructed without such discontinuities (as shown in the second illustration on the right). Curves of constant width can be generated by joining circular arcs centered on the vertices of a regular or irregular convex polygon with an odd number of sides (triangle, pentagon, heptagon, etc.).".
- Curve_of_constant_width thumbnail Rouleaux_triangle_Animation.gif?width=300.
- Curve_of_constant_width wikiPageExternalLink CurveofConstantWidth.html.
- Curve_of_constant_width wikiPageExternalLink ConstantWidth5.html.
- Curve_of_constant_width wikiPageExternalLink content_17738257.htm.
- Curve_of_constant_width wikiPageExternalLink CWStar.shtml.
- Curve_of_constant_width wikiPageExternalLink webstart.
- Curve_of_constant_width wikiPageExternalLink www.howround.com.
- Curve_of_constant_width wikiPageExternalLink CONSTANTWIDTH.PDF.
- Curve_of_constant_width wikiPageID "580238".
- Curve_of_constant_width wikiPageRevisionID "585726058".
- Curve_of_constant_width hasPhotoCollection Curve_of_constant_width.
- Curve_of_constant_width subject Category:Curves.
- Curve_of_constant_width subject Category:Euclidean_geometry.
- Curve_of_constant_width type Abstraction100002137.
- Curve_of_constant_width type Attribute100024264.
- Curve_of_constant_width type Curve113867641.
- Curve_of_constant_width type Curves.
- Curve_of_constant_width type Line113863771.
- Curve_of_constant_width type Shape100027807.
- Curve_of_constant_width comment "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.More generally, any compact convex planar body D has one pair of parallel supporting lines in any given direction.".
- Curve_of_constant_width label "Courbe de largeur constante".
- Curve_of_constant_width label "Curva ad ampiezza costante".
- Curve_of_constant_width label "Curva de ancho constante".
- Curve_of_constant_width label "Curve of constant width".
- Curve_of_constant_width label "Figura o stałej szerokości".
- Curve_of_constant_width label "Gleichdick".
- Curve_of_constant_width label "Кривая постоянной ширины".
- Curve_of_constant_width label "定宽曲线".
- Curve_of_constant_width label "定幅図形".
- Curve_of_constant_width sameAs Gleichdick.
- Curve_of_constant_width sameAs Curva_de_ancho_constante.
- Curve_of_constant_width sameAs Courbe_de_largeur_constante.
- Curve_of_constant_width sameAs Curva_ad_ampiezza_costante.
- Curve_of_constant_width sameAs 定幅図形.
- Curve_of_constant_width sameAs 정폭도형.
- Curve_of_constant_width sameAs Figura_o_stałej_szerokości.
- Curve_of_constant_width sameAs m.02s2tx.
- Curve_of_constant_width sameAs Q1192156.
- Curve_of_constant_width sameAs Q1192156.
- Curve_of_constant_width sameAs Curve_of_constant_width.
- Curve_of_constant_width wasDerivedFrom Curve_of_constant_width?oldid=585726058.
- Curve_of_constant_width depiction Rouleaux_triangle_Animation.gif.
- Curve_of_constant_width isPrimaryTopicOf Curve_of_constant_width.
