enow.com Web Search

Search results

  1. Results from the WOW.Com Content Network
  2. Surface of constant width - Wikipedia

    en.wikipedia.org/wiki/Surface_of_constant_width

    A sphere, a surface of constant radius and thus diameter, is a surface of constant width. Contrary to common belief the Reuleaux tetrahedron is not a surface of constant width. However, there are two different ways of smoothing subsets of the edges of the Reuleaux tetrahedron to form Meissner tetrahedra, surfaces of constant

  3. Reuleaux triangle - Wikipedia

    en.wikipedia.org/wiki/Reuleaux_triangle

    The first mathematician to discover the existence of curves of constant width, and to observe that the Reuleaux triangle has constant width, may have been Leonhard Euler. [5] In a paper that he presented in 1771 and published in 1781 entitled De curvis triangularibus , Euler studied curvilinear triangles as well as the curves of constant width ...

  4. Curve of constant width - Wikipedia

    en.wikipedia.org/wiki/Curve_of_constant_width

    In geometry, a curve of constant width is a simple closed curve in the plane whose width (the distance between parallel supporting lines) is the same in all directions. The shape bounded by a curve of constant width is a body of constant width or an orbiform, the name given to these shapes by Leonhard Euler. [1]

  5. Girth (geometry) - Wikipedia

    en.wikipedia.org/wiki/Girth_(geometry)

    All curves of constant width have the same perimeter, the same value πw as the circumference of a circle with that width (this is Barbier's theorem). Therefore, every surface of constant width is also a surface of constant girth: its girth in all directions is the same number πw. Hermann Minkowski proved, conversely, that every convex surface ...

  6. Barbier's theorem - Wikipedia

    en.wikipedia.org/wiki/Barbier's_theorem

    In particular, the unit sphere has surface area , while the surface of revolution of a Reuleaux triangle with the same constant width has surface area . [ 5 ] Instead, Barbier's theorem generalizes to bodies of constant brightness , three-dimensional convex sets for which every two-dimensional projection has the same area.

  7. Category:Constant width - Wikipedia

    en.wikipedia.org/wiki/Category:Constant_width

    Surface of constant width; This page was last edited on 9 November 2020, at 07:49 (UTC). Text is available under the Creative Commons Attribution ...

  8. Talk:Reuleaux triangle - Wikipedia

    en.wikipedia.org/wiki/Talk:Reuleaux_triangle

    Barbier's theorem says that for curves of constant width, perimeter is uniquely determined by width. Consequently, the isoperimetric inequality (the circle encloses the most area for a curve of given perimeter) says that the circle encloses the most area of any curve of given constant width. Dan Gardner 23:15, 6 Apr 2004 (UTC) Most area - of ...

  9. Differential geometry of surfaces - Wikipedia

    en.wikipedia.org/wiki/Differential_geometry_of...

    If a surface has constant Gaussian curvature, it is called a surface of constant curvature. [52] The unit sphere in E 3 has constant Gaussian curvature +1. The Euclidean plane and the cylinder both have constant Gaussian curvature 0. A unit pseudosphere has constant Gaussian curvature -1 (apart from its equator, that is singular).