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- Reuleaux_triangle abstract "A Reuleaux triangle [ʁœlo] is a shape formed from the intersection of three circular disks, each having its center on the boundary of the other two. It is a curve of constant width, the simplest and best known such curve other than the circle itself. Constant width means that the separation of every two parallel supporting lines is the same, independent of their orientation. Because all its diameters are the same, the Reuleaux triangle is one answer to the question \"Other than a circle, what shape can a manhole cover be made so that it cannot fall down through the hole?\"Reuleaux triangles have also been called spherical triangles, but that term more properly refers to triangles on the curved surface of a sphere.They are named after Franz Reuleaux, a 19th-century German engineer who pioneered the study of machines for translating one type of motion into another, and who used Reuleaux triangles in his designs. However, these shapes were known before his time, for instance by the designers of Gothic church windows, by Leonardo da Vinci, who used it for a map projection, and by Leonhard Euler in his study of constant-width shapes. Other applications of the Reuleaux triangle include giving the shape to guitar picks, pencils, and drill bits for drilling square holes, as well as in graphic design in the shapes of some signs and corporate logos.Among constant-width shapes with a given width, the Reuleaux triangle has the minimum area and the sharpest possible angle (120°) at its corners. By several numerical measures it is the farthest from being centrally symmetric. It provides the largest constant-width shape avoiding the points of an integer lattice, and is closely related to the shape of the quadrilateral maximizing the ratio of perimeter to diameter. It can perform a complete rotation within a square while at all times touching all four sides of the square, and has the smallest possible area of shapes with this property. However, although it covers most of the square in this rotation process, it fails to cover a small fraction of the square's area, near its corners. Because of this property of rotating within a square, the Reuleaux triangle is also sometimes known as the Reuleaux rotor.The Reuleaux triangle is the first of a sequence of Reuleaux polygons, curves of constant width formed from regular polygons with an odd number of sides. Some of these curves have been used as the shapes of coins. The Reuleaux triangle can also be generalized into three dimensions in multiple ways: the Reuleaux tetrahedron (the intersection of four spheres whose centers lie on a regular tetrahedron) does not have constant width, but can be modified by rounding its edges to form the Meissner tetrahedron, which does. Alternatively, the surface of revolution of the Reuleaux triangle also has constant width.".
- Reuleaux_triangle thumbnail ReuleauxTriangle.svg?width=300.
- Reuleaux_triangle wikiPageExternalLink cwidth.shtml.
- Reuleaux_triangle wikiPageID "580252".
- Reuleaux_triangle wikiPageLength "53234".
- Reuleaux_triangle wikiPageOutDegree "150".
- Reuleaux_triangle wikiPageRevisionID "697934794".
- Reuleaux_triangle wikiPageWikiLink Arbelos.
- Reuleaux_triangle wikiPageWikiLink Artificial_neural_network.
- Reuleaux_triangle wikiPageWikiLink Barbiers_theorem.
- Reuleaux_triangle wikiPageWikiLink Bavaria_Brewery_(Netherlands).
- Reuleaux_triangle wikiPageWikiLink Bismuth(III)_nitrate.
- Reuleaux_triangle wikiPageWikiLink Blaschke–Lebesgue_theorem.
- Reuleaux_triangle wikiPageWikiLink Borromean_rings.
- Reuleaux_triangle wikiPageWikiLink Brady_Haran.
- Reuleaux_triangle wikiPageWikiLink Bézier_triangle.
- Reuleaux_triangle wikiPageWikiLink Cam.
- Reuleaux_triangle wikiPageWikiLink Canada.
- Reuleaux_triangle wikiPageWikiLink Category:Curves.
- Reuleaux_triangle wikiPageWikiLink Category:Polygons.
- Reuleaux_triangle wikiPageWikiLink Category:Triangles.
- Reuleaux_triangle wikiPageWikiLink Circle.
- Reuleaux_triangle wikiPageWikiLink Circular_triangle.
- Reuleaux_triangle wikiPageWikiLink Circumscribed_circle.
- Reuleaux_triangle wikiPageWikiLink Cologne.
- Reuleaux_triangle wikiPageWikiLink Colorado_School_of_Mines.
- Reuleaux_triangle wikiPageWikiLink Compass.
- Reuleaux_triangle wikiPageWikiLink Compass-and-straightedge_construction.
- Reuleaux_triangle wikiPageWikiLink Compass_(drawing_tool).
- Reuleaux_triangle wikiPageWikiLink Conformal_map.
- Reuleaux_triangle wikiPageWikiLink Convex_hull.
- Reuleaux_triangle wikiPageWikiLink Cornell_University.
- Reuleaux_triangle wikiPageWikiLink Cross_section_(geometry).
- Reuleaux_triangle wikiPageWikiLink Curve.
- Reuleaux_triangle wikiPageWikiLink Curve_of_constant_width.
- Reuleaux_triangle wikiPageWikiLink Cut-the-Knot.
- Reuleaux_triangle wikiPageWikiLink Deltoid_curve.
- Reuleaux_triangle wikiPageWikiLink Diameter.
- Reuleaux_triangle wikiPageWikiLink Dihedral_group.
- Reuleaux_triangle wikiPageWikiLink Disk_(mathematics).
- Reuleaux_triangle wikiPageWikiLink Double_lattice.
- Reuleaux_triangle wikiPageWikiLink Drill_bit.
- Reuleaux_triangle wikiPageWikiLink Ellipse.
- Reuleaux_triangle wikiPageWikiLink English_Gothic_architecture.
- Reuleaux_triangle wikiPageWikiLink Equidiagonal_quadrilateral.
- Reuleaux_triangle wikiPageWikiLink Equilateral_triangle.
- Reuleaux_triangle wikiPageWikiLink Euclidean_distance.
- Reuleaux_triangle wikiPageWikiLink Fifty_pence_(British_coin).
- Reuleaux_triangle wikiPageWikiLink File:Leonardo_da_Vinci’s_Mappamundi.jpg.
- Reuleaux_triangle wikiPageWikiLink Fourier_transform.
- Reuleaux_triangle wikiPageWikiLink Franz_Reuleaux.
- Reuleaux_triangle wikiPageWikiLink Germany.
- Reuleaux_triangle wikiPageWikiLink Gothic_architecture.
- Reuleaux_triangle wikiPageWikiLink Guitar_pick.
- Reuleaux_triangle wikiPageWikiLink Hawaii.
- Reuleaux_triangle wikiPageWikiLink Hexagon.
- Reuleaux_triangle wikiPageWikiLink Hydrolysis.
- Reuleaux_triangle wikiPageWikiLink Incircle_and_excircles_of_a_triangle.
- Reuleaux_triangle wikiPageWikiLink Inscribed_square_problem.
- Reuleaux_triangle wikiPageWikiLink Integer_lattice.
- Reuleaux_triangle wikiPageWikiLink John_Dee.
- Reuleaux_triangle wikiPageWikiLink Kite_(geometry).
- Reuleaux_triangle wikiPageWikiLink Kölntriangle.
- Reuleaux_triangle wikiPageWikiLink Leonardo_da_Vinci.
- Reuleaux_triangle wikiPageWikiLink Leonhard_Euler.
- Reuleaux_triangle wikiPageWikiLink Linkage_(mechanical).
- Reuleaux_triangle wikiPageWikiLink Loonie.
- Reuleaux_triangle wikiPageWikiLink Manhole_cover.
- Reuleaux_triangle wikiPageWikiLink Map_projection.
- Reuleaux_triangle wikiPageWikiLink Mauna_Kea.
- Reuleaux_triangle wikiPageWikiLink Midpoint.
- Reuleaux_triangle wikiPageWikiLink Mohr–Mascheroni_theorem.
- Reuleaux_triangle wikiPageWikiLink Movie_projector.
- Reuleaux_triangle wikiPageWikiLink Oronce_Finé.
- Reuleaux_triangle wikiPageWikiLink Packing_density.
- Reuleaux_triangle wikiPageWikiLink Panasonic.
- Reuleaux_triangle wikiPageWikiLink Pencil.
- Reuleaux_triangle wikiPageWikiLink Pendentive.
- Reuleaux_triangle wikiPageWikiLink Perimeter.
- Reuleaux_triangle wikiPageWikiLink Petrofina.
- Reuleaux_triangle wikiPageWikiLink Plateaus_laws.
- Reuleaux_triangle wikiPageWikiLink Point_reflection.
- Reuleaux_triangle wikiPageWikiLink Poul_Anderson.
- Reuleaux_triangle wikiPageWikiLink Precipitation.
- Reuleaux_triangle wikiPageWikiLink Quadrilateral.
- Reuleaux_triangle wikiPageWikiLink Reciprocating_motion.
- Reuleaux_triangle wikiPageWikiLink Regular_polygon.
- Reuleaux_triangle wikiPageWikiLink Reuleaux_tetrahedron.
- Reuleaux_triangle wikiPageWikiLink Robotic_vacuum_cleaner.
- Reuleaux_triangle wikiPageWikiLink Rotation_around_a_fixed_axis.
- Reuleaux_triangle wikiPageWikiLink Schwarz_triangle.
- Reuleaux_triangle wikiPageWikiLink Semicircle.
- Reuleaux_triangle wikiPageWikiLink Simple_polygon.
- Reuleaux_triangle wikiPageWikiLink Soap_bubble.
- Reuleaux_triangle wikiPageWikiLink Space_Shuttle_Challenger_disaster.
- Reuleaux_triangle wikiPageWikiLink Sphere.
- Reuleaux_triangle wikiPageWikiLink Spherical_trigonometry.
- Reuleaux_triangle wikiPageWikiLink Square.
- Reuleaux_triangle wikiPageWikiLink Steam_engine.
- Reuleaux_triangle wikiPageWikiLink Submillimeter_Array.