
	Where results make sense

Topic: Reuleaux triangle

Related Topics

Equilateral curve

Reuleaux polygon

Curve of constant width

Franz Reuleaux

Regular polygon

Tiling

Manhole cover

Wankel engine

Epitrochoid

British coin Half Penny

Geometric shape

Quasiturbine

Epicycloid

Pentagon

Engine displacement

	Reuleaux triangle - Wikipedia, the free encyclopedia
		The Reuleaux triangle is a constant width curve based on an equilateral triangle.
		A Reuleaux polygon is a polygon that is a curve of constant width - that is, a curve in which all diameters are the same length.
		The Reuleaux triangle is the simplest nontrivial example of a curve of constant width - a curve in which the distance between two opposite parallel tangent lines to its boundary is the same, regardless of the direction of those two parallel lines.
	en.wikipedia.org /wiki/Reuleaux_triangle (484 words)

	Reuleaux triangle: Encyclopedia topic (Site not responding. Last check: 2007-10-21)
		A Reuleaux polygon is a polygon (polygon: A closed plane figure bounded by straight sides) that is a curve of constant width (curve of constant width: in geometry, a curve of constant width is a convex planar shape whose width,...
		The Reuleaux triangle is the simplest nontrivial example of a curve of constant width (curve of constant width: in geometry, a curve of constant width is a convex planar shape whose width,...
		Equivalently, given an equilateral triangle T of side length s, take the boundary of the intersection (intersection: A junction where one street or road crosses another) of the disks with radius (radius: The length of a line segment between the center and circumference of a circle or sphere) s centered at the vertexes of T.
	www.absoluteastronomy.com /reference/reuleaux_triangle (540 words)

	Homework Problems 12 (Site not responding. Last check: 2007-10-21)
		The area of a Reuleaux triangle is equal to the area of a circular region with the same width.
		The perimeter of a Reuleaux triangle is equal to the circumference of a circle with the same diameter.
		The area of the sector is (8\pi)/3 (i.e., 1/6 of the area of a circular region) and the area of the triangle is 4(square root of 3).
	www-math.cudenver.edu /~wcherowi/courses/m3210/hghw12.html (528 words)

	Barbier's theorem - Wikipedia, the free encyclopedia
		The most familiar examples of curves of constant width are the circle and the Reuleaux triangle.
		A Reuleaux triangle of width w consists of three arcs of circles of radius w.
		Each of these arcs has central angle π/3, so the perimeter of the Reuleaux triangle of width w is equal to ½ the perimeter of a circle of radius w and therefore is equal to πw.
	en.wikipedia.org /wiki/Barbier's_theorem (174 words)

	Reuleaux Triangle
		The ratio of the circumference to the width of the triangle is, remarkably, pi.
		The actual drill bit for the square is a Reuleaux triangle made concave in three spots to allow for unobstructed corner-cutting and the discharge of shavings.
		The Reuleaux triangle may also form the shape of the piston in a rotary, or Wankel, engine, in which gasoline burns in crescent-shaped chambers, turning a rotating piston that drives an axle through its center.
	www.daviddarling.info /encyclopedia/R/Reuleaux_Triangle.html (262 words)

	MMA Memo 214: Hybrid arrays: the design of reconfigurable aperture-synthesis interferometers
		Telescopes are considered whose basic configurations are concentric rings consisting either of circles or of Reuleaux triangles, both of which have a low ratio of the numbers of short baselines to long; moving some of the dishes to a smaller configuration then increases the ratio by providing additional short and medium baselines.
		Reuleaux triangles are found to be superior to circles for hybrid arrays not only because their radial profiles are smoother at all values of the scale factor but also because their desirable properties degrade more slowly as the scale factor is increased.
		Reuleaux triangles are based on three points sited at the vertices of an equilateral triangle, the `side' joining any two vertices being a circular arc centred on the third vertex.
	www.cv.nrao.edu /alma/almaweb/www/memos/html-memos/alma214/memo214.html (3098 words)

	Ivars Peterson's MathLand: Rolling with Reuleaux
		One simple way to generate this figure is to start with an equilateral triangle, then draw three arcs of circles, with each arc having as its center one of the triangle's corners and as its endpoints the other two corners.
		The resulting "curved triangle," as Reuleaux termed it, has a constant width equal to the length of the interior triangle's side.
		Like a circle, a Reuleaux triangle fits snugly inside a square having sides equal to the curve's width no matter which way the triangle is turned.
	www.maa.org /mathland/mathland_10_21.html (822 words)

	FastGeometry (Site not responding. Last check: 2007-10-21)
		Another interpretation of Reuleaux's triangle, at least the basic form above, is the intersection of 3 circles, which is highlighted below.
		An alternative, more general form of Reuleaux's triangle is to construct two arcs centered at each vertex, with the new arc typically located opposite the triangle with respect to the vertex.
		Reuleaux's triangle has not found many engineering applications, most likely because as it does not have a fixed centre as it rotates within a band or square equivalent to its width.
	www.fastgeometry.com /Reuleaux/Reuleaux_Intro.htm (367 words)

	Math Trek: Rolling with Reuleaux, Science News Online, Sept. 20, 2003 (Site not responding. Last check: 2007-10-21)
		One way to draw a Reuleaux triangle is to start with an equilateral triangle, which has three sides of equal length.
		Therefore, an unlimited number of curves of constant width are possible, and the Reuleaux triangle happens to be the family member of least area.
		To this day, Reuleaux triangles and their constant-width siblings remain objects of fascination in the classroom and elsewhere.
	www.sciencenews.org /20030920/mathtrek.asp (1030 words)

	Geometry :: 6-9 :: Chapter One (Site not responding. Last check: 2007-10-21)
		The triangle tray examines triangles according to their sides on top; the bottom three examine triangles according to their angles, at both levels.
		Beginning with the triangle turn all of the figures in their frames to show that the sides and angles are equal.
		: Exploration of the triangle as the constructor of triangles and quadrilaterals.
	www.moteaco.com /albums/geometry1.html (3813 words)

	Learning module on Reuleaux triangle
		The corners of a Reuleaux triangle are the sharpest possible on a curve with constant width.
		The Reuleaux triangle is the rotor of least area in a square.
		The least area rotor for the equilateral triangle is a biangle – lens shaped figure formed with two 60-degree arcs of a circle having a radius equal to the triangle’s altitude..
	kmoddl.library.cornell.edu /math/2 (1692 words)

	[No title] (Site not responding. Last check: 2007-10-21)
		A well-known example is the {\it Reuleaux triangle}, whose boundary consists of three equally long circular arcs with curvature $1/B$.
		Reuleaux polygons with any odd number of sides likewise enjoy the property of constant width It has long been known that among all two-dimensional convex bodies of constant width, the Reuleaux triangle has the smallest area.
		The Reuleaux triangle is only about 10% smaller than the disk of the same width, and the not quite tetrahedrally symmetric Meissner bodies [ChGr83], which are the best-known conjectured minimizers in the three--dimensional case, are less than 20% smaller than the ball.
	www.math.gatech.edu /~harrell/Pubs/reul.texold (1920 words)

	KMODDL - Kinematic Models for Design Digital Library (Site not responding. Last check: 2007-10-21)
		The curved triangle is a figure of constant width and its motion causes the slider to oscillate back and forth through contact with two parallel guides.
		The curved triangle cam was used in early 19th century steam engines to activate a control value as in a Woolf engine.
		In modern mathematical texts the constant width curved triangle has been called the Reuleaux triangle—not because he invented it—but because Reuleaux was the first to generalize the curved triangle to other curves of constant width.
	www.library.cornell.edu /kmoddl-test/model.php?m=60 (261 words)

	Reference.com/Encyclopedia/Reuleaux triangle
		The Reuleaux triangle is the simplest nontrivial example of a curve of constant width - that is, a curve in which all diameters are the same length.
		Center a compass at one vertex and sweep out the (minor) arc between the other two vertexes.
		Equivalently, given an equilateral triangle T of side length s, take the boundary of the intersection of the disks with radius s centered at the vertexes of T.
	www.reference.com /browse/wiki/Reuleaux_triangle (440 words)

	K-MODDL > Tutorials > Reuleaux Triangle
		Franz Reuleaux was the first to demonstrate its constant-width properties and the first to use the triangle in mechanisms.
		The solids with constant width that have the smallest volumes are derived from the regular tetrahedron in somewhat the same way that the Reuleaux triangle is derived from the equilateral triangle: Spherical caps are first placed on each face of the tetrahedron, and then three of tghe edges must be slightly altered.
		The least area rotor for the equilateral triangle is a biangle (a lens shaped figure) formed from two 60-degree arcs of the circle with radius equal to the triangle’s altitude.
	kmoddl.library.cornell.edu /tutorials/02 (1878 words)

	more circles (Site not responding. Last check: 2007-10-21)
		A Reuleaux polygon is a curvilinear polygon where the center of each circle arc is the opposite point of the polygon.
		In the case of three equal arcs beginning in the angles of an equal triangle, it is called the Reuleaux triangle.
		Given a triangle, put three circles in it, so that each circle is tangent to the other two and to two sides of the triangle.
	www.2dcurves.com /conicsection/conicsectioncm.html (1139 words)

	The Sliding Triangle
		If you read the Reuleaux Triangle lesson, you may have wondered about the curves traced by the centroid and vertices of the Reuleaux as it rotated within the rhombus.
		I discovered that each of these triangles has what I call a ghost, a different triangle which may be attached to the same pair of lines to generate the same ellipse.
		As the reuleaux triangle rotates in a rhombus, the centroid follows four distinct curves.
	whistleralley.com /ellipse/ellipse.htm (1022 words)

	KMODDL - Kinematic Models for Design Digital Library (Site not responding. Last check: 2007-10-21)
		Reuleaux called the line or point contact between machine components "higher order pairs" in contrast to bodies in surface contact constraint.
		Here he constructed a curved triangle from an equilateral triangle with circular arcs whose centers are at the three vertices of the triangle.
		While one's intuition might lead one to conclude that three points of contact of a plane figure would constrain the motion of the curved triangle in the square chamber, Reuleaux showed that it was possible for the object to rotate and slide since the three contact normals always meet at a point.
	www.library.cornell.edu /kmoddl-test/model.php?m=233 (253 words)

	Reuleaux triangle: Facts and details from Encyclopedia Topic (Site not responding. Last check: 2007-10-21)
		A Reuleaux polygon is a polygon (A closed plane figure bounded by straight sides)
		The Reuleaux triangle is the simplest nontrivial example of a curve of constant width (In geometry, a curve of constant width is a convex planar shape whose width, measured by the distance...)
		The Reuleaux triangle can be generalized to regular polygon (A polygon with all sides and all angles equal)
	www.absoluteastronomy.com /ref/reuleaux_triangle (1202 words)

	Reuleaux Triangle
		For every rotation of the reuleaux, the centroid makes three revolutions in the opposite direction, and its path is not circular.
		The reuleaux turns inside the square because the square is formed by two pairs of parallel lines, equally spaced.
		When I say that the reuleaux is inscribed in a rhombus, I mean that it touches every side, but crosses none of them.
	whistleralley.com /reuleaux/reuleaux.htm (854 words)

	12 Lateral Thinking Puzzles (Netalive.org)
		Another possibility is the Reuleaux triangle, named after engineer Franz Reuleaux, who was a teacher in Berlin, more than a hundred years ago.
		An example of a Reuleaux triangle can be found in your medicine cabinet.
		Place the pointed end of a pair of compasses at one corner of the triangle and stretch the arms until the pencil reaches another corner.
	www.netalive.org /topics/3571 (1063 words)

	A Reuleaux triangle (Site not responding. Last check: 2007-10-21)
		The figure is like an equilateral triangle except with arcs for each side.
		If each arc is a piece of a circle whose center is one vertex and whose radius equals the length of a side, the triangle is called a Reuleaux triangle (named after Franz Reuleaux, a French engineer).
		In general, a figure in the plane with three curved sides is called a curvilinear triangle.
	mathcentral.uregina.ca /QQ/database/QQ.09.04/bob3.html (82 words)

	Shapes of constant width
		Draw three arcs with radius equal to the side of the triangle and each centered at one of the vertices.
		The figure is known as the Reuleaux triangle.
		The angle between two intersecting curves is defined as the angle between their tangents at the point of intersection.
	www.cut-the-knot.org /do_you_know/cwidth.shtml (604 words)

	The CTK Exchange Forums
		A diameter of Reuleaux's triangle must be a line joining a vertex to a point on the opposite arc.
		To convince yourself that the shape should be 'inside out', note that the arcs remain the same way up when scaled, but the triangle of midpoints is upside down with respect to the original triangle.
		in pink is an equilateral triangle, around it in blue is Reuleaux's triangle and within (in red) is the shape described by sfwc.
	www.cut-the-knot.org /htdocs/dcforum/DCForumID3/287.shtml (275 words)

	Problem #35 (Site not responding. Last check: 2007-10-21)
		A Reuleaux triangle is constructed by taking an equilateral triangle ABC and drawing the three circular arcs: BC with center A, AC with center B, and AB with center C, as shown below.
		The Reuleaux triangle is an example of a "curve of constant width".
		This month's problem is to find the volume and the surface area of the solid obtained by rotating the Reuleaux triangle shown above around a vertical axis passing through vertex A.
	math.smsu.edu /~les/Adv35.html (93 words)

	T. Lachand-Robert & E. Oudet, Spheroforms (Site not responding. Last check: 2007-10-21)
		Orbiforms in particular have been studied a lot during the nineteenth century and later, particularly by Frank Reuleaux, whose name is now attached to those orbiforms you get by intersecting a finite number of disks of equal radii a, whose center are vertices of a regular polygon of diameter a.
		In particular the Reuleaux triangle is the intersection of three discs of radius a, centered on vertices of an equilateral triangle with side length a.
		To obtain spheroforms, a simple construction is to consider a two dimensional body of constant width having an axis of symmetry (like the Reuleaux triangle for instance): the corresponding body of revolution obtained by rotation around this axis is a spheroform.
	www.lama.univ-savoie.fr /sitelama/Membres/pages_web/LACHAND/Spheroforms.html (435 words)

	Wankel engine - Wikipedia, the free encyclopedia
		In the Wankel engine, the four strokes of a typical Otto cycle engine are arranged sequentially around an oval, unlike the reciprocating motion of a piston engine.
		In the basic single rotor Wankel engine, a single oval (technically an epitrochoid) housing surrounds a three-sided rotor (a Reuleaux triangle) which turns and moves within the housing.
		The sides of the rotor seal against the sides of the housing, and the corners of the rotor seal against the inner periphery of the housing, dividing it into three combustion chambers.
	en.wikipedia.org /wiki/Wankel_engine (2859 words)

Try your search on: Qwika (all wikis)