Reuleaux triangle

A Reuleaux triangle is a shape made when three circles cross. It looks like a triangle with round sides and pointed corners.

To make one, first draw two dots. Then put a compass on the two dots and draw a circle. Do the same thing again, this time with the other dot as the middle of the circle. Choose either the top or bottom points of the connecting circles as a new center, using the two drawn dots as the edge, and draw the third circle.

If a is how wide the Reuleaux triangle is, the area is [math]\displaystyle{ \frac{1}{2}(\pi - \sqrt3)a^2 }[/math]. The perimeter is [math]\displaystyle{ \pi a }[/math].

A Reuleaux polygon is a shape like the Reuleaux triangle with an odd number of sides.

A Reuleaux tetrahedron is made when four spheres cross. It looks like a Reuleaux triangle as a pyramid with three sides at the bottom.

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  Reuleaux triangle in gray

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  Reuleaux polygons

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  Reuleaux tetrahedron made with four spheres

Reuleaux Triangle Media

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  The boundary of a Reuleaux triangle is a constant width curve based on an equilateral triangle. All points on a side are equidistant from the opposite vertex.

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  To construct a Reuleaux triangle

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  Parallel supporting lines of a Reuleaux triangle

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  Centrally symmetric shapes inside and outside a Reuleaux triangle, used to measure its asymmetry

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  An equidiagonal kite that maximizes the ratio of perimeter to diameter, inscribed in a Reuleaux triangle

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  Rotation of a Reuleaux triangle within a square, showing also the curve traced by the center of the triangle

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  Comparison of a cylindrical and Reuleaux triangle roller

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  Reuleaux triangle based film advance mechanism in the Soviet Luch-2 8mm film projector

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  Reuleaux triangle shaped window of the Church of Our Lady, Bruges in Belgium

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  Leonardo da Vinci's world map in eight Reuleaux-triangle quadrants