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Reuleaux Triangle -- from Wolfram MathWorld

A curve of constant width constructed by drawing arcs from each polygon vertex of an equilateral triangle between the other two vertices. The Reuleaux triangle has the smallest area for a given width of any curve of constant width. Let the arc radius be r. Since the area of each meniscus-shaped portion of the Reuleaux triangle is a circular segment with opening angle theta=pi/3, A_s = 1/2r^2(theta-sintheta) (1) = (pi/6-(sqrt(3))/4)r^2. (2) But the area of the central equilateral...



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Reuleaux Triangle -- from Wolfram MathWorld

https://mathworld.wolfram.com/ReuleauxTriangle.html

A curve of constant width constructed by drawing arcs from each polygon vertex of an equilateral triangle between the other two vertices. The Reuleaux triangle has the smallest area for a given width of any curve of constant width. Let the arc radius be r. Since the area of each meniscus-shaped portion of the Reuleaux triangle is a circular segment with opening angle theta=pi/3, A_s = 1/2r^2(theta-sintheta) (1) = (pi/6-(sqrt(3))/4)r^2. (2) But the area of the central equilateral...



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https://mathworld.wolfram.com/ReuleauxTriangle.html

Reuleaux Triangle -- from Wolfram MathWorld

A curve of constant width constructed by drawing arcs from each polygon vertex of an equilateral triangle between the other two vertices. The Reuleaux triangle has the smallest area for a given width of any curve of constant width. Let the arc radius be r. Since the area of each meniscus-shaped portion of the Reuleaux triangle is a circular segment with opening angle theta=pi/3, A_s = 1/2r^2(theta-sintheta) (1) = (pi/6-(sqrt(3))/4)r^2. (2) But the area of the central equilateral...

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      Reuleaux Triangle -- from Wolfram MathWorld
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      A curve of constant width constructed by drawing arcs from each polygon vertex of an equilateral triangle between the other two vertices. The Reuleaux triangle has the smallest area for a given width of any curve of constant width. Let the arc radius be r. Since the area of each meniscus-shaped portion of the Reuleaux triangle is a circular segment with opening angle theta=pi/3, A_s = 1/2r^2(theta-sintheta) (1) = (pi/6-(sqrt(3))/4)r^2. (2) But the area of the central equilateral...
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      A curve of constant width constructed by drawing arcs from each polygon vertex of an equilateral triangle between the other two vertices. The Reuleaux triangle has the smallest area for a given width of any curve of constant width. Let the arc radius be r. Since the area of each meniscus-shaped portion of the Reuleaux triangle is a circular segment with opening angle theta=pi/3, A_s = 1/2r^2(theta-sintheta) (1) = (pi/6-(sqrt(3))/4)r^2. (2) But the area of the central equilateral...

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      Reuleaux Triangle -- from Wolfram MathWorld
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      A curve of constant width constructed by drawing arcs from each polygon vertex of an equilateral triangle between the other two vertices. The Reuleaux triangle has the smallest area for a given width of any curve of constant width. Let the arc radius be r. Since the area of each meniscus-shaped portion of the Reuleaux triangle is a circular segment with opening angle theta=pi/3, A_s = 1/2r^2(theta-sintheta) (1) = (pi/6-(sqrt(3))/4)r^2. (2) But the area of the central equilateral...

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      A curve of constant width constructed by drawing arcs from each polygon vertex of an equilateral triangle between the other two vertices. The Reuleaux triangle has the smallest area for a given width of any curve of constant width. Let the arc radius be r. Since the area of each meniscus-shaped portion of the Reuleaux triangle is a circular segment with opening angle theta=pi/3, A_s = 1/2r^2(theta-sintheta) (1) = (pi/6-(sqrt(3))/4)r^2. (2) But the area of the central equilateral...
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