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  2. Barbier's theorem - Wikipedia

    en.wikipedia.org/wiki/Barbier's_theorem

    For a circle, the width is the same as the diameter; a circle of width w has perimeter π w. 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 half the perimeter of a circle of radius w and therefore is equal ...

  3. Curve of constant width - Wikipedia

    en.wikipedia.org/wiki/Curve_of_constant_width

    A curve of constant width defined by an 8th-degree polynomial. Circles have constant width, equal to their diameter.On the other hand, squares do not: supporting lines parallel to two opposite sides of the square are closer together than supporting lines parallel to a diagonal.

  4. Reuleaux triangle - Wikipedia

    en.wikipedia.org/wiki/Reuleaux_triangle

    Its width, approximately 1.54, is the root of a degree-6 polynomial with integer coefficients. [17] [19] [20] Just as it is possible for a circle to be surrounded by six congruent circles that touch it, it is also possible to arrange seven congruent Reuleaux triangles so that they all make contact with a central Reuleaux triangle of the same size.

  5. Triangle - Wikipedia

    en.wikipedia.org/wiki/Triangle

    Triangles have many types based on the length of the sides and the angles. A triangle whose sides are all the same length is an equilateral triangle, [3] a triangle with two sides having the same length is an isosceles triangle, [4] [a] and a triangle with three different-length sides is a scalene triangle. [7]

  6. Blaschke–Lebesgue theorem - Wikipedia

    en.wikipedia.org/wiki/Blaschke–Lebesgue_theorem

    The Blaschke–Lebesgue theorem states that this is the unique minimum possible area of a curve of constant width, and the Blaschke–Lebesgue inequality states that every convex set of width has area at least this large, with equality only when the set is bounded by a Reuleaux triangle. [1]

  7. Shuffleboard - Wikipedia

    en.wikipedia.org/wiki/Shuffleboard

    The 10 scoring zone is at the peak of the overall scoring triangle, and is 3 feet in height, from the Top-8 line to the peak of the triangle. A further dead-line or lag-line runs from side to side 12 feet from the base-line. The dead-line is therefore 3 feet from the tip of the triangle. There are two dead-lines, 12 feet apart.

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