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Stadium


Stadium

A stadium, also called a discorectangle, obround, or sausage body, is a geometric figure consisting of a rectangle with top and bottom lengths a whose ends are capped off with semicircles of radius r. The area of a stadium is therefore given by

 A=pir^2+2ra,
(1)

and the perimeter by

 p=2(pir+a).
(2)

Defining the ratio gamma=a/r gives the alternate forms

 A=r^2(2gamma+pi)
(3)

and

 p=2r(pi+gamma).
(4)

The term is most commonly encountered in the context of stadium billiards.

The stadium is implemented in the Wolfram Language as StadiumShape[lbr{x1, y1}, {x2, y2}}, r].

A stadium of revolution might be termed a capsule.


See also

Capsule, Ellipse, Oval, Rectangle, Rounded Rectangle, Semicircle, Square, Stadium Billiards

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References

Trott, M. The Mathematica GuideBook for Symbolics. New York: Springer-Verlag, pp. 1030-1031, 2006. http://www.mathematicaguidebooks.org/.

Referenced on Wolfram|Alpha

Stadium

Cite this as:

Weisstein, Eric W. "Stadium." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/Stadium.html

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