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 BilliardsExplore with Wolfram|Alpha
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References
Trott, M. The Mathematica GuideBook for Symbolics. New York: Springer-Verlag, pp. 1030-1031, 2006. https://www.mathematicaguidebooks.org/.Referenced on Wolfram|Alpha
StadiumCite this as:
Weisstein, Eric W. "Stadium." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/Stadium.html