\input zb-basic
\input zb-matheduc
\iteman{ZMATH 2016a.00585}
\itemau{Priest, Dean B.; Smith, Ronald G.; Carlisle, Christin; Mays, Rebecca}
\itemti{The diver problem: the surfer problem in 3D.}
\itemso{Math. Teach. (Reston) 106, No. 9, 710-714 (2013).}
\itemab
From the text: A surfer, shipwrecked on an island in the shape of an equilateral triangle, wants to build a hut so that the sum of its distances to the three beaches is minimal. Where should the hut be located? The authors demonstrate several solutions to this problem, including a coordinate geometry proof and an area proof. In all cases, they show that the hut can be located anywhere on the island by proving that the sum of the distances equals the height of the triangle. In addition, they challenge readers to discover other approaches for themselves.
\itemrv{~}
\itemcc{G40 G70}
\itemut{elementary geometry; triangles; equilateral triangular prisms; polygons; right regular polygonal prisms; tetrahedra; polyhedra; solid geometry; volume; coordinates; analytic geometry; vectors; proofs; generalization}
\itemli{http://www.nctm.org/Publications/mathematics-teacher/2013/Vol106/Issue9/Delving-Deeper\_-The-Diver-Problem\_-The-Surfer-Problem-in-3D/}
\end