
06512803
j
2016a.00585
Priest, Dean B.
Smith, Ronald G.
Carlisle, Christin
Mays, Rebecca
The diver problem: the surfer problem in 3D.
Math. Teach. (Reston) 106, No. 9, 710714 (2013).
2013
National Council of Teachers of Mathematics (NCTM), Reston, VA
EN
G40
G70
elementary geometry
triangles
equilateral triangular prisms
polygons
right regular polygonal prisms
tetrahedra
polyhedra
solid geometry
volume
coordinates
analytic geometry
vectors
proofs
generalization
http://www.nctm.org/Publications/mathematicsteacher/2013/Vol106/Issue9/DelvingDeeper_TheDiverProblem_TheSurferProblemin3D/
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.