||Shortest Total Distance Traveled Among Curves, Surfaces and Lagrange Multipliers
||Wei-Chi YANG and Yunhao FU
This paper was inspired by students at Guangzhou University in 2014, and the problems are variations from those described in a reference. We seek the shortest total distance from curve 1 to curve 2, curve 2 to curve 3 and curve 3 back to curve 1. In 3D, we want to find the shortest total distance between surface 1 and surface 2, surface 2 and surface 3, surface 3 and surface 4, and finally surface 4 and surface 1. We assume curves and surfaces are not intersecting. We start with the simplest case for circles in 2D and we link to higher dimensions through the Lagrange multipliers method.