On Rectangular Food Trolley Problem
Dewi Sinta- Denny Ivanal Hakim, Ph. D- Dr. Rizal Afgani

Institut Teknologi Bandung

Abstract

In literatures, there are at least three famous problems about the movement of an object around a corner, namely the food trolley problem, the moving sofa problem, and the piano mover^s problem. In this paper, we investigate the problem of the movement of a rectangular-shaped food trolley around a corner between two corridors. This problem asks the maximum area of a rectangle that can be moved around a corner between two corridors subject to the width of each corridor and the angle of the corner. In 1998, Eriksson et al gave some partial solutions to the rectangular food trolley problem. They give an upper bound of the area of any rectangular trolley. They also consider the candidate of the size of rectangle with maximum area for right angle, obtuse angle, and acute angle of the corner between two corridors. In addition, various pushing strategies were discussed in their work. In this paper, we discuss an elementary approach to the solution of rectangular food trolley problem based on the idea of Eriksson et al. In particular, we give the more detailed explanation about the dimension of rectangle of maximum area and the movement strategies of the rectangle. Our proof uses only some elementary trigonometric formulas, congruence of triangles, and concept of translation and rotation. Our results can be viewed as an interesting example of application of high school geometry and trigonometry concept to a partial solution to an advance problem.

Keywords: The Dimension of Rectangle, Rectangular Food Trolley Area, The Movement Strategies of The Rectangle

Topic: MATHEMATICS AND SCIENCE EDUCATIONS