Pustaka Ilmiah Universitas Padjadjaran

Abstrak

An Application Of Classical Polynomial Theory In Optimal Ladder Reclining Problem

The paper has twofold purposes. First, the paper demonstrates a stage-by-stage problem solving which is an important process that should be experienced by all mathematics students. It can be regarded as a model in teaching mathematics in the context of meaningful learning and constructivism. Second, in this paper we consider an application of classical polynomial theory in determining the existence of a ladder reclining problem. A ladder with 5 meters length is supposed to be placed so that the upper edge of the ladder reclines to a vertical wall while its lower edge touch the horizontal floor. It is also required that a part of the ladder touches a corner of certain geometric object (in this case a cube that has edges 1-meter length). We address the question on how many ways the ladder can be placed to satisfy such condition. Surprisingly, it was found that there are only two ways to place the ladder. Furthermore, in this paper we also give a necessary and sufficient condition in order a ladder with length l can be placed in the intended way so that a part of the ladder touches a part of a cube with edge k.