ABSTRACT
Consider a large-sized vertical wooden board mounted on a wall. A smallsized block, such that it can be treated as a particle, has to slide down from a point P with coordinates (x1, y1) to another point Q with coordinates (x2, y2) under the influence of gravity. Figure 7.1 shows points P and Q joined by an arbitrary curve. In order to slide the small block from point P to Q, one can carve a curved or straight slot joining points P and Q. The block will move within the slot. Let us assume that there is no friction between the block and the slot, and just as the block is treated as a particle, the slot is treated as a line. The question is what type of slot should be made, so that the block starting from rest from point P reaches point Q in the least possible time.
