ABSTRACT
Computer animation is one application of how one uses transformations to give the appearance of motion. Actually, what the computer does to accomplish this is a combination of a large number of matrix multiplications and additions. Another application would be the design of robots that, for example, are used in industry, medicine, armed forces, and police work to perform tasks that humans would find tedious, sometimes dangerous, and even impossible. Specifically, robots are used in building cars and a variety of manufacturing processes, as well as in microscopic surgery. Every robotic movement can be described by some transformation or composition of transformations that is represented by matrices and programmed into the computer. This chapter shows how motion can be represented in these ways, and how, surprisingly, a calculator uses rotations to compute quantities like sines, cosines, and logarithms. The most basic transformation is the translation. The next transformation included in the secondary school curriculum is reflection in a line.
