Mathematical animations: The art of teaching

Mathematical visualization is the art of creating a tangible experience with abstract mathematical objects and concepts. The advent of high-performance interactive computer graphics systems has opened a new era, its ultimate significance can only be imagined. Computer visualization has become an important tool in several fields of mathematics, helping mathematical understanding and communication. Mathematicians can now use computers to generate pictures that would be tedious or impossible to generate by hand. However, the process of approximating a picture seen on a computer monitor is nontrivial. The paper begins with some general background and then focuses on some of the visualization methods that have been used to bring computer graphics technology to model mathematical problems, from calculus to complex numbers. Examples of computer-generated images are supplied throughout the paper and an overview of selected animations concerned with mathematical visualization is constantly made. Animation can make mathematics more interesting and stimulating. It features a "hands-on" exploratory and experiential learning tool, making mathematics more dynamic and meaningful. This problem solving through visualization illustrates the processes and behaviours of equations and formulae as they are graphically mapped out.