After calculating Taylor polynomials of several rational functions in this way, and graphing the functions, polynomials and remainders, students are prepared to understand Taylor polynomial approximations for general functions and Lagrange's formula for the remainder. A differential equation satisfied by the pursuit spirals is found and a plot of sample paths suggests several exercises for calculus students. The geometry of a binary tree can be described by a lower triangular stochastic matrix, the ramification matrix of the tree. Conversely, given such a matrix, by interpreting its entries as probabilities one can generate collections of random trees with visually similar branching behaviors. By adjusting the probabilities in the matrix we can tailor the model to produce trees with a variety of realistic shapes.
Suggestions follow on extensions for modeling natural branching processes with computer graphics.
Software Review Standard Math Interactive is a compact disk version of the CRC Standard Mathematical Tables and Formulae that makes possible quick computer searches of the contents of this large reference handbook. Once a mathematical expression is found, operations on it such as evaluation, plotting, integration, or expansion in series can be selected from menus and performed by a special version of the computer algebra system Maple V that is an integral part of Standard Math Interactive .