 
Summary: U S I N G M A T H E M A T I C A T O I L L U S T R A T E T H E R A C E T R A C K P R I N C I P L E I N C A L C U L U S
Using Mathematica to Illustrate the
Race Track Principle in Calculus
by Alkiviadis G. Akritas and Zamir Bavel
A
n astonishing innovation in the teaching of Cal
culus is the use of the race track principle. This
littleknown principle is elegantly used in the Cal
culus and Mathematica (C&M) series of books ([1], [2], [4])
to explain and prove many concepts. Below we present
two different versions of this principle and, using Mathe
matica, we show how it is used to explain the power
series expansion of a function and the roundoff errors
that appear in certain computations.
Although implicitly used in most Calculus books (see
for example [5] and [6]) the Race Track Principle is ex
tensively used in the Calculus and Mathematica (C&M)
book series by Davis, Porta and Uhl ([1][4]). This series
of books is a valuable and well thoughtout method for
teaching Calculus. As indicated by the title of this series
