
02364100
a
2005e.02387
Ligh, Steve
Wills, Randall
Families of linear functions and their envelopes.
Bogacki, Przemyslaw (ed.), Proceedings of the 7th annual international conference on technology in collegiate mathematics, ICTCM 7, Orlando, FL, USA, November 1720, 1994. Norfolk, VA: Old Dominion University, Dept. of Mathematics and Statistics (ISBN 0201870207). Electronic paper (1994).
1994
Norfolk, VA: Old Dominion University, Dept. of Mathematics and Statistics
EN
I25
R25
functions
envelopes
families of linear functions
computer algebra
The topic of envelopes of families of curves was present in calculus texts forty years ago, but has since been deleted. With the advent of computer algebra systems such as Maple, Mathematica, and Derive, this topic is accessible to our calculus students and is a good example of the type of problem where the computer can be used as a tool to aid in the solution of a problem. The purpose of this note is to introduce envelopes of families of lines, to study some of the geometric properties of envelopes, and finally to present a closed form expression of the envelope. We have used Maple V to generate pictures of various families of lines and have used these pictures to help us make conjectures about the corresponding envelope. (authors' abstract) (The article is available under http://archives.math.utk.edu/ICTCM/EP7.html)