 |
George
Baloglou is an associate professor of mathematics at SUNY Oswego,
where he has been teaching since 1988. He is currently working on a
book on planar crystallographic groups (wallpaper patterns), largely
influenced by a symmetry course he has been teaching since 1995. His
other mathematical interests include elementary inequalities, convexity,
and basic number theory.
E-mail: Baloglou@oswego.edu
Michel Helfgott is an assistant professor of mathematics
at SUNY Oswego. His main interests are the history of mathematics and
its use in teaching, as well as the use of physics and chemistry as
pedagogical tools in the mathematics classroom.
E-mail: Helfgott@oswego.edu |
| A
calculus-free approach is offered for determining the equation of lines
tangent to conics. Four types of problems are discussed: line tangent
to a conic at a given point, line tangent to a conic passing through a
given point outside the conic, line of a given slope tangent to a conic,
and line tangent to two conics simultaneously; in each case, a comparison
to the standard calculus method is made by way of specific examples. Extending
an idea of Descartes, this calculus-free approach is based on the fact
that a quadratic has a double root if and only if its discriminant is
equal to zero. It should be appropriate for both precalculus and calculus
students. |
