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Parametric Integrals and Symmetries of Functions
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Dana-Picard, Thierry – Mathematics and Computer Education, 2005
An integral, either definite or improper, cannot always be computed by elementary methods, such as reversed usage of differentiation formulae. Graphical properties, in particular symmetries, can be useful to compute the integral, via an auxiliary computation. We present graded examples, then prove a general result. (Contains 4 figures.)
Descriptors: Mathematics, Problem Solving, Graphs, Geometry
On the Curvature Function: Where Does a Curve Bend the Fastest?
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Chrysafi, Loucas; Gordon, Sheldon – Mathematics and Computer Education, 2006
We examine the behavior of the curvature function associated with most common families of functions and curves, with the focus on establishing where maximum curvature occurs. Many examples are included for student illustrations. (Contains 18 figures.)
Descriptors: Science Activities, Equations (Mathematics), Mathematics Instruction, Mathematical Concepts
The Reflective Property of the Conics--A Different Approach.
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Blistain, Margaret L.; Phillips, Paul H. – Mathematics and Computer Education, 1988
Presents a method of viewing the reflective properties of the parabola and ellipse. Reinforces previously studied concepts of mathematics useful for individual or classroom projects. (PK)
Descriptors: Analytic Geometry, College Mathematics, Computer Assisted Instruction, Computer Graphics