Mapping the Landscape of Mathematics
Those who enjoy or need the visual side of mathematics certainly benefit from access to graphics capabilities of computing technologies. The "mathematics" it is possible to see today was nearly impossible yesterday.
For example, consider National Curve Bank, the brain-child of Shirley Gray, Stewart Venit, and Russ Abbott (Professors at California State University, Los Angeles). An encyclopedic
resource for students and teachers of mathematics, the National Curve Bank offers animation, interactive experiences, and streaming videos that provide insightful views of mathematical curves that would not be possible via a printed page. Complementary information includes "geometrical, algebraic, and historical aspects of curves, the kinds of attributes that make the mathematics special and enrich classroom learning."
In addition to checking out your favorite curve, consider these possibilities:
Plus, the web site includes a list of birthdays of mathematicians (annotated), a bank of curves specific to science, and much more.
- Precalulus-level curves involving trigonometry functions, polar graphs, parametric graphs, transcendentals, and general geometry
- Calculus-level curves involving limits, integrals, derivatives, vectors, and series
- Java applets that provide interactive experiences with special curves (e.g. pursuit curves or vector fields)
- Fractals such as the Mandelbrot set, Sierpinski Triangles (2-D and 3-D versions), and Baravelle Spirals
- And a lot more...a world of curves galore!
Finally, the coordinators of the website openly invite others to submit new curves or variations....all designed to "illustrate, in a way not possible on the printed page, the features of an interesting curve." Why not give it a try...or push your students to do so as a project? There even is an award, the Renie, for the best new submission each year.