Many properties of plane curves, such as cusp, tangent, evolute, involute, or envelope, are most easily explained by means of an illustration or animation. Xah Lee's pages offer QuickTime animations, Geometer's Sketchpad files, in-line graphics, and dozens of Mathematica packages and notebooks illustrating the following curves and many more:
- Archimedean Spiral - Cassinian Oval - Conic Sections - Lemniscate of Bernoulli - Limacon of Pascal - Quadratrix of Hippias - Trisectrix of Maclaurin - Witch of Agnesi
The formulas, properties, history, and nomenclature of special plane curves are presented at a beginning college level. Overall, the project is designed to educate and entertain.
Other features of Xah Lee's MATHEMATICS GRAPHICS GALLERY include illustrations of Spheres and Cubes; Transformation of the Plane; Tilings of the Plane; Nested Inversion of Circles; and a FRACTAL GRAPHICS GALLERY of images in the public domain.
The Math Forum offers a collection of links to Web sites dealing with reform in mathematics education and the NCTM Standards. Pros and cons are covered in articles hosted by the Eisenhower National Clearinghouse (ENC) and others.
Here in addition to the Standards themselves you'll find "Developing Educational Standards for Math," an annotated list of Internet sites with K-12 educational standards and curriculum frameworks documents, maintained by Charles Hill and the Putnam Valley Schools in New York. Sites for math education standards are listed by organization and by state.
"I am trying to figure out how the Golden Ratio and the Fibonacci series are related..." "Is there a formula to calculate the nth Fibonacci number?" "I have figured out that the ratio of a number in the Fibonacci series over the previous gets increasingly closer to the Golden Ratio but I don't know how to relate this to some mathematical reason or logic..."
These and other frequently asked math questions are answered in the newly redesigned DR. MATH FAQ. Explanations, illustrations, links to answers in the Dr. Math archives, and suggestions for good sites on the Web for supplementary information are included with each topic.