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Interactive Gallery of Quadric Surfaces
A suite of mathlets for interactive exploration of quadric surfaces
Constructing Mathlets Quickly using LiveGraphics3D
This is a Developer's Area article that describes how to use a Java applet called LiveGraphics3D to speed up the process of creating interactive graphics by removing the need to create a graphics engine in Java, Flash, or other programming languages.
Loci
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Parameterized Knots
Abstract
We discuss two families of parameterized knots (polynomial and trigonometric) and include an interactive gallery of selected knots and their equations. We survey results related to parameterizations and suggest avenues for further investigation. Finally, we include an applet that graphs three-dimensional parametric curves to aid the interested reader in exploring additional parameterizations.
Contents
- Introduction
- Knot Software and LiveGraphics3D
- Polynomial Knots
- Trigonometric Knots
- Parametric Curve Plotter
- Activities
- References
This article uses LiveGraphics3D, a Java applet which displays three-dimensional figures as generated by Mathematica. Any figure displayed with LiveGraphics3D can be rotated by clicking and dragging the mouse on the image.
Stemkoski, Lee, "Parameterized Knots," Loci (November 2010), DOI: 10.4169/loci003596