## Miscellaneous Sketches

Conics
This file dynamically describes the relationships of parabola, hyperbola, and ellipse from an eccentricity point of view. The illustration of their geometric properties is also provided. The envelope and dotted curves were constructed uing the principles of Inversive Geometry described in Geometry Revisited (Coxeter, H.S.M. and Greitzer, S.L., 1967). By Pao-Ping Lao of the Department of Mathematics and Science Education, Taipei Municipal Teachers College, Taipei, Taiwan, The Republic of China.

Pythagorean Theorem This file provides four ways to demonstrate (manipulate) Pythagorean theorem - shear & rotation, shear & translation, similarity, and tessellation. Using the button to move the objects is recommended; direct manipulation using the mouse needs to be done according to the sequences as to what the button control does or this may yield meaningless relations. By Pao-Ping Lao of the Department of Mathematics and Science Education, Taipei Municipal Teachers College, Taipei, Taiwan, The Republic of China.

Parameter Effects This file provides a way to study the parameter effects of function y=ax^2+bx+c (a can be 0) in a "variable" coordinate system in a dynamic, linked environment. A view of functional operations as successive variations on their parameters is implemented. Adding y=5x to y=4x^2-2x-1, obtaining y=4x^2+3x-1, is viewed as varying the coefficient -2 of x in y=4x^2-2x-1 to 3. The effects of "screw-eye" (Goldenberg 1991?) - varying the coefficient of x in a quadratic function, "tilting" (Kaput 1989); changing the slope of a linear function; and "bending" - adding x^2 terms to a linear function; can be studied. By Pao-Ping Lao of the Department of Mathematics and Science Education, Taipei Municipal Teachers College, Taipei, Taiwan, The Republic of China.

Parabola Tracer This sketch illustrates one way to trace out a parabola. By Roberto Allen of the University of Maryland.

Rolling Rouleaux Triangle Change its size and shape, and observe as it rolls along a plane.

Inversion in a Circle A sketch with an accompanying article that explains the construction and suggests some things to explore. The article is available in Binhexed MacWrite II format or Postscript. By John Olive.

Regular 17-gon A construction of a regular 17-gon using Conway's Quadruple Quadrisection method.

Bezier Curve Sketch 1 and Bicubic Bezier Patch (1130 Kb)
By Nick Jackiw of Key Curriculum Press.

Stewart's Theorem Investigate this theorem by observing the equality of two given calculations. By Nick Jackiw of Key Curriculum Press.