Flash content (faded out below) will not run after the end of 2020 (thanks to Adobe for their lack of support); I'll be getting on the task of getting Flash animations ported to HTML5 (and giving up any reliance on Adobe), one at a time!

Note that some browsers will require you to click once on a Flash animation before any keystrokes will be recognized.

Please see also our sister site, NearNumbers.net!

Shape/Mapping explorer (click image at left to view demo)
  • Instructions coming at a later time; in the meantime, the demo shows a bit!

Download the pre-alpha version:  
  • Windows (no installer—just unzip the file and run mapping.exe from the Install folder)
  • Mac OS X (copy the application from the disk image and run it)
Linear system explorer (click image at left to view)
  • Instructions  [Suggested browsers: Chrome for mobile, FireFox on desktop]

Examples:  
Linear Combination Explorer (click image at left to view)
  • Starts with an assortment of examples of linear combinations; press [Page-Down] to scroll through them. Rational numbers can be entered as coefficients; use [Space] to cycle through the coefficients and [C] to clear all coefficients to 0.
  • On the last page, pressing [V] and [S] display labels indicating the notation used for vectors and scalars, respectively.
  • [Home] restarts the examples with "linear combination problems" of building some vector as a linear combination of the given collection. Press the [Up] and [Down] arrows to change targets: some are possible to build (i.e., give consistent systems) and some are impossible (i.e., give inconsistent systems); most examples are linearly dependent and allow multiple solutions when consistent, so that this concept can be explored. To show the solution (or best approximation), press [?].
Complex Powers & Roots (click image at left to view)
  • Press "2"-"6" to change the exponent.
  • Hold [shift] / [ctrl] to hold magnitude / argument fixed while moving point.
  • "B" toggles display of the branch cut and branches of the inverse function.
  • "D" toggles visualization of the derivative for the left-to-right function.
Complex Exponential & Logarithm (click image at left to view)
  • Hold [shift] / [ctrl] to hold magnitude/argument (or real/imaginary part) fixed while moving point.
  • "B" toggles display of the branch cut and branches of the inverse function.
  • "D" toggles visualization of the derivative for the left-to-right function.
Möbius Transformations (click image at left to view)
  • Click the four coefficients to enter values.
  • ">" and "<" increase/decrease the radius of a circle drawn about the domain point.
  • "C", "P", and "N" draw Cartesian, Polar, or No coordinate lines on the domain.