Version 0.6 of g(z) allows users to run mathematical demonstrations through a web browser. This page has been established to provide links to a set of g(z) demonstrations that have been written by the author. To start a demonstration, simply click on the appropriate link below. Note that to use these demonstrations you you must have already downloaded and installed version 0.6 of g(z).

List of demonstrations currently available:

• template.gsv : A blank template with just a domain window and a constants window. Use this to launch g(z) from the web with no demonstration to load..

• exponential.gsv : The simplest example: the complex exponential . Take note of what happens when you move the domain vertically or horizontally. What effect does resizing the domain have, and why?

• rotate_and_scale.gsv : Visualize complex multiplication. Move the constant "a" around the constants window, and watch what happens. See what happens when you move "a" along a circle (i.e., keep the distance from the origin constant.) Then try moving "a" along a line of constant angle.

• realvars.gsv: g(z) can plot real-valued functions of two variables, too! See this surface plot of f(x,y) = sin(x²+y²)...

• complex_polynomials.gsv : A visualization of a general fourth degree complex polynomial: (z-a)(z-b)(z-c)(z-d), using the domain coloring technique. Zeroes appear as the white spots in the window. Note that the colors wrap once around single zeroes, twice around double zeroes, etc. Try inserting a pole, and see what happens.

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  List of new demonstrations:

• inverse_exponential.gsv: A visualization of the many-valued logarithm function as the inverse of the exponential function. The projection window provides two projections: one for the real-part of the inverse, and one for the imaginary-part. Watch what happens when you slide between them. Explain the appearance of the real and imaginary parts. What effect does moving or resizing the domain have, and why?

• zsquared_and_cutting_plane.gsv: Version 0.6 of g(z) can display multiple functions in a single window. (Right click on a function to pop-up a menu for insertion/deletion.) This example shows the complex function f(z) = z², together with a slicing plane. Try moving the slicing plane up and down (by moving the constant "a".)

• tangentplane.gsv: Version 0.6 of g(z) is capable of computing Taylor series expansions of functions (by symbolic differentiation.) This example shows a first order taylor expansion of sin(z). What relationship does the approximation surface have to the function surface? What happens if you increase the degree of the expansion? What happens when you move the constant "a" (the point around which the series is expanded)?

• taylor_sin.gsv: Here's another example of a Taylor series computed for sin(z). Here I've kept the function and the Taylor series in separate windows so you can see the differences. Also notice that another mapping window provides a look at the error of the approximation, computed as a simple difference between the two functions.

• trig_intersections.gsv: Ever wondered what sin(z), -sin(z), cos(z) and -cos(z) look like together? Check out this demo, and you'll find out.

• poincare.gsv: An illustration of hyperbolic geometry, created by John Leen. This is a map between the Poincaré disc and the upper half plane preserving angles and sending circles to other circles.

• 4dtorus.gsv: Also by John Leen: the flat torus, parametrized in four pieces.

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