**Dragoslav Herceg and Đorđe Herceg**

Department of Mathematics and Informatics

Faculty of Science and Mathematics, University of Novi Sad, Serbia

{hercegd, herceg}(at)im.ns.ac.yu

This is the accompanying web site of the paper "Numerics with GeoGebra in High School" by Dragoslav and Đorđe Herceg.

The tools on this page perform one step of the following numerical methods for finding roots of functions:

- Fixed point method
- Bisection method
- Secant method
- Newton-Raphson method

In all cases, you are required to give some input to the tools; they will then calculate and draw geometrical representation of one iterative step. The input is usually a function (you must click on the curve) and one or two initial points on the x-axis. For example, to use the NewtonRaphson tool, you first need to click on the curve and then on an initial point on the x-axis. The tool will then generate a point as a result of one iterative step of the Newton-Raphson method. This point can then be used as a new initial point for another iterative step.

The tools are provided as a means for visualization of numerical iterative methods and they generate new lines and points. Some points are auxiliary, but some can be used as approximations of the equation roots and they are shown in the algebra window.

The following examples demonstrate use of our tools. Intial points in the examples are bigger than the rest and can be moved with the mouse.

- Empty example
- Fixed point method 1 example
- Fixed point method 2 example
- Bisection method example
- Secant method example
- Newton-Raphson method example

You can download the tools by clicking on the links. Once you have saved the tools (.ggt files) on your computer, open them in GeoGebra (File -> Open) and they will show up in the toolbar. You can add the tools to an existing drawing by first opening the drawing and then opening the tools.

Page published on 28.9.2007