Spreadsheet

The spreadsheet in GeoGebra has most of the regular spreadsheet-features. When it comes to just doing numerical calculations, regular spreadsheet software is more advanced than the GeoGebra spreadsheet; the object-oriented way of doing things in GeoGebra, however, makes it a much stronger tool than regular spreadsheets. Apart from manipulating numbers and formulas, you can also manipulate all GeoGebra-objects in the spreadsheet view.

Whenever you need many objects that follow some regular pattern, you can use the spreadsheet.

The basic features of the GeoGebra spreadsheet, features such as: how to make relative copies, how to plot points from the spreadsheet on the drawing pad, and how to use sliders when generating numbers in the spreadsheet, are explained on the pages Functions - Tables and Spreadsheet and Functions - Percentage Change.

Geometrical objects and functions

The recording below demonstrates how to make a simple pattern of circles. It also shows a demonstration of how the Taylor expansion of \(f(x)=e^x\) approximates the graph better and better as more terms are used. It is meant as a demonstration of how functions are handled in the spreadsheet, if you just want to demonstrate Taylor expansion, you can use the command:

TaylorPolynomial[<Function>, <x-Value>, <Order Number>]

When inserting geometrical objects into the spreadsheet, you must write the command for the object needed. In most cases you can guess the name of the command, start writing and then the code-completion will help.

Dynamic Colour

The applet below demonstrates the Fourier series for a square wave. The yellow/red function is the sum of the green/blue sinus-functions.

The function is: $$f(x)=\sum_{x=0}^{\infty}\frac{1}{2k+1}\sin ((2k+1)\pi x)$$

You specify a dynamic colour by specifying values for red, green and blue. Each value should be between 0 and 1. It is dynamic since you can use variables when specifying the values.

The Fourier series is created in exactly the same way as the series in the recording above. Then the following is entered under the Advanced-tab for the first function (in cell B1), these values are then relatively copied when dragging the small rectangle.

From trace to spreadsheet

Move the point!

You can make a parabola using trace, as on this page Functions - The Parabola. These traces can instead be created as lines in a spreadsheet.

If you let the y-axis be the directrix and a free point A be the focus, then you must make a number of perpendicular bisectors between points on the y-axis and the point A.