GeoGebra demo of the upper and lower sums for finding the value of the area under a curve

GeoGebra is a Java based dynamic graphics program. You can set points, lines, circles and other geometrical objects, and you can make some of them dynamic in that dragging a point alters parameters. The example GeoGebra worksheet above, down-loadable from the site, shows the upper and lower sum for the area under a cubic curve. Dragging the point along the slider increases or decreases the number of bars that the area is divided into – as n increases the difference between the upper and lower sum decreases. Neat.

As the package is written in Java, it runs cross platform (Windows, Mac OS X and Linux) and may be run without ‘installation’ so that administration rights might not be needed. There is also a ‘run time’ .jar file available so that ‘worksheets’ can be included on a Web site or Intranet, although the ‘highly compressed’ .jar file weighs in at 1 Mb.

The software is free and comes with a quick start guide and some examples. There is a wiki for people to upload their own examples – I shall certainly be developing some around common functions found in biology and in statistics. The GUI makes the package easier to use than the Geometry Applet.

Thanks to John C at Gorway Road for the link.

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