New Views in GeoGebra
As suggested by its name, GeoGebra started as a program that brought together an algebraic and a geometric view of mathematical objects. Through the years and versions, it has continued to add capabilities, to be easier and more intuitive to use, to do a better job of connecting an algebraic and geometric view.
Starting with release 4.0, the added capabilities add fundamentally new perspectives, so that GeoGebra is a more general, dynamic mathematical modeling tool. We want to consider some of the new views that are either available with the latest release, 4.0, or are planned for the near future.
It is useful to identify some general sources of information. Any GeoGebra user should be aware of the GeoGebra forum. It is a nice place to go when you have questions about using GeoGebra. It is also a place where you can find information on releases that are under development. <http://www.geogebra.org/forum/>
Everyone should also be aware of GeoGebraTube. It is a place where users from around the world post their GeoGebra files. At the very least, it is a place to go to see what others have tried. <http://www.geogebratube.org/>
Current release: (4.0)
You can find more detailed information about this release in the release note. <http://wiki.geogebra.org/en/Release_Notes_GeoGebra_4.0>
This release has a lot of new features, which are beyond the scope of this presentation. The reader may want to look at <> to find some more of those details.
View 1: The Spreadsheet view (4.0) – data entry and analysis, with attention to statistics and linear algebra. The spreadsheet view appeared in release 3.2. With 4.0 it has matured. One of the indications that we are doing something new is this view has its own toolbar.
This view changes things in two ways. The subtle change is that it provides a reasonable interface fro entering and editing data. I think the curriculum we teach is significantly shaped by the kinds of problems we can easily have students write down and what we can do on tests. This means we tend not to have data driven questions because they are too hard to enter and edit. Spreadsheets change that picture. The subtle change with the spreadsheet in release 4.0 is that it easily allows data to be entered, then imported to another view as a list, list of points, or matrix. This makes linear algebra more manageable.
The second, but more obvious change to the spreadsheet is the addition of tools for doing statistics on collections of data. These tools provide popup windows with visualizations and data for one, two, or more samples.
View 2:Pop-up tools (4.0) – Analysis of functions, with attention to probability and discrete math
Another shift with release 4.0 are a couple of tools that create their own popup display, giving information, but not creating objects in the standard views. The function inspector and probability calculator are two of these tools. (Along with the probability calculator, release 4.0 brings support for a substantial collection of probability distributions.)
View 3: CAS (4.2) – Symbolic mathematics, functions of other variables
< http://wiki.geogebra.org/en/Release_Notes_GeoGebra_4.2>
< http://wiki.geogebra.org/en/CAS_View>
< http://wiki.geogebra.org/en/CAS_Commands>
< http://wiki.geogebra.org/en/CAS_tools>
The CAS capabilities of GeoGebra have been growing under the hood for a while. It shows up in release 4.0 in the way algebraic descriptions are handled. In previous releases all formulas were converted to a decimal or integer approximation. With release 4.0, the algebra view is presented in TeX so surds are maintained. The under the hood CAS converted to Reduce, so it has significantly more power.
With Release 4.2 there is a full CAS window. It does have its own toolbar. It also has a slightly different syntax. As is typical with CAS, assignment is separated from equality. Thus x=y is an equation, while x:=y is an assignment. The links above give fuller notes.
(My favorite new features of 4.2 are the SlopeFields command, and the freehand tool, which allows a function to be defined by a freehand drawing.
At some level of development
View 4: GeoGebraWeb – (tablets, in alpha)
While this is still in alpha stage, it is the most exciting development in my book. The plan is to have a version of GeoGebra that runs on tablets and smartphones, which means that it runs without Java.
Some notes form the forum are worthwhile.
You can try it out here: http://www.geogebra.org/web
<http://www.geogebra.org/forum/viewtopic.php?f=48&t=26023>
GeoGebraTube has experimental support for showing applets in GeoGebraWeb. On devices without Java, it will automatically use GeoGebraWeb or you can force it to by adding ?mobile=true on the end of the URL, eghttp://www.geogebratube.org/student/m1302?mobile=true
In particular, if you have applets (or demonstrations) that only use one graphics window and don’t use a toolbar, then uploading them to GeoGebraTube makes them accessible to people using tablets. This is currently in alpha, so the interface may change on a daily basis.
View 5: 3-D view (5.0) -
< http://wiki.geogebra.org/en/Release_Notes_GeoGebra_5.0>
This is still a bit cumbersome, but the plan is to have a 3D window in release 5.0.
Once again, this release is evolving quickly. The view has its own list of tools. Many of the tools from the 2D window have analogs for the 3D window. We also get graphs of functions of two variables. Along with function graphs we have curves in space and parameterized surfaces.
View 6: Python (5.0) – Programming
< http://dev.geogebra.org/trac/wiki/Jython>
I have not yet played with this feature much,
View 7: Kinect view (5.0) – Recording human action
<http://www.geogebra.org/forum/viewtopic.php?f=22&t=25426>
This is another experimental feature that I have not played with. It does have great potential for fun, This would digitize live data and feed it into GeoGebra.