My High School Mathematics Teacher would have loved the above interactive page for teaching Calculus.
Instead of having to hand-draw lots of Tangents on a whiteboard, the blue dot on the Parabolic curve can be dragged along, (by clicking on it and holding down the mouse button on the blue “T” dot), and it traces out the blue derivative straight line as we move the Tangent along the curve. (Keep going backwards and forwards with the tangent "T", until the straight line is nice and thick and clear).
Absolute Magic and sheer delight for math nerds like me !
But unfortunately no fun on Apple devices. The iPad fails to deliver yet again, because GeoGebra runs Java applications, and Apple devices don't do Java. Why any school would want to used IPads, and not wait for Android Java and Flash enabled tablets to be available, or just use Laptops, just doesn't make sense.
Click the link below to try out this interactive screen at the GeoGebra site:
(Note that it can take a minute or two for all of the Java to load in).
Use the web browser's back button to return to this Blog.
Do the "Tangent" Interaction at the GeoGebra Website
GeoGebra is officially at : http://www.geogebra.org , but the list in English of all the free resources is actually in their Wiki at:
http://www.geogebra.org/en/wiki/index.php/English .
Here is how the GeoGebra site describes itself :
"GeoGebra is a dynamic mathematics software for all levels of education that joins arithmetic, geometry, algebra and calculus. On the one hand, GeoGebra is an interactive geometry system. You can do constructions with points, vectors, segments, lines, conic sections as well as functions and change them dynamically afterwards. On the other hand, equations and coordinates can be entered directly. Thus GeoGebra has the ability to deal with variables for numbers, vectors and points, finding derivatives and integrals of functions and offers commands like Root or Extremum. These two views are characteristic of GeoGebra: an expression in the algebra view corresponds to an object in the graphics view and vice versa”
(The web pages run Java applets to make this happen, and so there could be occasional security blocking issues on some school networks, but at home on the web it all works fine. Eg. At home simply click Yes or OK when your browser asks if it is ok to trust and run the Java).
There are many great interactive resources at GeoGebra.
Here is one, where the equation of a Circle can be manipulated, and the Circle auto re-draws, and can also be transformed into ellipses.
Eg. We can double click in the top left hand corner, where the circle's algebra equation is, and add number values in front of the x-squared, and y-squared, to graph elliptical shapes. (We can also edit the radius "r" value).
Click the link below to try out the Circle interactive screen at the GeoGebra site:
(Note that it can take a minute or two for all of the Java to load in).
Use the web browser's back button to return to this Blog.
Do the above "Circle" Interaction at the GeoGebra Website
Finally, here is another GeoGebra resource that is good for practicing the geometrical shapes of the different Quadrilaterals: Square, Rectangle, Rhombus, etc.
Click the link below to try out the Quadrilaterals interactive screen at the GeoGebra site:
(Note that it can take a minute or two for all of the Java to load in).
Use the web browser's back button to return to this Blog.
Do the "Quadrilaterals" Interaction at the GeoGebra Website
And so that is just some of GeoGebra; it's great for maths classroom demonstrations, and for students to use as well. Remember to always use this link to the Wiki, to get to the full list of interactive resources that are in English language: http://www.geogebra.org/en/wiki/index.php/English .
If you want to make your own GeoGebra resources, then you can join the community, and download the "How to Build Stuff" software onto your PC. learn how to use it, and contribute to the community. I have not yet investigated this aspect of GeoGebra. There are so many useful resources already made, and ready to go, that I have not actually been able to think of something I could add to the collection.
Finally, a couple of my favorite Geometry jokes:
Q. What did the Square do when he missed the last train home ?
A. He caught the Rhom Bus !
Q. What happened to the cute angle after she went out Night-Clubbing ?
A. She came home a wrecked angle !
Enjoy,
Big Passy Wasabi
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