Saturday, December 31, 2011

Top 20 Posts for 2011

It's year end again. This year, I together with other guest bloggers  have created more than 100 applets this year.  The top 20 posts are shown below.


  1. Circle Approximation Graph
  2. Embedding GeoGebra Applets in Wordpress
  3. The Pantograph
  4. Approximating Pi
  5. GeoGebra 4.0 release candidate and GeoGebra 4.2
  6. Approximating the area of a circle
  7. Graphing Piecewise Function
  8. Triangle Angle Sum Proof
  9. Centroid of a Triangle
  10. Circumcircle of a Triangle
  11. Graphs and Their Properties
  12. Ferris Wheel
  13. The Dancing Triangle
  14. Pythagorean Theorem
  15. Triangles and Quadrilaterals
  16. Paper Folding and Proof
  17. Visualizing Multiplication of Fractions
  18. Folding a Hyperbola
  19. Tracing the Ellipse
  20. Viviani's Theorem
If you want to become a contributor of this blog, just email me at mathandmultimedia@gmail.com. You may also want to visit my two other blogs - Math and Multimedia and School of Freebies

Have a happy new year to all. 

Wednesday, December 21, 2011

Sine Difference Formula and Cosine Addition Formula

This applet shows a proof of the difference formula for sine,  and a proof of the addition formula for cosine,  using the formula .

This is a Java Applet created using GeoGebra from www.geogebra.org - it looks like you don't have Java installed, please go to www.java.com


Reference:

Contributed by: Izidor Hafner

Monday, December 19, 2011

Minimum Area

Move the slider and observe the graph. 

This is a Java Applet created using GeoGebra from www.geogebra.org - it looks like you don't have Java installed, please go to www.java.com

The figure shows a semicircle of radius one and a horizontal line parallel to the diameter. What central angle corresponds to the minimum shaded area? This problem can be solved by either integration or trigonometry. The shaded area is equal to , where  is the central angle. The minimum shaded area occurs when the central angle is .


Download GGB File


Source:

"Minimum Area between a Semicircle and a Rectangle"
 http://demonstrations.wolfram.com/MinimumAreaBetweenASemicircleAndARectangle/
 Wolfram Demonstrations Project
 Published: July 1, 2011

Sunday, December 18, 2011

Java having trouble again?

I'm not really sure but for some reason GeoGebra Central does not load in two computers that I'm using. I wanted to post since last week, but I can't preview the applets. I'll see if I can post tomorrow using another computer.

Happy holidays everyone. 

Monday, December 12, 2011

Constructing triangles given the side lengths

Move AD, BE and CF to determine the side length of the triangle.
1 This is a Java Applet created using GeoGebra from www.geogebra.org - it looks like you don't have Java installed, please go to www.java.com
1.) Use the segment to construct the following triangles:
 a.) equilateral
 b.) scalene
 c.) isosceles
 d.) right

2.) Construct a triangle with side lengths 2, 2, and 4. What do you observe?
3.) Explain why your observations are such.

Download GGB file

Tuesday, December 6, 2011

The Parabola in Vertex Form


  1. Move sliders a, h, and k. What do you observe? 
  2. How are a, h, and k relates to the graph's movement? 
  3. Make a generalization about the relationship between the parameters a, h, and k and the movement of the appearance of the graph.

This is a Java Applet created using GeoGebra from www.geogebra.org - it looks like you don't have Java installed, please go to www.java.com

The parabola has vertex form .

Download GGB File


Sunday, December 4, 2011

You can now Like GeoGebra Applet Central on Facebook

You can now like GeoGebra Applet Central on Facebook. You can use the box below or the box  is located at the upper right part of the page.





You can also follow GAC on Twitter and Friendfeed. You can also subscribe to GACs Feedburner feeds

Friday, December 2, 2011

Rectangle-Triangle Area Relationship

Consider the rectangle and the triangle below.

  1.  What do you observe? What are common properties between the two polygons?
  2. Drag point D to change the height of the triangle and drag point A or B to change the length of the base. What do you observe?
  3. What can you say about the areas of the two figures? Justify your answer. 
  4. Click the Show Areas check box in the applet.  Was your answer in 3 correct? 
  5. Drag point E. What is the relationship between the area of the rectangle and the area of a triangle? Explain why this is so. 

This is a Java Applet created using GeoGebra from www.geogebra.org - it looks like you don't have Java installed, please go to www.java.com
The applet above demonstrates that the area of a triangle is half the area of a rectangle with the same base and height.

Download GGB file