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. 

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:

Proof of the Difference Formula for Sine and of the Addition Formula for Cosine" from the Wolfram Demonstrations Project
 http://demonstrations.wolfram.com/ProofOfTheDifferenceFormulaForSineAndOfTheAdditionFormulaFor/

Contributed by: Izidor Hafner

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:

 Abraham Gadalla

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

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

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

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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