## 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.

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 .

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.

## 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 $y = a(x-h)^2 + k$.

## 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?