## 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?
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.

## Monday, November 28, 2011

### The Parallel Postulate

In the figure below, AB and CD are parallel lines. EF is a transversal.
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 parallel postulate states that given two parallel lines (on the same plane) and a transversal, their corresponding angles are congruent. Using this postulate as shown above, determine the measure of the other angles and record your observations. Make a conjecture about them.

## Thursday, November 24, 2011

### GeoGebra Graphics 2 and the Sine and Cosine Functions

Move the point on the circle in the left window (Graphics 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

This applet demonstrates how to use Graphics 2 of GeoGebra. Graphics 1 shows the distances on the circle: distance traveled (a)  by a point about the circle from (1,0), it's distance from the x-axis (b), and its distance from the y-axis (c).

Graphics 2 shows the two points with coordinates (a,b) and (a,c). The traces of the points in Graphics 2 forms the graph of the sine function and the consine function from 0 to pi.

## Monday, November 21, 2011

### The Mean Proportion

Move point Q and observe what happens.

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
In the figure, PSR is a semi-circle and with PR as the diameter.  Given a rectangle with side QR, and a triangle PSR, a square is formed using its height. The  square has the same are as the rectangle.

## Thursday, November 17, 2011

### GeoGebra 4.0 Tutorials and more...

This is to inform everyone that I am currently updating my GeoGebra Tutorials in Mathematics and Multimedia. I have updated the following tutorials so that they are compatible to GeoGebra 4.0.

I will be updating three or more tutorials this weekend. If you are new to GeoGebra, I have created more than 50 GeoGebra tutorials categorized as follows.

Please share the tutorials to people who might be interested.

## Tuesday, November 15, 2011

### Polygons and Tessellation

Move the slider and observe what happens.
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. Which of the regular polygons tessellate? Can you explain why they do?
2. As n increases can we can find a regular polygons that tessellate?
• If yes, how many of them can be found? Are they finite?
• If no, what is the maximum number of side of a polygon that can tessellate? Why?

If you want to know more about tessellation, you may want to check out the following articles that I have written:

## Wednesday, November 9, 2011

### van Aubel's Theorem

Squares are placed outwardly at each side of quadrilateral ABCD. The center of the squares on the opposite sides are connected with segments (PN and MO). Move points A, B, C and D and observe what happens. Make a conjecture about your observations.

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

Van Aubel's Theorem

Given an arbitrary planar quadrilateral, place a square outwardly on each side, and connect the centers of opposite squares. Then van Aubel's theorem states that the two lines are of equal length and cross at a right angle.

## Sunday, November 6, 2011

### GeoGebra 4.0 offline installer, now available

If your PC/Mac is not always connected to the internet, or you have a computer laboratory with no internet connection, you can now download the GeoGebra 4.0 offline installer.

GeoGebra 5.0 Beta is also in development

## Thursday, November 3, 2011

### Area of a Trapezoid

Move point A to change the shape of the trapezoid.  Then move slider $\alpha$ to the extreme right to rotate the trapezoid.

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.) What kind of quadrilateral  is formed when $\alpha$ equals 180 degrees? Justify your answer.
2.) What is the relationship between the area of trapezoid ABCD and the area of the quadrilateral formed in 1?
3.) Using the quadrilateral formed in 1, find the area of the trapezoid. Hint: Use $b_1, b_2$ and $h$.

## Wednesday, November 2, 2011

### Testing Post - Social Network Integration

Recently, GeoGebra Central's automatic feed to Facebook and Twitter stopped. I am currently troubleshooting so please ignore this post.

## Saturday, October 29, 2011

### GeoGebra 4.0 now available

This is a repost from Math and Multimedia, my main blog.
The long awaited  GeoGebra 4.0 is now available online. The Webstart files and Applet Start can be are fully functional.  Hopefully the offline installers will be available soon.
Some of the new features according to the website (haven’t explored all of them yet) are the following:
• GeoGebraTube: easily share worksheets online (see “File” menu)
• User interface: drag & drop, style bar, perspectives, accessibility
• New tools: data analysis, chart dialog, probability calculator, function inspector
• Copy & Paste, two Graphics views
• Inequalities and implicit equations
• Improved text tool, better equation displaying
• Filling options with hatching and images
• Animation of points on lines, dynamic limits for sliders & axes
• Buttons, input boxes, scripting
• Export to animated GIF
• 50 languages
To know more about the other features, go to the GeoGebra 4.0 Release Notes and the updated GeoGebra Manual. The GeoGebra Prim, the version for younger students is also now available.
I will be revising my GeoGebra tutorials soon to make them compatible with the new version.