Saturday, April 30, 2011

SOF moved to a new URL

My other blog, School of Freebies, has moved to a new server and a new URL.

You may also want to check out my other blog Mathematics and Multimedia, home of more than 50 GeoGebra tutorials.

For a little history, GeoGebra Central was an offshoot of Math and Multimedia. I created it because Wordpress (host of Math and Multimedia) does not allow GeoGebra applet embedding.

Don't blame them. It's for security purposes. :-)

Friday, April 29, 2011

Thursday, April 28, 2011

Good news: Downloadable applets

Hi guys, this is to inform you that from now on, all applets that I will post will be available for download. I will look for the old files and upload them this weekend.  I will also encourage other contributors to do the same.

Thank you very much.

Tuesday, April 26, 2011

Folding a Hyperbola

Click the Play button at the lower-left corner of the applet and observe what happens.

The border of the locus of lines formed by the perpendicular bisector of the segment connecting  the point moving on the circle and the fixed point outside the circle forms a hyperbola. The applet below is the simulation of the activity below.


Sorry, the GeoGebra Applet could not be started. Please make sure that Java 1.4.2 (or later) is installed and active in your browser (Click here to install Java now)

Activity
  1. Draw a circle on a piece of paper.
  2. Draw a point outside the circle.
  3. Draw an arbitrary point on the circle.
  4. Fold the paper such that the at point on the circle and the point outside the circle are coinciding.
  5. Repeat steps 3-4 over and over again.
The creases in the paper will form a hyperbola. The construction above is the simulation of this activity.

Monday, April 25, 2011

Cycloid

One applet in wich you can see how the curve of cycloid is created.

Properties of cycloid:
  1. It is the curve of fastest descent under gravity.
  2. The period of an object in descent without friction inside this curve does not depend on the ball's starting position

Sunday, April 24, 2011

Shape properties of quadrilaterals resources from www.MathsMaster.Org

Two fantastic Geogebra applets have been included in the 'shape properties of quadrilaterals' resources on www.MathsMaster.Org. The first is a great activity where you have to drag the vertices of a quadrilateral to make different shapes, watching the angles and the side lengths change in real time. The second looks at the rotational symmetry properties of quadrilaterals.

View the Geogebra applets here.

Enjoy!

Parameters of Trigonometric Functions

Use the sliders to investigate the graph of the trigonometric function f(x) = a sin (bx - c) + d. Use the check boxes to show the graphs of the other trigonometric functions.


Sorry, the GeoGebra Applet could not be started. Please make sure that Java 1.4.2 (or later) is installed and active in your browser (Click here to install Java now)
This applet can be used to investigate the parameters a, b, c, and d, in the trigonometric functions with the following equations: f(x) = a sin (bx - c) + d, g(x) = a cos (bx - c) + d, and f(x) = a tan (bx - c) + d.

Wednesday, April 20, 2011

Circumcenter of a Triangle

Drag the vertices of the triangle and check the check boxes to investigate.


Sorry, the GeoGebra Applet could not be started. Please make sure that Java 1.4.2 (or later) is installed and active in your browser (Click here to install Java now)

In any triangle, a circle maybe drawn such that it passes through the three vertices of the triangle. This circle is called the circumcircle of the triangle. The intersection of the perpendicular bisectors is the center of the circumcircle. The center of the circumcircle is called the circumcenter.

GeoGebra Applet Central opens up for contributors

If you are a GeoGebra user, or a blogger that uses GeoGebra, and you want to promote your blog, I am inviting you to post some of  your applets here. Your applets will be credited to you, and if you have a blog or website, you are permitted to link back.  There is no pressure in your posting frequency. You can post once a month if you are too busy, or ten times a month if you have nothing to do.

You are encouraged (but not required)  to post K-12 mathematics applets.

 If you are interested, please contact me at mathandmultimedia@gmail.com.

***
Check out my other blogs: School of Freebies and Mathematics and Multimedia.

Monday, April 18, 2011

The Inscribed Angle Theorem

1.) Move the points on the circle. What do you observe?
2.) Explain why your observation will always be true for all angles.


Sorry, the GeoGebra Applet could not be started. Please make sure that Java 1.4.2 (or later) is installed and active in your browser (Click here to install Java now)

Theorem: If an inscribed angle and a central angle has the same intercepted arc, then the measure of the inscribed angle is half that of the measure of the central angle.

I have written a detailed proof of the Inscribed Angle Theorem in Mathematics and Multimedia.

Saturday, April 16, 2011

The Hypocycloid

In geometry a hypocycloid is a special plane generated by the trace of a fixed point on a small circle that rolls within a larger circle. It is comparable to the cycloid but instead of the circle rolling along a line, it rolls within a circle. To animate the circle, click the Play button located at the bottom-left of the applet.


Sorry, the GeoGebra Applet could not be started. Please make sure that Java 1.4.2 (or later) is installed and active in your browser (Click here to install Java now)

Creating a hypocycloid is included in the GeoGbra Intermediate Tutorial Series . It will be the next GeoGebra tutorial post

Thursday, April 14, 2011

Rectangle Area

Move the sliders that represent the base and the height of the rectangle. What do you observe?


Sorry, the GeoGebra Applet could not be started. Please make sure that Java 1.4.2 (or later) is installed and active in your browser (Click here to install Java now)


1.) What is the relationship between the base and the height of the rectangle to its shape?
2.) What is the relationship between the height, base, and the number of unit squares (area) of the rectangle?
3) What conjecture can you make based on your answers above?

Wednesday, April 13, 2011

Teaching coordinates of points

This applet is used in the lesson in the post Investigating coordinates from Teaching K-12 Mathematics


Sorry, the GeoGebra Applet could not be started. Please make sure that Java 1.4.2 (or later) is installed and active in your browser (Click here to install Java now)

Circle Approximation Graph

1.) Move slider r below to adjust the radius of the circle.
2.) Move slider n and observe what happens.
3.) 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


The area of a circle can be approximated by inscribing and circumscribing a polygon with n sides. As the number of sides of the inscribed/circumscribed polygon increases, their areas approach the area of the circle.

Monday, April 11, 2011

The Nine-Point Circle

Move the vertices of the triangle 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

The nine-point circle is the circle passing through the nine significant points defined from a triangle. It includes the midpoint of each side, the foot of each altitude, and the midpoints of the orthocenter and the three vertices.  

Error in Posting and New Blog Contributor

Hi guys. I have been trying to post applets since Saturday, but no luck so far (I always get an error). Maybe it's a GeoGebra bug. I'll email Michael Borcherds (Lead Developer) later.

By the way, I am welcoming another  new contributor of this blog, William Emeny of Great Maths Teaching Ideas. William Emeny is also a great GeoGebra fan.

Erlina Ronda, one of the contributors of this blog, has a new URL and a new name for her blog. She has named here new blog Teaching K-12 Mathematics.

All other GeoGebra users are welcome to contribute here. If you are interested, contact me at mathandmultimedia@gmail.com

Friday, April 8, 2011

Making Triangles from www.MathsMaster.Org

The following is a lovely activity to get pupils discussing triangle shape properties. This and many more fantastic Geogebra applets are available from www.MathsMaster.Org. The site also contains lots of excellent maths video tutorials and activities.


Sorry, the GeoGebra Applet could not be started. Please make sure that Java 1.4.2 (or later) is installed and active in your browser (Click here to install Java now)

Wednesday, April 6, 2011

Paper folding and proof

In this applet, we will show how to construct a quadrilateral by simulating the paper folding process.

Sorry, the GeoGebra Applet could not be started. Please make sure that Java 1.4.2 (or later) is installed and active in your browser (Click here to install Java now)


Questions:

1.) After step 1 (at p=3), what can you observe? What statements can you make?
2.) After step 2 (at p= 3 and q = 3), what can you say about the overlapping triangles?
3.) After step 3, what kind of quadrilateral is ABCD?  Justify your answer.

Centroid of a Triangle


  1. Drag the vertices or the sides of a triangle and observe what happens. 
  2. What do you observe?


Sorry, the GeoGebra Applet could not be started. Please make sure that Java 1.4.2 (or later) is installed and active in your browser (Click here to install Java now)

The centroid of the triangle is the point where its three medians meet. The median is the segment connecting the vertex and the midpoint of the side opposite to it.

I have a tutorial  on how to locate a triangle centroid. You may want to check it out.

Sunday, April 3, 2011

What's New

Hi everyone. This blog has been quite inactive in the past, but I will try my best to create more applets in the future. As you can see, we have a lot of new stuff:

  1. I have created five more tabs: Post List, Top Posts, Blogroll, Links and Tutorials. The tutorials contains links of more than 50 tutorials I have written in Mathematics and Multimedia, my main blog.
  2. I have created a Facebook page. You can Like it and follow from there. It automatically posts GeoGebra Applet Central's articles.
  3. I have created the GAC Twitter account which means that you can now follow GAC on Twitter.
  4. There is also and email subscription box located at the side bar and you can also now subscribe to  GAC's rss feed
  5. If you plan to follow my three blogs(including School of Freebies), you can add me up on Facebook (mathandmultimedia@gmail.com). The linked account contains the feeds of all the three blogs
I am opening GeoGebra Applet Central for collaboration. If you have a Google account, I am inviting you to contribute your applets. Of course, they will be credited to you. If you are interested contact me at mathandmultimedia@gmail.com

Friday, April 1, 2011

Addition of Integers


Sorry, the GeoGebra Applet could not be started. Please make sure that Java 1.4.2 (or later) is installed and active in your browser (Click here to install Java now)