## Tuesday, June 28, 2011

### You are invited to a GeoGebra Seminar!

The University of the Philippines National Institute for Science and Mathematics Education Development (UPNISMED) will conduct a three-Saturday seminar-workshop on using GeoGebra in the teaching and learning of high school mathematics on August 6, 13, & 20, 2011 at UP NISMED. This is a first level seminar and will cover the basic tools of GeoGebra. Sample lessons, activities,  applets will be presented. The participants are expected to develop at least one activity/ GeoGebra applet for high school mathematics lessons as output.

## Sunday, June 26, 2011

### The Excess (or Missing) Area

Click the Play button at the bottom-left of the applet to animate. 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. Click the Pause button and refresh your browser.
2. What is the area of the square made up of the two triangles and two trapezoids?
3. Check the Assemble Manually check box to show the slider.
4. Set the slider $\alpha$ and $\beta$ to 90, and then a to 0 and e to 8. What is the area of the rectangle?
5. Can you explain why there is an excess area?

## Saturday, June 25, 2011

### What is a square?

A square is the locus of all the points in a plane for which the sum of the distances from two given perpendicular lines is constant. Drag point I to find out.

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)

If you want to know eleven more definitions of a square, go to my post Twelve Definitions of a Square posted in Mathematics for Teaching.

## Thursday, June 23, 2011

### Rectangle with Constant Perimeter

Move the dot on Slider A. 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)

## Sunday, June 19, 2011

### The Eutrigon Theorem

Move point B or point C. 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 central triangle with one angle equal to 60 degree is called a eutrigon. The areas of equilateral triangles constructed on the three facesobey the eutrigon theorem, which gives the area of the central triangle in terms of the areas of the other three triangles as shown in the illustration.

Reference: "The Eutrigon Theorem" from The Wolfram Demonstrations Project
http://demonstrations.wolfram.com/TheEutrigonTheorem/

## Tuesday, June 14, 2011

### The Pantograph

A pantograph is a mechanical linkage connected in a special manner based on parallelograms so that the movement of one pen, in tracing an image, produces identical movements in a second pen.

If a line drawing is traced by the first point, an identical, enlarged or miniaturized copy will be drawn by a pen fixed to the other. The pantograph was invented by Cristoph Scheiner.

## Monday, June 13, 2011

### Trisection of an Angle

The segment ΓΔ and the angle ΑΟΒ are moving with constant speed and agree with OA at the same time. The point Z is the section of segments OB and ΓΔ, and the red curve is the trace of Z. Using this curve we can find the trisects of an acute angle as seen in the applet.

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

theorhma.blogspot.com

## Saturday, June 11, 2011

### Visualizing Multiplication of Fractions

Drag slider m to determine the fraction m/10 and drag sliders n to determine the fraction n/10. The area of the overlapping rectangles is the product of the fraction.

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

## Wednesday, June 8, 2011

### Circles and Arbelos

The area of the circle determined by the tangent line to the two internal circles equals the area of the arbelos (the red area).

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

## Sunday, June 5, 2011

### Viviani's Theorem created with GeoGebra 4.0 beta

Viviani's theorem, named after Vincenzo Viviani, states that the sum of the distances from a point to the sides of an equilateral triangle equals the length of the triangle's altitude.

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 theorem can be extended to equilateral polygons and equiangular polygons. Specifically, the sum of distances from a point to the side lines of an equiangular (or equilateral) polygon does not depend on the point.

Text Source: Wikipedia