Square Rectangle Tessellation

The applet below is another tessellation. It is composed of rectangles and equilateral triangles. It is one of the demiregular tessellations.
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

Hexagon Triangle Tessellation

Move Points A and B to explore the figure. Explain why the figure tessellates. 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 tessellation above is one of the 8 semi-regular tessellations. Semi regular tessellations are regular tessellations of the plane by two or more convex regular polygons such that the same polygons in the same order surround each polygon vertex are called semiregular tessellations, or sometimes Archimedean tessellations.

Weisstein, Eric W. "Semiregular Tessellation." From MathWorld--A Wolfram Web Resource. http://mathworld.wolfram.com/SemiregularTessellation.html

Area of Triangles Under a Curve

Given: Right triangle BCD whose hypotenuse is tangent to the function f(x) = a/x. 

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. Move slider a and observe what happens? How is the appearance of the graph relate to a?
2. Move point A and observe the triangle? What do you observe?
3. What conjecture can you make based on your observation in 2. Prove your conjecture. 

Download GGB file

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

The Kite Polygon

Move points A, D, or O to change the shape and position of the kite.

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A kite is a parallelogram whose four sides can be grouped into two pairs of equal-length sides that are next to each other.

Download GGB file

Embedding GeoGebra Applets in Wordpress

I created this blog to accommodate the GeoGebra applets I used in Mathematics and Multimedia. Math and Multimedia was created using Wordpress.com and was later migrated to a hosted Wordpress blog. Despite the transfer, I still had difficulty in embedding GeoGebra applets until recently Micky Bullock wrote a tutorial about it.

My colleague, Erlina Ronda of Mathematics for Teaching, one of the contributors of this blog, discovered another way. I have written a tutorial about her discovery here.

Math and Multimedia houses more than 50 GeoGebra step by step tutorials, the most current of which is the GeoGebra 4.0 sneak peek series. 

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.

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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.

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.

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

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.

Addition of Integers

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Activity for constructing quadrilateral with equal areas

This is one of the activities on problem solving involving quadrilaterals posted at Keeping Mathematics Simple. Click here to read the post.

Task
Move F. Describe the path it traces.
Explain or prove that the quadrilaterals formed have equal areas.
Write a procedure for constructing quadrilaterals with equal area using compass and straight edge.





















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)

Graphing Piecewise Function

This is the output file of step-by-step GeoGebra Tutorial 32 - Graphing Piecewise Functions from Mathematics and Multimedia.

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Equilateral Triangle

Drag the vertices of the equilateral triangle below.

1. What do you observe?
2. Can you think of other ways of creating an equilateral triangle?

Notes:

1. Click here to download the ggb file.
2. Click here to read the step-by-step tutorial.
3. Click here to go to the Mathematics and Multimedia GeoGebra Tutorial Series.
4. Click here to go to Mathematics and Multimedia

Quadrilaterals and Midpoints

1. Use the Move tool (leftmost tool) to move the vertices of the quadrilateral. What do you observe?
2. Use the Distance tool to find the distance between the points and move the points. Do your observations hold true?
3. What conjecture can you make based on your observations?
4. Select the Angle tool (right button) and click the interior of the polygon. Does your conjecture still hold?
5.  Challenge: Prove your conjecture.

Notes:

1. Click here to download the ggb file.
2. Click here to read the step-by-step tutorial.
3. Click here to go to the Mathematics and Multimedia GeoGebra Tutorial Series.
4. Click here to go to Mathematics and Multimedia