## Tuesday, January 31, 2012

### Sum of Vectors

This applet shows the graphical represenentation of the sum of two vectors. In the graph, u and v are vectors, and w = u + v. BD is the translation of AC and CD is the translation of AB. AD represents the sum of the vectors.
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

## Friday, January 27, 2012

### Math and Multimedia Carnival will be hosted here

The Mathematics and Multimedia Carnival is on its 20th edition and will be hosted here.  If you have a blog post about school mathematics, mathematics teaching and learning, multimedia tools, or any related article, you may submit here or email me directly at mathandmultimedia@gmail.com.  The deadline of submissions is on February 18, 2012 and the post date is on February 20.

You may want to visit the following recent math carnivals:
To those who do not know what a carnival is, I have written a carnival primer in Math and Multimedia

## Wednesday, January 25, 2012

### Deriving the Equation of the Parabola

Instructions: Move point A to adjust the position of the vertical line and move F along the x-axis as desired. Move C along the line 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

Questions
1. What can you say about line a in relation to C and F?
2. Make a conjecture about segments PC and PF.
3.) Suppose P has coordinates (x,y), F has coordinates (2,0), and line d has equation x = 2, write the equation that would describe your conjecture in 2.
4.) Generalize the equation in 3 by changing the coordinates of F to (a,0) and line d has equation x = -d. Find the value of y.

## Friday, January 20, 2012

### Tangram Puzzle: Constructing a Square

Move the tangrams to construct a square. Drag the interior to change their position and use the 'blue point' on the vertex to rotate.
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

## Tuesday, January 17, 2012

### Squaring a Convex Polygon

This applet constructs a triangle with an area equal to the area of any convex polygon ABCDEF. The applet Squaring a Triangle shows how any triangle can be transformed to a square with an equal area. The combination of these two constructions shows how to square any convex polygon.

• Click on point F.
• Drag F to the right as far as it can go.
• Repeat these two steps three times, until the triangle is constructed.
To repeat the construction,  press the "Reset" button or click again on the vertex F of the triangle.

Author:    The Ohio State University at Lima

## Monday, January 16, 2012

### Squaring a Triangle

This applet shows the construction of a square with the same area as a given triangle.
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

Author: Irina Boyadzhiev of Ohio State University.

## Monday, January 9, 2012

### 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 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.

## Thursday, January 5, 2012

### Equation of a Circle

Move sliders h, k, and r to form the desired circle.

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 shows that a circle can be determined given a center (h,k) and a radius r.

## Monday, January 2, 2012

### Routh's Theorem

Move ABC to determine the shape of a desired triangle and move the slider. What do you observe?
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 Routh's theorem determines the ratio of areas between a given triangle and a triangle formed by the intersection of three cevians. The theorem states that if in triangle ABC points DE, and F lie on segments BCCA, and AB, then writing $\tfrac{CD}{BD}$ x $\tfrac{AE}{CE}$ y, and $\tfrac{BF}{AF}$ z, the signed area of the triangle formed by the cevians ADBE, and CF is the area of triangle ABC times $\frac{(xyz - 1)^2}{(xy + y + 1)(yz + z + 1)(zx + x + 1)}.$
This theorem was given by Edward John Routh on page 82 of his Treatise on Analytical Statics with Numerous Examples in 1896.

Source: Wikipedia