Thursday, August 23, 2012

Reflecting the Exponential Function

The red point is the reflection of the green point over the blue line. Move the green point 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
Guillermo P. Bautista, Created with GeoGebra

Questions


  1. What is the relationship between the coordinates of the points?
  2. If the coordinates of the green point are (x,y), what will be the coordinates of the reflected point? 
  3. If the green point and red point are connected with a line, what will be the relationship of that line to the line of reflection? 

Friday, August 17, 2012

Exploring Triangles

Triangle ACD and triangle BCD are equilateral triangles. 
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
Guillermo Bautista, Created with GeoGebra

Questions

  1. What can you say about triangle BCD and the red triangle? Move the slider confirm your answer.
  2. Change the shape of the triangle by moving point C, and use the slider to compare the triangles. Does your observation still hold?
  3. Make a conjecture about triangle ACE and triangle BCD
  4. Prove your conjecture. 
Snapshot

Thursday, August 16, 2012

Circle Area Approximation

Move slider r to change the length of the radius and move slider n to the extreme right. 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
Linda Fahlberg Stojanovska, August 2011, Created with GeoGebra

The applet above shows that as the number of divisions of a circle with radius r increases, the sectors can be arranged into a rectangle with base πr and base r

Snapshot



Wednesday, August 15, 2012

Parabola by Definition

Move point C 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
Guillermo Bautista, Created with GeoGebra

The green trace generated by point D is a parabola.  A parabola is the set of points equidistant from a given point (focus) and from a given point (directrix). In the applet above, point B is the locus and the red line is the directrix. 

Snapshot





Tangram Puzzle 1

Use the tangrams below to construct a square.  Drag the interior of the polygons to move them and drag the point 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
Guillermo Bautista, Created with GeoGebra

Snapshot

Sunday, August 12, 2012

Tracing the Sine Function

Move point C about the circle. Observe what happens to point P.

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
Guillermo Bautista, Created with GeoGebra

Questions
  1. What can you say about the lengths of segment CD and segment PE?
  2. What can you say about the distance of E from the origin? What is it equal to? 
  3. What do x and y represent in P(x,y)? 
  4. What do the traces of P represent? 

Friday, August 10, 2012

Dice Rolling Simulation

The applet below is a simulation of rolling of two dice. Click the Roll Dice button to roll the dice.  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
Guillermo Bautista Jr. , Created with GeoGebra

Do this 30 times and record the Sum. What do you observe? 

Thursday, August 9, 2012

Locating Pi on the Number Line

Move slider t to the extreme right 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 circumference of a circle with diameter 1 is approximately equal to 3.1416 or .

Sunday, August 5, 2012

Area Under the Curve

The applet below shows the relationship among the area under the curve, the lower sum, and the upper sum. As the number of rectangles (n) increases, the sum of the areas of the rectangles get closer and closer to the actual area under the curve.
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
Guillermo Bautista Jr. , Created with GeoGebra

The method of approximation above is called the Riemann Sum. It was named after Bernhard Riemann, a German mathematician. 

Angle Sum Theorem

Move points A, B, and C to choose the triangle size and shape you want.  Move sliders and  to the extremer right

  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
By Guillermo Bautista Jr. , Created with GeoGebra

  1. What do you observe about angles t, u and v
  2. What is the sum of  v, u, and t? Justify your answer. 
  3. Based on your observations above, what can you say about the sum of the interior angles of a triangle? Explain your answer. 
Snapshot


Wednesday, August 1, 2012

The Missing Area

Move sliders and to the extreme right and move sliders a and e to the extreme left. What do you observe? Where is the missing 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
By Guillermo Bautista Jr. , Created with GeoGebra