# GeoGebra Applets

GeoGebra is a GNUed software package for mathematics visualization.  The home for the applications is http://www.geogebra.org.

Educational material for GeoGebra is available at http://www.geogebra.org/en/wiki

The following are some Applets pages I have either created with the software or downloaded from the wiki.

Some of the applet pages look at standard constructions from calculus, making the pictures dynamics and subject to manipulation by the instructor.
1. The tangent as the limit of secant lines.
2. The slope of tangents and the derivative of a function
3. The graph of a function and its first and second derivatives in the same window.
4. The Differentiability and Continuity applet gives a visualization of how these formal limit definitions of these concepts connect with each other.
5. The Newton's Method page illustrates the use of tangent lines to find roots of functions.  It also gives examples where the technique fails.  A variation of this is the Newton-Raphson page which uses a different technique with sequences.
6. The Riemann sum applet was written by Pascal Coubard of Lycée Professional France.  It compares various Riemann sums to the integral.  It illustrates the use of functions on lists and other list functions that are int he pre-release.
7. The Taylor polynomial approximation of a function.
8. The barcos applet was written by Rafael Losada in Spain.  It looks at the classical problem of asking if two objects with crossing paths will collide.  It has some nice graphics and a second position grid with dramatic ship sinkings
Some of the applets are simple graphers in an appropriate context:
1. The grapher applet gives a simple graphing window with easy control over the viewing window.
2. The parametric grapher applet was written by Marc Renault of Shippensburg University.  It has some nice javascript controls that interact with the applet.
3. The polar grapher applet was written by Marc Renault of Shippensburg University.  It has some nice javascript controls that interact with the applet.

Some pages look at precalculus material to allow a quick review,
1. The Linear Equations page connects the normal ways of defining a line, either by giving two points, or by giving a point and a slope, or by giving the slope and intercept.  Each window connects a set of information with a line and derives the other presentations of the line.
2. The Quadratic Equations applet allows you to make connections between the graph of a quadratic function, and various ways to write the equation, focusing either on roots or the vertex of the parabola.
3. Conic Sections - The Ellipses and Hyperbolas applet lets you specify a conic section by specifying the length from the center to a vertex on the major axis and the length to a focus.  You get either an ellipse or a hyperbola, depending on which length is bigger.  A second Ellipse Applet uses the "string construction" and looks at the points from which the sum of the distances to the foci is fixed.  The Parabolas applet looks at Parabolas defined by a focus and a directrix.  The General Conic Sections applet lets you explore the graph of a quadratic relation in general format.
4. Graphs of related functions -The family of curves applet lets you graph a function with three parameters and then vary those parameters with a slider.  The Translations and Compressions Applet lets you compare the graph of a function with the graph of a function transformed by translations and compressions or expansions.
5. Trigonometric Functions - The Unit Circle applet reviews the sin and cos functions with regard to the standard angles of the unit circle.  Measurements are given in degrees and radians for the angles and decimal and root form for the coordinates.  The Trig Review applet connects the values of the 6 basic trig functions with segments on the unit circle.  The Sin Curve Fitting applet lets you fit a sinusoidal curve to a pair of specified points.
6. The Lissajous figure applet applet was produced by Miguel Bayona at the Lawrenceville School.  It is part of his larger mathplotter site which has a nice collection of math applets.
7. The spirograph applet was written by Marc Renault of Shippensburg University.  Like the child's toy of the same name, it allows exploration and makes pretty pictures.
8. The level curves applet was written by Marc Renault of Shippensburg University.  It does families of curves and can be used to show how general quadratic equations turn into conic.
Some of the applet pages look at standard results in the construction of triangles.
1. The side-side-side applet, lets you construct a triangle by specifying the lengths of the three sides.  If such a triangle can be constructed, it is unique.
2. The side-angle-side applet, lets you construct a triangle by specifying the lengths of two of the sides and the included angle.  If such a triangle can be constructed, it is unique.
3. The angle-side-angle applet, lets you construct a triangle by specifying the lengths of two of the sides and the included angle.  If such a triangle can be constructed, it is unique.
4. The side-side-angle applet, lets you construct a triangle by specifying the lengths of two of the sides and an non-included angle.  If such a triangle can be constructed, it may not be unique.
5. The angle bisector applet looks at the theorem that the three angle bisectors of a triangle all meet in a single point.  The first frame lets the student explore the result with various triangles.  A second construction adds details that give a framework for a proof.  A Student angle bisector applet walks the student through their doing construction by giving rolling instructions.
6. The side bisector applet looks at the theorem that the three perpendicular bisectors of the sides of a triangle all meet in a single point.  The first frame lets the student explore the result with various triangles.  A second construction adds details that give a framework for a proof.
7. The concurrent medians applet looks at the theorem that the three medians of a triangle all meet in a single point.  The first frame lets the student explore the result with various triangles.  A second construction gives a framework for establishing a lemma about tiling an area with congruent triangles.  The third construction uses the lemma to adds details that give a framework for a proof.
8. The concurrent altitudes applet looks at the theorem that the three altitudes of a triangle all meet in a single point.  The first frame lets the student explore the result with various triangles.  A second construction adds details that give a framework for a proof.
9. The Pythagorean theorem applets walks through a visual proof of the Pythagorean theorem.
One page collects standard Ruler and Compass constructions.  These include:
1. The construction of a line bisecting an angle
2. The construction of the bisector of a line segment
3. The construction of a line perpendicular to a segment from a point on the segment
4. The construction of a line perpendicular to a segment from a point not on the segment
5. The construction a line through a given point parallel to a given line
6. The construction of a segment that is an integer multiple of the length of a segment
7. The division of a segment in an integer number of pieces, all of the same length.
8. The Ruler and Compass applet is written to illustrate how the toolbar can be modified to give students access to a mode limited set of tools.
Marc Renault of Shippensburg University showed how GeoGebra can be used to generate random questionswith feedback for doing studnet drills.  These are some pages that use that approach:
1. A first proof of concept page shows how to drill students on plotting a point in Cartesian coordinates.
2. A second page has students plotting a line given in general form.
3. A third page has students plot a Sine curve from an equation.
4. A fourth page has the student produce the equation of a Sine curve from the graph.

With release 3.2, GeoGebra has some nice capabilities for demonstrating basic statistics.
1. The Random Numbers and Spreadsheets applet looks at how random numbers can be set to regenerate when a value is changed.  This applet also illustrates best fit curves and the use of a spreadsheet.
2. A box and whiskers applet explores the boxplot command which gives a box and whiskers diagram more on making divisions of the right size.
3. A statistics demo worksheet looks at a number of the statistics commands.

Some of the pages are of interest to explore some of the features of GeoGebra.

1. The 3D Prism applet plays with the uses matrices to explore being able to do rotations of 3D objects.
2. The prism applet was written by Lucio Ferrari, SM Pregassona, Switzerland.  It allows you to unwrap a right polygon prism and illustrates working with 3D objects
3. The pyramid applet was written by Lucio Ferrari, SM Pregassona, Switzerland. It lets you rotate the image of a pyramid in 3-space.  It includes a number of tools and uses the feature of multiplication of matrices on a list.
4. The Regular Polygon and Circle applet looks at constructions with sequences.
5. The applet on constructing triangles and quadrilaterals has two copies of the applet running on the same page.
6. This Blank GeoGebra page applet opens with a blank page, but double clicking on the page launches the application on your machine.  From there you can make clean constructions and save them yourself.
7. The butterfly applet was written by Mohamed Alsayes of the Emirates College for Advanced Education in the UAE.  It gives a pretty picture but also illustrates how you can change colors in an objects based on a variable value.
8. The clock applet was written by Mohamed Alsayes of the Emirates College for Advanced Education in the UAE.  It illustrates putting a picture into an applet.
9. The ellipse sequence applet was created by António Ribeiro is a Math Teacher at Gondomar Secondary School (Portugal).
10. The Circle intersection applet was created by António Ribeiro is a Math Teacher at Gondomar Secondary School (Portugal).  It illustrates the use of a tool that was created by the user to simplify a complicated construction,
11. The visualizing eigenvectors applet was written by Marc Renault of Shippensburg University.  Illustrates how the current release version uses matrices.