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.

- The tangent as the limit of secant lines.
- The slope of
tangents and the derivative of a function.

- The graph of a function and its first and second derivatives in the same window.
- The Differentiability
and
Continuity
applet gives a visualization of how these formal
limit definitions of these concepts connect with each other.

- 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.
- 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.
- The Taylor polynomial approximation of a function.
- 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

- The grapher applet
gives a simple graphing window with easy control over the viewing
window.

- The parametric grapher applet was written by Marc Renault of Shippensburg University. It has some nice javascript controls that interact with the applet.
- 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,

- 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.

- 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.

- 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.

- 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.
- 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.
- 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.

- 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.

- 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.

- 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.
- 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.
- 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.
- 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.
- 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.

- 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.
- 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.
- 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.
- The Pythagorean theorem
applets walks through a visual proof of the Pythagorean theorem.

- The construction of a line bisecting an angle
- The construction of the bisector of a line segment
- The construction of a line perpendicular to a segment from a point on the segment
- The construction of a line perpendicular to a segment from a point not on the segment
- The construction a line
through
a
given point parallel to a given line

- The construction of a segment that is an integer multiple of the length of a segment
- The division of a segment in an integer number of pieces, all of the same length.
- 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.

- A first proof of concept page shows how to drill students on plotting a point in Cartesian coordinates.
- A second page has students plotting a line given in general form.
- A third page has students plot a Sine curve from an equation.
- 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.

- 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.

- A box and whiskers applet explores the boxplot command which gives a box and whiskers diagram more on making divisions of the right size.
- 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.

- The 3D Prism applet plays with the uses matrices to explore being able to do rotations of 3D objects.
- 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

- 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.
- The Regular Polygon and Circle applet looks at constructions with sequences.
- The applet on constructing triangles and quadrilaterals has two copies of the applet running on the same page.
- 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.
- 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.
- 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.
- The ellipse sequence applet was created by António Ribeiro is a Math Teacher at Gondomar Secondary School (Portugal).
- 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,

- The visualizing eigenvectors applet was written by Marc Renault of Shippensburg University. Illustrates how the current release version uses matrices.

Return to the Applets for courses below calculus page.

Return to the Calculus Applet page.

Last updated By Mike May, S.J., July 31, 2010.