tag:blogger.com,1999:blog-85395825869932607322025-07-28T22:12:32.005+08:00GeoGebra Applet CentralFree and downloadable GeoGebra applets for math teachers, students, and enthusiasts.Anonymoushttp://www.blogger.com/profile/18132845314578313766noreply@blogger.comBlogger196125tag:blogger.com,1999:blog-8539582586993260732.post-35224771943042421362015-12-09T12:14:00.000+08:002015-12-09T12:28:52.514+08:00Christmas Wreath
Drag the sliders to create different Christmas wreaths.
Irina Boyadzhiev, Dec.8, 2015, Created with GeoGebra
Download appletUnknownnoreply@blogger.com0tag:blogger.com,1999:blog-8539582586993260732.post-16889385891666562482015-04-19T11:56:00.001+08:002015-04-19T12:09:15.403+08:00On the Geometric Definition of EllipseThe applet demonstrates the following:
An ellipse is the set of all points in the plane, the sum of whose distances to two fixed points (foci) remains constant.
Select the length of a piece of string by dragging the endpoints of the blue segment.
Drag the orange point to select the position of the focus F1 along the x-Axis or the y-Axis. The other focus F2 is symmetrical to F1 with Unknownnoreply@blogger.com0tag:blogger.com,1999:blog-8539582586993260732.post-80766499574849124942015-01-10T01:49:00.000+08:002015-01-17T23:08:37.591+08:00Radians, Number Line and the Unit CircleThis applet demonstrates the correspondence between the points on the number line and the points on the unit circle.
Enter a real number in the “step” input box. Try the applet with whole numbers, fractions, multiples or fractions of pi. (Example: pi/4)
Select “Wrap Positive Numbers” or “Wrap Negative Numbers”.
Notice, you have to deselect one checkbox in order to be able to select the Unknownnoreply@blogger.com0tag:blogger.com,1999:blog-8539582586993260732.post-79773975966899969682014-04-17T22:34:00.001+08:002014-04-19T01:24:38.131+08:00Applet on Counting the Number of Squares in a Chessboard
This applet models how to count the number of squares in the chessboard.
UP NISMEDhttp://www.blogger.com/profile/02022887344285868484noreply@blogger.com0tag:blogger.com,1999:blog-8539582586993260732.post-65102686446915681662014-02-10T08:47:00.000+08:002014-02-10T08:47:56.390+08:00Midsegmens and Congruent TrianglesA midsegment of a triangle is a segment that connects the midpoints of any two sides of the triangle.
This applet demonstrates that the three midsegments of any triangle divide the original triangle in four congruent triangles.
The demonstration is based on the following properties:
The midsegment is parallel to the third side of the triangle.
Any parallelogram has a rotational symmetryUnknownnoreply@blogger.com1tag:blogger.com,1999:blog-8539582586993260732.post-29242343863363316882014-01-29T11:20:00.000+08:002014-01-29T11:39:06.481+08:00The Area of the Median Triangle - Dynamic ProofLet ABC be a given triangle. The triangle with sides equal to the medians of ABC is called the Median Triangle.
We will show that the area of the median triangle is 3/4 of the area of the original triangle ABC.
Drag the two sliders to the end to construct the median triangle by translating the medians.
To rearrange the area of the median triangle:
Click the Rearrange checkbox. This will Unknownnoreply@blogger.com0tag:blogger.com,1999:blog-8539582586993260732.post-30395562503949580642013-12-13T05:39:00.001+08:002014-01-29T11:37:32.220+08:00Pythagorean Theorem
Irina Boyadzhiev, 13 December 2013, Created with GeoGebra
Download applet
Irina Boyadzhiev's GeoGebra Applets Unknownnoreply@blogger.com0tag:blogger.com,1999:blog-8539582586993260732.post-50420978932277323642013-10-03T01:04:00.000+08:002014-01-28T05:10:21.128+08:00Vertical Line TestThis applet can be used to determine whether one relation is a function or not by using the Vertical Line Test.
The Vertical Line Test says that if some vertilcal line meets the graph in more than one point then the relation is not a function.
In the input box enter a polynomial equation of x and y in the form "polynomial = number".For example, to graph y = x2, enter y - x2 = 0
DragUnknownnoreply@blogger.com0tag:blogger.com,1999:blog-8539582586993260732.post-85598177809906224202013-09-26T09:58:00.000+08:002014-01-26T09:51:46.020+08:00Inverse FunctionThis applet can be used to study inverse functions.
Enter a function of x in the input box f(x).
Set the domain of the function by dragging the endpoints of the blue line at the bottom of the window.
Click on the “Horizontal Line Test” and drag the vertical slider. Is f(x) a one-to-one function?
Click on the “Reflect f(x)” button.
Drag the horizontal slider to run the Vertical Line Test. Is theUnknownnoreply@blogger.com0tag:blogger.com,1999:blog-8539582586993260732.post-77147553250448553362013-09-20T01:25:00.004+08:002014-01-26T10:03:14.871+08:00 Horizontal Line TestThis applet can be used to determine whether a function is one-to-one or not, and also to restrict the domain to some interval where the function is one-to-one.
Enter a function of x in the input box.
Drag the vertical slider up or down (or press the Play button) to find the intersecting points of the graph and the horizontal line.
To see the x-coordinates of the intersection pointsUnknownnoreply@blogger.com0tag:blogger.com,1999:blog-8539582586993260732.post-55301826384505386612013-05-02T07:16:00.000+08:002014-01-26T10:07:59.748+08:00The Sum of the Cubes of the First N Natural Numbers Dynamic Geometric ProofThis applet shows a dynamic geometric proof of the formula for the sum of the cubes of the first n natural numbers.
Drag the slider “NumberCubes” to create up to seven cubes.
Think of each cube as a collection of n nxn square layers of unit cubes. To find a formula for the sum of the cubes of the first natural numbers we will rearrange the square layers.
Drag the slider “Rearrange” or pressUnknownnoreply@blogger.com0tag:blogger.com,1999:blog-8539582586993260732.post-8397225107714105672013-04-15T09:00:00.000+08:002013-04-15T09:00:00.118+08:00Octagon to Square Dissection
The applet below shows the octagon to square dissection.
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
Reference:
"Bennett's Octagon-to-Square Dissection" from the Wolfram Demonstrations Project
http://demonstrations.wolfram.com/BennettsOctagonToSquareDissection/
UP NISMEDhttp://www.blogger.com/profile/02022887344285868484noreply@blogger.com0tag:blogger.com,1999:blog-8539582586993260732.post-67014223103346288282013-04-08T10:37:00.003+08:002014-01-26T10:16:31.633+08:00Square Root of a Sum? - Geometric Interpretation
We know that for non-negative numbers Can we apply the same for the sum?
In the example below a and b are the legs of a right
triangle. According to the Pythagorean Theorem the hypotenuse is
Drag to the left the blue point A to rotate the leg AC around point C
until the two legs form one segment.
Drag to the left the orange point A to rotate the hypotenuseUnknownnoreply@blogger.com0tag:blogger.com,1999:blog-8539582586993260732.post-56521321582564436652013-03-07T12:31:00.001+08:002014-01-26T10:26:04.078+08:00The Sum of the First n Natural Numbers - Dynamic Geometric ProofThis applet gives a dynamic proof of the formula for the sum
of the first n natural numbers.
Irina Boyadzhiev, 6 March 2013, Created with GeoGebra
Download the file
See the general case - Arithmetic Series.
Irina's GeoGebra AppletsUnknownnoreply@blogger.com0tag:blogger.com,1999:blog-8539582586993260732.post-10906223670925538212013-03-03T02:28:00.001+08:002014-01-26T10:33:59.098+08:00 The Sum of Squares - dynamic proofThis applet gives a dynamic proof of the formula for the
sum of
the squares of the first n natural
numbers. We start with three
times the sum of the squares and rearrange the parts of one of the sums.
Click on "Color the third column".
Drag the slider to rearrange the parts of the third column.
The area of the formed rectangle equals three times the sum of
the
squares.
Click on&Unknownnoreply@blogger.com0tag:blogger.com,1999:blog-8539582586993260732.post-84615101982188712022013-01-23T12:25:00.000+08:002014-01-26T10:38:48.136+08:00Domain and Range of a Function by Flattening to the AxisThis applet can be used to introduce the concept of Domain and Range of
a function by flattening the graph of the function over the coordinate
axes.
Click on a button to select one of the three functions.
Drag the "domain" slider. The graph of the function is
flattened to the x-axis. The trace that is left on the x-axis is the
domain of the function.
Drag the "range" slider. The graph of the Unknownnoreply@blogger.com0tag:blogger.com,1999:blog-8539582586993260732.post-14355200035070756622013-01-13T11:56:00.000+08:002014-01-26T10:58:45.860+08:00Domain and Range of a FunctionThis applet can be used to demonstrate the concept of Domain
and Range
of a function.
Click on a button to select one of the three functions.
Drag the "domain" slider. A vertical ray will scan the
viewing window and will project the intersection point of the ray
and the function to the x-axis. The domain appears as red
interval(s) on the
x-axis.
Drag the "range" slider. A horizontal ray Unknownnoreply@blogger.com0tag:blogger.com,1999:blog-8539582586993260732.post-46347190898865130812013-01-02T20:00:00.000+08:002013-01-02T20:00:03.183+08:00Square Octagon Tessellation
One of the objectives of GeoGebra Applet Central this year is to update the output files of my GeoGebra Tutorial Series. The previous outputs were still in version 3.2. The applet below is the output of GeoGebra Tutorial 10 - Vectors and Tessellation. I just changed the color of the vectors to make it more visible. In this tutorial, the Vector between Two Points tool is used to translate UP NISMEDhttp://www.blogger.com/profile/02022887344285868484noreply@blogger.com0tag:blogger.com,1999:blog-8539582586993260732.post-20914287834579774642012-12-31T19:30:00.000+08:002012-12-31T19:30:39.468+08:00Year 2012 in Review - The Most Popular Posts
It's the end of the year and it's time to look back your favorite posts. Below are the most popular posts for 2012 in terms of traffic (Source: Google Analytics).
GeoGebraTube: 12000+ applets and counting
Pythagorean Theorem Proof
Animation Using Bezier Curves
Math and Multimedia Carnival 20
The Arithmetic-Mean Geometric-Mean Inequality
Deriving the Equation of the Parablola
Fibonacci Number UP NISMEDhttp://www.blogger.com/profile/02022887344285868484noreply@blogger.com0tag:blogger.com,1999:blog-8539582586993260732.post-70036763483439588632012-12-08T16:26:00.000+08:002012-12-08T16:26:00.302+08:00Square 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
UP NISMEDhttp://www.blogger.com/profile/02022887344285868484noreply@blogger.com0tag:blogger.com,1999:blog-8539582586993260732.post-43321980915754113792012-12-07T05:12:00.001+08:002012-12-07T05:12:47.365+08:00GeoGebra 4.2 Released
GeoGebra 4.2, the newest version of GeoGebra, is now available for download. Here are the links to know more about the new features.
Overview of the New Features
The Official Release Notes
A more detailed explanation of the Release Notes
GeoGebra 4.2 Sneak Peek Series
Please visit my GeoGebra Tutorials page to learn about GeoGebra. I will update them to the newest version as UP NISMEDhttp://www.blogger.com/profile/02022887344285868484noreply@blogger.com0tag:blogger.com,1999:blog-8539582586993260732.post-72030159803121130772012-11-27T19:00:00.000+08:002012-11-27T19:00:06.299+08:00Hexagon 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 UP NISMEDhttp://www.blogger.com/profile/02022887344285868484noreply@blogger.com0tag:blogger.com,1999:blog-8539582586993260732.post-33685891150615109372012-11-18T07:44:00.005+08:002012-11-18T07:45:31.546+08:00GeoGebra 4.2 Release Candidate
The Release Candidate of GeoGebra 4.2 is now available. Several of its new features are explained by Balazs Koren in the official GeoGebra blog. I have also written a Sneak Peek on its new features. The Sneak Peek includes the following topics:
Sneak Peek 1: The GeoGebra Window
Sneak Peek 2: The Object Properties
Sneak Peek 3: Graphics and Layout
Sneak Peek 4: Defaults and Advanced UP NISMEDhttp://www.blogger.com/profile/02022887344285868484noreply@blogger.com0tag:blogger.com,1999:blog-8539582586993260732.post-69729301004886477862012-10-25T10:32:00.000+08:002014-01-26T11:03:11.660+08:00Slope of a Line
The line below can be changed by dragging the blue points to a different location or by
dragging the entire line. Points C and D can be moved along the line, but they cannot change the line.
Move C and D along the line and calculate the ratio
m= ∆y/∆x=(y2- y1)/(x2- x1) for several different positions of the points.
Show the equation of the line and look for a relationship Unknownnoreply@blogger.com0tag:blogger.com,1999:blog-8539582586993260732.post-24124538000638990252012-10-18T19:00:00.000+08:002012-10-18T19:00:14.322+08:00Tessellation 2: Square, Hexagon, Triangle
The figure below shows that a plane can be tessellated using 3 regular polygons: squares, hexagons, and 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
UP NISMEDhttp://www.blogger.com/profile/02022887344285868484noreply@blogger.com0