Free online apps bundle from GeoGebra: get graphing, geometry, algebra, 3D, statistics, probability, all in one tool! GeoGebra Classic’s user interface also provides a variety of dialogs. Different accessibility features as well as keyboard shortcuts allow you to access many features of GeoGebra. Download GeoGebra Apps Free offline GeoGebra apps for iOS, Android, Windows, Mac, Chromebook and Linux. Graphing Calculator. Graph functions, investigate equations, and plot data with our free graphing app. Graph 3D functions, plot. GeoGebra Math Apps Get our free online math tools for graphing, geometry, 3D, and more! GeoGebra, the free, open-source mathematics software is designed for math classrooms in secondary schools, but anyone who uses geometry, algebra, or calculus should check it out.

What is GeoGebra?

GeoGebra is an interactive geometry, algebra, statistics and calculus application, intended for learning and teaching mathematics and science from primary school to university level. Geogebra is available on multiple platforms with its desktop applications for Windows, MacOS and Linux, as a tablet app for Android, iPad and Windows, and as a web application based on HTML5 technology.

Constructions can be made with points, vectors, segments, lines, polygons, conic sections, inequalities, implicit polynomials and functions. All of them can be changed dynamically afterwards. Elements can be entered and modified directly via mouse and touch, or through the “Input bar”. GeoGebra has the ability to use variables for numbers, vectors and points, to find derivatives and integrals of functions. Teachers and students can use GeoGebra to make conjectures and to understand mathematical topics.

How to install GeoGebra?

Go to : http://www.geogebra.org/cms/en/

Click on “Download” on the menu bar. Click on the appropriate option applicable for you.

To get help, tutorials, user manual, tips and tricks go to :
http://wiki.geogebra.org/en/Main_Page
http://www.geogebra.org/workshop/en/GerritStols-GeoGebra-in10Lessons.pdf

To explore and see some good uses of GeoGebra go to :
http://www.geogebratube.org/?lang=en

There is also support available for selective Indian languages like Hindi and Marathi.

Exploring GeoGebra Tools

Point Tool

• Create point by clicking with mouse
• Set of points which adds to a constant number
• Representing the set of points algebraically
• Geometric representation of the set of points

Line Tool

Create a line using line tool

Line Sets

Parallel lines

Perpendicular lines

Line Properties

Slope of a line

Line intercept

Polygon Tool

Construct various polygons, specifically triangle and find the mid-points of the sides

Trying Different Constructions

Finding centres of a triangle

Centroid (Click here for further details)

Try finding other centres of the triangles. (Hint: Orthocentre, Circumcentre, In-centre)

Exploring further properties and theorems

Does the centroid divides each median in the same ratio for all triangles?

Is there any relation between the centres? Which are they?

Try mid-point theorem.

Try corollaries of the mid-point theorem.

Making a Parabola

Draw two points on the drawing pad using the ‘New Point’ tool. Join the two point using the ‘Line through two points’ tool. This line is our directrix.
Take another point not lying on the line. This new point is our focus.

Take a point, say C on the directrix using the ‘New Point’ tool. Notice that this point will move only on the directrix.
Draw a line perpendicular to the directrix, passing through the point C, using the ‘Perpendicular line’ tool.

Join C on the directrix and the focus. Use the ‘Perpendicular bisector’ tool and find the perpendicular bisector of this line segment. Use the ‘Intersect two objects’ tool and find the intersection of the perpendicular bisector and the perpendicular line passing through C. Say E.

Here we have made a isosceles triangle CDE, where CD and DE are equally.

Right click of this intersection point, and put the trace on.
Move the point C on the directrix and see that the point D is tracing a parabola.

Click here to download the GeoGebra file: Parabola

Making an Ellipse

Draw two points on the drawing pad using the ‘New Point’ tool. Use the ‘Slider’ tool and define two sliders, say d and r.

Use the “Circle with centre and radius’ tool and draw a circle with A as the centre and r as the radius. Draw another circle with B as the centre and d -r as the radius. Use the intersect tool and find the intersection points of these two circles. Right click of these points and put their trace on.

Animate the slider by right clicking on that particular slider and putting on the animation.

Click here to download the GeoGebra file: Ellipse

Making a Hyperbola

Draw two points on the drawing pad using the ‘New Point’ tool. Use the ‘slider’ tool and define two sliders, say d and r.

Use the “Circle with centre and radius’ tool and draw a circle with A as the centre and r as the radius.

Draw another circle with B as the centre and d +r as the radius. Use the intersect tool and find the intersection points of these two circles. Named as point C and point D.

Use the ‘Perpendicular bisector’ tool and find the perpendicular bisector of AB.

We know that the two arms of the hyperbola are mirror images of each other when reflect along the perpendicular bisector of the line segment between the two focii. So we will reflect the construction to get the second arm.

Use the ‘Reflect about line’ tool and reflect the point C and point D along the perpendicular bisector.

Now you have two points of intersection and their images. Right click on all the four and put their trace on.

Keep the slider d constant. Animate the slider r by right clicking on that and putting on the animation.

Click here to download the GeoGebra file: Hyperbola

Do it yourself

(Use GeoGebra to solve this problem)

1. Construct different pair of straight lines. Identify algebraic forms for the pair of lines. Demonstrate solution graphically.
2. Following is the statement for basic proportionality theorem: Demonstrate its working and proof geometrically. Basic proportionality theorem: A line parallel to one side of a triangle divides the other two sides into parts of equal proportion.
3. Take three non-collinear points. Construct a circle passing through these three points. Now can you locate the centre of this circle? Record your work below.

Interesting problems using GeoGebra

Cat on the ladder

A ladder standing on a smooth floor against a wall slides down. Along what line does a cat sitting at the middle of the ladder move?

Assume that the length of the ladder is L units.

Use the ‘New point’ tool and mark a point A on the X-axis.

Use the ‘ Circle with centre and radius’ tool and draw a circle with A as the centre and L as the radius.

Use the ‘Intersect two objects’ tool and find the intersection of this circle with the Y axis. Hid the point on the negative Y axis.

Join the two points( One on the X-axis and the another on the Y axis). Use the midpoint tool and find the midpoint of this line segment. Right click on the midpoint and put the trace on.

Move the point on the X axis to see trace.

Download this file of ladder problem and answer the solution. Click here

Copernicus Planetary Motion

Copernicus constructed a planetary motion for a planet (M) in an orbit in space.
We can see the planetary motion in the given GeoGebra file, what do you think will be the path (or locus) of planet M?

Geogebra Download For Windows 10

Download this file and answer the solution. Click here

GeoGebra (the name is a portmanteau made from the two words Geometry and Algebra) is an interactive geometry, algebra, statistics and calculus application, intended for learning and teaching mathematics and science from primary school to university level. GeoGebra is available on multiple platforms, with apps for desktops (Windows, macOS and Linux), tablets (Android, iPad and Windows) and web.

GeoGebra's creator, Markus Hohenwarter,^[2] started the project in 2001 as part of his master's thesis at the University of Salzburg. After a successful Kickstarter campaign, GeoGebra expanded its offering to include an iPad, an Android and a Windows Store app version.^[3] At the same year it incorporated Bernard Parisse's Giac into its CAS view.^[4] The project is now open-source and multi-lingual, and Hohenwarter continues to lead its development at the University of Linz.

GeoGebra includes both commercial and not-for-profit entities that work together from the head office in Linz, Austria, to expand the software and cloud services available to users.

Interactive geometry, algebra, statistics and calculus[edit]

GeoGebra is an interactive mathematics software suite for learning and teaching science, technology, engineering, and mathematics from primary school up to the university level. Constructions can be made with points, vectors, segments, lines, polygons, conic sections, inequalities, implicit polynomials and functions, all of which can be edited dynamically later. Elements can be entered and modified using mouse and touch controls, or through an input bar. GeoGebra can store variables for numbers, vectors and points, calculate derivatives and integrals of functions, and has a full complement of commands like Root or Extremum. Teachers and students can use GeoGebra as an aid in formulating and proving geometric conjectures.

GeoGebra's main features are:

• Interactive geometry environment (2D and 3D)
• Built-in spreadsheet
• Built-in computer algebra system (CAS)
• Built-in statistics and calculus tools
• Large number of interactive learning and teaching resources at GeoGebra Materials

GeoGebra Materials Platform[edit]

The GeoGebra Materials platform^[5] is a cloud service that allows users to upload and share GeoGebra applets with others. GeoGebra Materials was originally launched as GeoGebraTube in June 2011, and was renamed in 2016. As of April 2016 the service hosts more than 1 million resources, 400,000+ of which are public. 'Materials' include interactive worksheets, simulations, games and e-books created using GeoGebraBook.

GeoGebra Materials can be also exported in several formats, including SVG, Animated GIF, Windows Metafile, PNG, PDF and EPS, as well as copied directly to the clipboard. GeoGebra can also generate code for use in LaTeX files.

Licensing[edit]

GeoGebra's source code is licensed under the GNU General Public License (GPL) and all other non-software components are under Creative Commons BY-NC-SA.^[6][7] Commercial use is subject to a special license and collaboration agreement.

Community[edit]

The International GeoGebra Institute (IGI) is the nonprofit arm of the GeoGebra Group. The institute coordinates research, development, translation and deployment efforts of the GeoGebra system across a global network of user groups at universities and non-profit organizations, as well as provide certification to GeoGebra experts and trainers.

Awards[edit]

Desmos

• Archimedes 2016: MNU Award in category Mathematics (Hamburg, Germany)
• Microsoft Partner of the Year Award 2015: Finalist, Public Sector: Education (Redmond, WA, USA)
• MERLOT Award for Exemplary Online Learning Resources – MERLOT Classics 2013 (Las Vegas, Nevada, USA)
• NTLC Award 2010: National Technology Leadership Award 2010 (Washington D.C., USA)
• Tech Award 2009: Laureate in the Education Category (San Jose, California, USA)
• BETT Award 2009: Finalist in London for British Educational Technology Award
• SourceForge.net Community Choice Awards 2008: Finalist, Best Project for Educators
• AECT Distinguished Development Award 2008: Association for Educational Communications and Technology (Orlando, USA)
• Learnie Award 2006: Austrian Educational Software Award for 'Wurfbewegungen mit GeoGebra' (Vienna, Austria)
• eTwinning Award 2006: 1st prize for 'Crop Circles Challenge' with GeoGebra (Linz, Austria)
• Les Trophées du Libre 2005: International Free Software Award, category Education (Soisson, France)
• Comenius 2004: German Educational Media Award (Berlin, Germany)
• Learnie Award 2005: Austrian Educational Software Award for 'Spezielle Relativitätstheorie mit GeoGebra' (Vienna, Austria)
• digita 2004: German Educational Software Award (Cologne, Germany)
• Learnie Award 2003: Austrian Educational Software Award (Vienna, Austria)
• EASA 2002: European Academic Software Award (Ronneby, Sweden)

See also[edit]

References[edit]

1. ^Versions – GeoGebra, dev.geogebra.org, retrieved 2014-09-14
2. ^JKU | IDM » Markus Hohenwarter, Jku.at, 2013-06-13, retrieved 2013-08-29
3. ^GeoGebra for tablets (iPad and Android), Kickstarter.com, retrieved 2013-08-29
4. ^Kovács, Zoltán; Parisse, Bernard (2013-11-25), Giac and GeoGebra: improved Gröbner basis computations(PDF), RICAM Institute, Linz, Austria, retrieved 2015-01-23
5. ^GeoGebra Materials: http://www.geogebra.org/materials
6. ^'GeoGebra License'. International GeoGebra Institute. Retrieved 23 February 2014.
7. ^'Sources for used libraries'. International GeoGebra Institute. Retrieved 22 April 2016.

External links[edit]

Geogebra Download

• Official website
• GeoGebra's channel on YouTube

Geogebra 3d Graph