GeoGebra
GeoGebra is a free, open-source dynamic mathematics software designed for education at all levels, integrating geometry, algebra, spreadsheets, graphing, statistics, and calculus into a single interactive platform.[1] Developed initially by Markus Hohenwarter as part of his master's thesis in 2001 at the University of Salzburg, Austria, it has evolved into a global tool supporting STEM learning through web-based apps, downloadable software, and mobile applications available on multiple platforms.[2] Since its acquisition by BYJU'S in 2021, GeoGebra operates as an independent unit led by its original founders and developers, maintaining its commitment to non-commercial free use while powering educational resources worldwide.[1] The software's core strength lies in its intuitive interface that allows users to construct and manipulate mathematical objects dynamically, fostering exploration and visualization of concepts such as functions, loci, and statistical distributions.[1] Key features include the GeoGebra Calculator Suite for graphing and computation, an authoring tool for creating interactive materials, and GeoGebra Classroom for real-time collaboration and progress tracking in educational settings.[3] With over 100 million students and teachers utilizing it globally, the platform hosts more than 1 million user-contributed resources, supports multiple languages, and integrates with learning management systems to enhance teaching innovations.[4] GeoGebra's impact is recognized through awards such as the Archimedes Award in 2016 and its status as a Microsoft Partner of the Year finalist in 2015, underscoring its role in advancing interactive mathematics education.[1]Overview and Development
Founding and Early Development
GeoGebra was founded in 2001 by Markus Hohenwarter as part of his master's thesis in mathematics education and computer science at the University of Salzburg in Austria. The software was conceived to dynamically link geometry and algebra, bridging the gap between interactive geometry tools like Cabri Geometry or Geometer's Sketchpad and computer algebra systems such as Mathematica or Maple, thereby enabling users to construct geometric objects while simultaneously viewing and manipulating their algebraic representations.[5][6] The initial Java-based prototype was released in March 2002, following the completion of Hohenwarter's thesis, and quickly gained traction in educational settings due to its free availability and focus on mathematics teaching. This prototype allowed for basic dynamic constructions where changes in geometric elements automatically updated linked algebraic expressions, laying the foundation for GeoGebra's integrated approach. By 2008, the software had evolved to a more stable form with enhanced features, including spreadsheet integration for handling lists and data, which supported explorations in numerical and tabular mathematics.[7][8] During its early years, GeoGebra expanded its scope to include basic calculus tools, with initial testing in Austrian classrooms around 2005. By 2008, statistics functionalities were added, enhancing the spreadsheet view with tools for data visualization and analysis. These developments were part of Hohenwarter's ongoing PhD research at the University of Salzburg, which focused on the pedagogical applications of the software in schools.[6][8] In 2008, GeoGebra adopted ANTLR (ANother Tool for Language Recognition) for improved expression parsing, boosting the accuracy and efficiency of input processing for complex mathematical commands. The software transitioned toward broader accessibility with web-based applets in 2009, allowing constructions to run directly in browsers without installation, followed by the launch of mobile apps in 2010 to support touchscreen interactions on devices like iPhones and Android phones. The International GeoGebra Institute, established at the end of 2007, began coordinating these advancements to foster global academic and community involvement.[9][10][11]Acquisitions and Current Ownership
To support its growing international community and coordinate development efforts, the non-profit International GeoGebra Institute (IGI) was established at the end of 2007 at Johannes Kepler University in Linz, Austria, serving as an umbrella organization for regional institutes and providing training, certification, and resources for educators worldwide.[12][11] On December 8, 2021, Indian edtech company Byju's acquired GeoGebra for $100 million, marking a significant corporate milestone that aimed to integrate its tools into broader learning platforms while preserving its educational focus.[13] Byju's committed to maintaining GeoGebra's operations as an independent unit under the leadership of its original team, including founder Hohenwarter, ensuring continued free access to its apps and web services without immediate changes to its open-source model.[1][14] Byju's faced severe financial challenges starting in 2024, including insolvency proceedings initiated by an Indian court in July 2024 and Chapter 11 bankruptcy filing by its U.S. arm in February 2024, amid allegations of mismanagement and creditor disputes that eroded its once-$22 billion valuation.[15][16] Despite these issues, GeoGebra has sustained independent development and releases. Version 5, released in 2015, introduced a redesigned interface, and in 2013, full computer algebra system (CAS) capabilities were added via integration with Giac/Xcas. The stable version 6.0.901 was issued on September 24, 2025, demonstrating operational stability under its core team.[17] A dedicated group of approximately 45 employees and additional contributors, supported by grants, academic partnerships, and community involvement, continues to drive updates and enhancements from its headquarters in Linz.[18][1]Core Functionality
Integrated Mathematical Tools
GeoGebra's core strength lies in its dynamic linking of geometric and algebraic elements within a unified coordinate system, enabling real-time interactions between visual constructions and symbolic representations. Users can create geometric objects such as points, lines, and conics that are directly tied to algebraic variables and equations; for example, dragging a point defined by variables a and b automatically updates the equation of an associated line or curve, fostering an intuitive exploration of mathematical relationships. This integration stems from GeoGebra's design as dynamic mathematics software that combines geometry and algebra seamlessly.[4][19] The software incorporates a built-in Computer Algebra System (CAS) for advanced symbolic computations, supporting operations like differentiation and integration. The Derivative command computes the derivative of a function, such as \frac{d}{dx} f(x) = f'(x), while the Integral or IntegralSymbolic command evaluates definite or indefinite integrals, for instance \int f(x) \, dx. These capabilities allow users to perform exact manipulations without numerical approximation, extending algebraic tools to calculus-level tasks.[20][21] Complementing these features, GeoGebra's spreadsheet facilitates data management and statistical analysis, including tools for regression and probability. As of October 2024, spreadsheet functionality has been integrated into the Calculator Suite and Graphing Calculator, allowing users to input datasets and apply commands like Fit to generate linear regressions, such as y = mx + b, or explore probability distributions through built-in functions for normal, binomial, and other models. This integration supports quantitative investigations, linking numerical data back to geometric or algebraic views for holistic analysis.[19][22][23] Graphing capabilities enable visualization of functions with interactive sliders for parameter adjustment, allowing dynamic exploration of how changes in variables affect plots, such as varying a in f(x) = a \sin(x). In three dimensions, users can plot vectors and surfaces, like z = x^2 + y^2, to examine spatial relationships. GeoGebra provides specialized commands to enhance these tools, including Sequence[expression, variable, from, to] for generating iterative lists or plots, and Root[polynomial] for finding roots of equations numerically within specified intervals. These features are available across GeoGebra's calculator suite for consistent mathematical integration.[24][25][26]User Interfaces and Apps
GeoGebra provides desktop applications compatible with Windows, macOS, and Linux operating systems, offering offline access to its full suite of tools without requiring an internet connection. These installable versions, known as GeoGebra Classic, mirror the user interface of the web-based platform and support advanced features like scripting and custom tools. Initially developed using Java technology for cross-platform compatibility, the desktop applications have transitioned to web-based technologies such as HTML5 and JavaScript, enabling seamless updates and improved performance across modern systems.[27][28] The web-based interfaces form the core of GeoGebra's accessibility, allowing users to access specialized calculators directly through a web browser without any installation. Key components include the Graphing Calculator for plotting functions and data, the Geometry app for constructing and manipulating shapes, and the 3D Calculator for visualizing surfaces and solids, all powered by a shared backend including the Computer Algebra System (CAS) for symbolic computations. These tools run on standard browsers like Chrome, Firefox, and Safari, supporting real-time collaboration and dynamic interactions on devices ranging from laptops to tablets.[29][30][24] Mobile applications for iOS and Android extend GeoGebra's reach to handheld devices, with dedicated apps released starting in the early 2010s to support on-the-go mathematics exploration. These apps feature offline functionality, allowing users to save and work on constructions without internet access, and are optimized for touch input with gesture-based controls for dragging points, pinching to zoom, and intuitive tool selection. Specialized versions, such as the Graphing Calculator and Geometry apps, provide tailored interfaces for mobile screens, ensuring responsive performance on smartphones and tablets. As of December 2024, GeoGebra launched the Math Solver app for iOS and Android, which uses artificial intelligence to solve math problems by analyzing photos or text inputs, integrating with core computational tools.[27][31][32][9][33][34][35] In 2020, GeoGebra introduced the Calculator Suite, integrating multiple calculators into a single, unified platform for streamlined access across all interfaces. This all-in-one application combines graphing, geometry, 3D modeling, CAS, and probability tools within a cohesive environment, where views like algebra input and graphics output remain dynamically linked regardless of the selected mode. Available on desktop, web, iOS, and Android, the Suite enhances workflow by eliminating the need to switch between separate apps, making it ideal for comprehensive mathematical tasks.[36][37] Users can export GeoGebra constructions in various formats to facilitate sharing and embedding, including HTML5 for interactive dynamic worksheets that preserve functionality in web pages. Graphics views can be saved as high-resolution images in formats like PNG or SVG for static presentations, while interactive applets—generated as self-contained HTML files—allow embedding in websites or learning management systems without requiring the full GeoGebra software. These options support educational integration by enabling customizable, responsive outputs that adapt to different platforms.[38][39][40]Educational Resources and Platforms
Materials Sharing Platform
GeoGebra Materials serves as a cloud-based repository enabling educators and learners to share and discover user-generated educational content focused on mathematics and science. Originally launched as GeoGebraTube in 2011 to support the sharing of interactive applets, the platform evolved into a more comprehensive resource hub and was rebranded as GeoGebra Materials in 2016.[41] This rebranding coincided with enhancements that expanded its scope beyond applets to include diverse formats like worksheets, interactive simulations, and lesson plans, all categorized by mathematical topics and educational levels.[42] As of 2025, the platform hosts over 1 million free resources, fostering a vast library of community-contributed materials under Creative Commons licensing.[1] These resources cover more than 150 mathematical topics, from algebra and geometry to statistics and calculus, with examples including dynamic visualizations of functions or geometric constructions that promote conceptual exploration.[43] Users can refine searches through a dedicated search bar and filters for resource types (such as activities or books), topics, subtopics, and grade levels, aligning with educational standards like the Common Core.[43] Additionally, the platform supports content in over 60 languages, enabling global accessibility and adaptation for multilingual classrooms.[44] Authoring tools integrated within GeoGebra apps allow users to create and upload content directly, such as by building interactive applets or compiling multi-page books from existing constructions.[45] Creators can publish resources by selecting options in the app's menu, adding descriptions, categories, topics, and language tags to enhance discoverability.[46] User accounts further personalize the experience, permitting the saving of favorites, organization into custom collections, and management of personal libraries for repeated use in teaching or learning.[47] Community contributions to the platform are coordinated in part through the International GeoGebra Institute, which supports resource development and certification.[6]Classroom and Collaborative Features
GeoGebra Classroom provides educators with a dedicated platform for creating and managing interactive mathematical assignments, enabling teachers to distribute tasks directly to students without requiring individual logins. This feature facilitates the assignment of GeoGebra activities and books, allowing instructors to monitor task completion status in real time and provide targeted feedback to support personalized learning.[48] Teachers can view live updates on student progress, including pending and completed items, which helps in adjusting instruction dynamically during lessons.[49] A key collaborative aspect of GeoGebra Classroom is its support for real-time synchronization in shared sessions, where multiple users can edit mathematical constructions simultaneously. This enables seamless interaction in both in-person and digital environments, with teachers and students co-authoring dynamic geometry, graphs, or algebraic models on a shared canvas.[48] The platform allows for discussions at the class, group, or individual level, fostering collaborative problem-solving while maintaining oversight of contributions.[1] For assessment, GeoGebra Classroom integrates tools such as interactive quizzes built within math applets, which provide immediate feedback and can be assigned as part of lessons. These quizzes support formative evaluation by tracking student responses to dynamic problems, such as geometric constructions or algebraic manipulations.[50] Additionally, built-in progress analytics offer teachers insights into individual and class-wide performance, including anonymized response data and completion rates, to inform instructional decisions.[48] The platform connects with learning management systems through APIs, notably enabling direct assignment and progress tracking via Google Classroom, where teachers can push GeoGebra tasks and receive real-time updates within the LMS workflow.[48] For Moodle, integration occurs via embedding GeoGebra activities, allowing seamless incorporation of Classroom-assigned content into course modules while storing scores and timestamps for traceability.[51] In response to the shift toward remote education following 2020, GeoGebra Classroom introduced enhancements for hybrid and fully online teaching, including co-teacher access for team instruction and features to pause sessions for announcements.[52] These updates support group workspaces for divided class interactions and allow embedding of multimedia elements, such as videos, within activities to enrich remote lessons with explanatory content alongside interactive math tools.[52] Resources from the GeoGebra Materials platform can be briefly referenced and assigned as foundational content in these collaborative setups.[48]Licensing and Distribution
Open-Source Components
GeoGebra's source code for the core desktop and web applications is licensed under the GNU General Public License version 3 or later, enabling users to view, modify, and redistribute it while ensuring compatibility with free software principles.[53] However, the distributed applications, installers, and web services are subject to additional non-commercial restrictions under the GeoGebra Non-Commercial License Agreement. This permissive open-source licensing has applied to the software since its first release in 2002, fostering widespread adoption in educational settings by allowing free access and adaptation for non-commercial purposes.[54] The source code for these applications is publicly hosted on GitHub, where developers can fork the repository, submit pull requests, and collaborate on enhancements.[55] Since the repository's establishment, the project has benefited from community-driven contributions, including bug fixes, performance optimizations, and the implementation of new mathematical commands to extend functionality.[53] These efforts align with GeoGebra's commitment to open collaboration, as the licensing explicitly supports such modifications under GPL terms.Restrictions and Commercial Use
GeoGebra's educational materials, including language files, documentation, and user interface elements, are licensed under the Creative Commons Attribution-NonCommercial-ShareAlike 3.0 (CC BY-NC-SA 3.0) license, which explicitly prohibits commercial reuse, distribution for profit, or any application that generates revenue without obtaining prior permission from the International GeoGebra Institute.[53] This non-commercial restriction ensures that resources remain freely accessible for educational purposes, such as teaching and personal learning, while requiring attribution to GeoGebra, including a copyright notice and a link to the official website.[56] For any commercial applications, users must enter into a separate License and Collaboration Agreement with GeoGebra, obtainable by contacting [email protected].[53] The core GeoGebra software is distributed under the GNU General Public License version 3 (GPL-3.0) or later, allowing modification and redistribution for non-commercial use, though the accompanying non-commercial terms have sparked debates regarding GPL compliance, particularly for web embeds and mobile ports that might integrate proprietary elements.[53] Critics argue that imposing non-commercial restrictions on GPL-licensed code violates the license's terms, which do not permit additional limitations on use; GeoGebra has addressed such concerns by emphasizing its focus on non-commercial educational applications and clarifying that commercial distributions require bespoke agreements.[57] While the software remains free for all users worldwide, including students and educators, the 2021 acquisition by BYJU'S has enabled general integration of GeoGebra's tools into BYJU'S product offerings.[14] Following BYJU'S financial and operational challenges in 2024, including insolvency proceedings and significant valuation losses, concerns arose about the stability of GeoGebra's licensing model under its parent company.[58] As of November 2025, BYJU'S remains under insolvency proceedings in India, with ongoing asset bids, but GeoGebra continues to operate as an independent unit with no alterations to the core open-source and non-commercial terms, maintaining the CC BY-NC-SA 3.0 and GPL-3.0 licenses unchanged for accessibility to non-commercial users.[59][53]Community and Global Reach
International GeoGebra Institute
The International GeoGebra Institute (IGI) is a non-profit organization established in 2008 at Johannes Kepler University Linz in Austria to coordinate the global development of GeoGebra, manage its intellectual property, and promote international expansion through community support and educational initiatives.[6] As the philanthropic arm of the GeoGebra Group, the IGI focuses on non-commercial aspects, ensuring free access to the software while retaining copyrights and trademarks under GeoGebra GmbH for broader licensing oversight.[60][53] The IGI's core activities center on teacher training, material development, research coordination, and outreach to build a robust global network.[6] It oversees the certification of GeoGebra trainers and the creation of local institutes, with more than 130 institutes operating in over 60 countries to localize resources and support regional adoption.[61] Certification levels range from basic users (Level 1) to expert trainers (Level 4), with local institutes authorized to issue credentials based on standardized guidelines provided by the IGI.[62] Additionally, the IGI facilitates grants and funding opportunities for educational projects, assisting local institutes in securing resources for curriculum materials, textbooks, and training programs.[63] In the wake of the 2021 acquisition of GeoGebra by BYJU'S, the IGI has been instrumental in preserving the project's independence, functioning as a separate non-profit entity dedicated to open educational access and community-driven innovation amid the group's commercial expansion.[14][1] This structure allows the IGI to prioritize global STEM outreach without commercial constraints, supporting GeoGebra's use in nearly 190 countries.[64] Since the inaugural International GeoGebra Conference in 2009, the IGI has hosted annual conferences and workshops for developers, educators, and researchers, fostering collaboration on software enhancements, pedagogical strategies, and research applications.[65][66] These events, held in various locations worldwide, emphasize innovative teaching practices and have contributed to the establishment of dozens of local institutes, enhancing GeoGebra's role in mathematics education globally.[66]User Engagement and Support
GeoGebra boasts over 100 million users worldwide as of 2025, encompassing students, teachers, and educators who leverage its tools for dynamic mathematics exploration.[4] This extensive user base reflects its global reach, where it supports diverse educational curricula and STEM initiatives.[67] The platform's appeal lies in its accessibility across devices and its integration into classrooms, fostering widespread engagement among users of varying ages and proficiency levels. Support for users is facilitated through robust online mechanisms, including a comprehensive help center offering tutorials, FAQs, and troubleshooting guides, alongside community-driven forums for peer assistance.[68] Multilingual documentation and interfaces have been available since the mid-2000s, enabling users in over 70 languages to access resources tailored to their needs and enhancing inclusivity in non-English speaking regions.[69] Additionally, user groups and local meetups are organized by certified GeoGebra institutes worldwide, providing hands-on workshops, training sessions, and networking opportunities to build local communities and promote best practices.[70] Feedback from the user community directly shapes GeoGebra's development, with mechanisms such as GitHub issue tracking allowing developers and users to report bugs, suggest features, and collaborate on improvements.[55] Annual user surveys further inform updates by gathering insights on usability and desired enhancements, ensuring the software evolves in response to real-world needs. Coordinated by the International GeoGebra Institute, these engagement efforts maintain a vibrant ecosystem. To promote inclusivity, accessibility features including screen reader compatibility and keyboard navigation were enhanced in 2022, aligning with WCAG 2.1 AA standards to support users with disabilities.[71]Recognition and Impact
Awards and Honors
GeoGebra has received numerous accolades recognizing its innovative approach to integrating dynamic geometry, algebra, and other mathematical tools into educational software. These awards highlight the program's impact on enhancing interactive learning experiences for students and educators worldwide.[1] In 2009, GeoGebra was named a laureate in the Education Category of The Tech Awards, formerly known as the LES Tech Awards, for its pioneering role in making advanced mathematical concepts accessible through free, open-source software that fosters innovation in STEM education. This recognition underscored GeoGebra's global reach and its ability to empower teachers in over 190 countries to create engaging, dynamic lessons.[1] The program earned the MERLOT Classics Award in 2013 from the Multimedia Educational Resource for Learning and Online Teaching consortium, celebrating its sustained excellence as a top-tier online learning resource in mathematics instruction. This award emphasized GeoGebra's enduring value in providing high-quality, peer-reviewed tools that support conceptual understanding over rote memorization.[72][1] Earlier honors include the Comenius Award in 2004, a German Educational Media Award presented in Berlin for excellence in multimedia applications in education, which acknowledged GeoGebra's early success in combining geometric constructions with algebraic computations to visualize mathematical relationships. Complementing this, the European eLearning Award in 2008, conferred in London, recognized the software's contributions to advancing e-learning methodologies through interactive and collaborative features.[1][73] Among other notable recognitions, GeoGebra received the digita Educational Software Award in 2004 in Cologne, Germany, for its effective integration of multiple mathematical domains into a user-friendly platform. In 2016, it was awarded the Archimedes Award by MNU in the Mathematics category in Hamburg, Germany, for its contributions to mathematical education. In the 2010s, the software's compatibility with Microsoft tools led to integrations highlighted in the Microsoft Partner of the Year Award finalist status in 2015 for Public Sector: Education, reflecting its role in supporting innovative teaching practices within Microsoft ecosystems. Community growth has been a key factor in GeoGebra's eligibility for such honors, as its expanding user base of educators and developers has amplified its educational influence.[1]| Award | Year | Organization | Location | Focus |
|---|---|---|---|---|
| The Tech Awards (Education Laureate) | 2009 | The Tech Interactive | San Jose, California, USA | Educational software innovation |
| MERLOT Classics Award | 2013 | MERLOT | Las Vegas, Nevada, USA | Sustained excellence in online learning resources |
| Comenius Award | 2004 | German Educational Media Award | Berlin, Germany | Multimedia in education |
| European eLearning Award | 2008 | BECTA | London, UK | Advancements in e-learning |
| digita Educational Software Award | 2004 | digita | Cologne, Germany | Integration of mathematical tools |
| Archimedes Award | 2016 | MNU | Hamburg, Germany | Contributions to mathematical education |
| Microsoft Partner of the Year (Finalist) | 2015 | Microsoft | Redmond, Washington, USA | Innovative education integrations |