The landscape of interactive mathematics software has long been dominated by two powerful platforms: GeoGebra, known for its dynamic geometry and algebraic capabilities, and Desmos, celebrated for its sleek graphing calculator interface. However, a new contender has emerged that aims to combine the best of both worlds while adding unique features that address long-standing gaps in geometric visualization. This article explores P.S.Euclid—an innovative tool that merges plane and stereo (3D) geometry into a single, cohesive environment.
According to a detailed report on Habr, the developers of P.S.Euclid set out to create a platform that not only replicates the functionality of GeoGebra and Desmos but also introduces original solutions for problems that have frustrated mathematicians, educators, and students alike. The project, as described in the source article, is built on the premise that existing tools, while powerful, often force users to switch between different applications for 2D and 3D work, or lack the precision required for advanced Euclidean constructions. P.S.Euclid aims to be the single workspace where plane and stereo geometry coexist seamlessly.
What Makes P.S.Euclid Different?
The core innovation of P.S.Euclid lies in its hybrid approach. While GeoGebra excels at algebraic geometry and dynamic constructions, and Desmos offers an intuitive graphing experience, P.S.Euclid introduces a unified interface that treats plane and stereo geometry as two sides of the same coin. The developers encountered a common challenge: when working with 3D objects, many tools either simplify them into 2D projections or require complex scripting to achieve basic interactions. P.S.Euclid solves this by implementing a native stereo rendering engine that allows users to manipulate points, lines, and planes in three dimensions without leaving the familiar 2D construction environment.
For example, a user can draw a triangle on a plane, then instantly extrude it into a triangular prism in 3D space, adjusting the height and angles in real time. This is not just a visual trick; the underlying mathematical relationships are preserved, meaning that any change to the base triangle automatically updates the 3D object. This level of integration is rarely seen in consumer-grade geometry software, and it positions P.S.Euclid as a serious tool for both education and professional visualization.
The GeoGebra and Desmos Influence
The article on Habr highlights that P.S.Euclid draws heavily from the strengths of GeoGebra and Desmos. From GeoGebra, it borrows the concept of dynamic constructions—where moving one point automatically recalculates all dependent elements. This is essential for exploring geometric theorems and conjectures. From Desmos, it inherits the clean, responsive user interface that lowers the barrier to entry for new users. However, P.S.Euclid goes further by allowing users to define custom construction rules using a built-in scripting language that is more accessible than GeoGebra's JavaScript-based scripting.
One of the most praised features is the ability to save and share constructions as live, interactive documents. Unlike static screenshots or exported videos, these documents retain full interactivity, allowing colleagues or students to manipulate the geometry themselves. This is particularly useful for remote learning or collaborative research, where multiple parties need to experiment with the same model.
Practical Applications in Education and Research
P.S.Euclid is not just a novelty; it has immediate practical applications. In education, it can be used to teach concepts like perspective, projection, and solid geometry without requiring expensive 3D printers or physical models. For instance, a teacher can construct a cube and show how its 2D projections change as the viewpoint rotates. Students can then interact with the model to discover properties of parallel lines in projective geometry.
In research, mathematicians and engineers can use P.S.Euclid to visualize complex surfaces or spatial relationships that are difficult to grasp from equations alone. The tool supports parametric equations and implicit surfaces, making it suitable for fields like computer graphics, architecture, and physics. The source article notes that the development team has already used the tool to model non-Euclidean geometries, which is a testament to its flexibility.
Technical Foundations and User Experience
Behind the scenes, P.S.Euclid is built on a modern web stack, ensuring cross-platform compatibility. It runs in any modern browser without plugins, making it accessible on laptops, tablets, and even smartphones. The rendering engine uses WebGL for hardware-accelerated graphics, allowing smooth manipulation of even complex scenes with hundreds of objects.
The user interface is deliberately minimalist, with toolbars that expand based on context. When working in plane mode, only relevant 2D tools are shown; switching to stereo mode reveals additional controls for depth, rotation, and lighting. This design philosophy reduces cognitive load and helps users focus on the mathematics rather than the software.
For those familiar with GeoGebra, the transition to P.S.Euclid is smooth, as many keyboard shortcuts and interaction patterns are similar. However, the developers have also introduced gesture controls for touch devices, making it possible to pinch-zoom and rotate 3D models with intuitive finger movements.
Comparison with Existing Tools
To better understand P.S.Euclid's place in the ecosystem, it helps to compare it directly with GeoGebra and Desmos:
| Feature | GeoGebra | Desmos | P.S.Euclid |
|---|---|---|---|
| 2D Geometry | Excellent | Limited | Excellent |
| 3D Geometry | Add-on or separate app | Not available | Native, integrated |
| Scripting | JavaScript | No | Custom, simplified |
| Real-time collaboration | Limited | Yes (with account) | Yes, built-in |
| Export formats | Image, GIF, HTML | Image, HTML | Image, HTML, interactive document |
| Learning curve | Steep | Gentle | Gentle to moderate |
This table, derived from the Habr article and public documentation, shows that P.S.Euclid fills a niche that neither GeoGebra nor Desmos fully addresses: a single, user-friendly environment for both plane and stereo geometry with advanced interactivity.
Real-World Case Studies
The source article provides several examples of how P.S.Euclid has been used in practice. One case involves a university professor who used the tool to demonstrate the concept of duality in projective geometry. By constructing a set of points and lines in 2D, then switching to stereo mode, students could see the corresponding dual configuration in 3D, which made the abstract concept tangible.
Another example comes from an architectural firm that used P.S.Euclid to prototype spatial layouts. The ability to quickly switch between 2D floor plans and 3D volumetric models allowed designers to iterate faster than with traditional CAD software, which often requires separate tools for each view.
These cases highlight that P.S.Euclid is not just a toy for hobbyists but a viable tool for professional work. The developers have also released a series of tutorials and sample constructions on their website, making it easy for new users to get started.
What the Future Holds
According to the Habr article, the P.S.Euclid team is actively working on new features, including support for animated constructions, integration with external data sources, and a plugin system that will allow third-party developers to extend the tool's capabilities. There is also talk of a community repository where users can share their constructions, similar to GeoGebra's resource platform.
The timing of this release is particularly relevant in 2026, as the demand for remote and hybrid learning tools remains high. P.S.Euclid offers a solution that is both powerful and accessible, potentially becoming a staple in mathematics classrooms worldwide.
Conclusion
P.S.Euclid represents a significant step forward in interactive geometry software. By merging the best of GeoGebra and Desmos with original innovations in stereo visualization, it provides a unified platform for exploring plane and solid geometry. Whether you are a teacher looking for a better way to explain spatial concepts, a student struggling with 3D visualization, or a researcher needing a flexible modeling tool, P.S.Euclid is worth exploring.
The source article from Habr provides a detailed account of the development journey and technical decisions behind the tool, and it serves as a valuable resource for anyone interested in the future of mathematical software. As P.S.Euclid continues to evolve, it has the potential to redefine how we interact with geometry in the digital age.
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