Discover the Beauty of Non-Euclidean Space
WarpDisk is an educational laboratory designed for visualizing and interacting with hyperbolic geometry. By utilizing the Poincaré disk model, this app transforms abstract mathematical concepts into a vivid, interactive experience for students, mathematicians, and curious minds.
Interactive Poincaré Disk In hyperbolic space, the rules of geometry change. WarpDisk allows you to explore these changes directly. Place points within the unit disk to see how distances grow exponentially toward the boundary, and generate unique "straight lines" (geodesics) that define the shortest path in curved space.
Saccheri Quadrilaterals Study the historical foundation of non-Euclidean geometry. Build and manipulate Saccheri quadrilaterals to witness their unique properties. Unlike Euclidean geometry, where the summit angles are always 90 degrees, WarpDisk provides live calculations that show how these angles become acute in hyperbolic space, along with real-time data on area defects.
Hyperbolic Tessellations Generate intricate {p,q} tilings based on Schläfli symbols. Explore how regular polygons can tile the entire hyperbolic plane in ways impossible in standard geometry. Choose from famous presets like the {7,3} tiling or configure your own to create complex, infinite patterns.
Comprehensive Learning Tools WarpDisk is more than just a drawing tool—it is a learning platform. Every module includes:
• Theoretical Insights: Detailed cards explaining the math behind the visuals.
• Integrated Guide: A dedicated "How it Works" section covering the Poincaré model, geodesics, and tiling rules.
• Live Metrics: Real-time data and measurements as you interact with the models.
Share Your Discoveries Capture high-fidelity visualizations of your arcs, quadrilaterals, and tilings to share with colleagues or students. WarpDisk makes it easy to export your geometric experiments for further study.
Start your journey into the warped world of hyperbolic geometry and see mathematics from a new perspective.