A developer has created Poincake, an infinite canvas note-taking application that uses hyperbolic geometry to organize content in non-Euclidean space. The tool employs the Poincaré disk model to project infinite space into a finite disk, allowing users to navigate notes through fluid spatial distortion while leveraging spatial memory.
LLMs Enable Complex Mathematical Implementation
The creator had conceptualized the project years ago but faced roadblocks with the complex mathematics required for non-Euclidean geometry. Using LLM assistance, they successfully implemented the coordinate systems and optimization algorithms needed for hyperbolic navigation. "It turns out that LLMs can handle the mathematical heavy lifting quite well, specifically in designing the coordinate systems and optimization algorithms, provided that you guide them with a solid architectural design," the developer explained on Hacker News.
The project addresses fundamental limitations in modern UI design, where many patterns serve as workarounds for limited screen real estate. By using hyperbolic space, Poincake keeps everything contextually visible while providing infinite expansion capacity.
Technical Challenges and Community Feedback
The Hacker News community responded positively to the concept, with one user noting it feels "weirdly intuitive, like navigating on the surface of a sphere." However, users identified technical issues with text rendering. While arrows and points deform correctly in hyperbolic space, text does not, creating readability problems as notes overlap during navigation.
The developer acknowledged these limitations and suggested level-of-detail (LOD) rendering as a potential solution. A complete fix would require text to be "rendered in hyperbolic space" itself. Community members proposed additional use cases including tablet implementation with stylus input and applications for large argument mapping.
Key Takeaways
- Poincake uses the Poincaré disk model to create an infinite note-taking canvas in hyperbolic geometric space
- LLM assistance enabled the developer to implement complex non-Euclidean mathematics that previously blocked the project
- The tool reached 119 points on Hacker News with 22 comments on June 2, 2026
- Current technical limitations include text rendering that doesn't deform correctly in hyperbolic space, causing overlap issues
- Community members identified potential applications in argument mapping and tablet-based stylus interfaces