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🌿 This time, I decided to build a universe with different geometry.
I created The Hyperbolic Garden, an interactive mathematical observatory.
✨ Enter the Hyperbolic Garden
Inside, you can explore three experiments:
- Triangles: Drag three vertices and discover how a triangle's area is encoded in its angles. Try making the angle sum approach zero!
- Distance: Discover why the boundary of a perfectly ordinary-looking disk is infinitely far away.
- Circles: Watch circumferences grow exponentially rather than linearly, revealing just how much space negative curvature contains.
You can also change the curvature, explore unusual configurations, and save your geometric creations as illustrations.
The calculations use genuine hyperbolic geometry, including the Gauss–Bonnet theorem.
The phenomenon I particularly wanted to capture: In this universe, a triangle becomes larger as its angles become smaller. In the limit, its area approaches when the curvature is , while all three angles approach zero.
Everything runs offline in your browser. I tested the interactive calculations and controls. ✨
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