About This Site
Spacetime Manifolds is a free educational resource for exploring classical topology concepts through interactive 3D visualizations. Every demo runs entirely in your browser — no downloads, no plugins, no accounts.
The goal is simple: make beautiful, abstract mathematics tangible. Drag a Möbius strip to see its single side. Rotate a Klein bottle to watch its figure-8 self-intersection. Spin a tesseract through the fourth dimension. Trace closed curves on a torus and see why some can never be shrunk to a point.
"Mathematics is not about numbers, equations, computations, or algorithms: it is about understanding."
— William Paul Thurston
What You Can Explore
- 01Möbius Strip — Non-orientable surfaces and half-twist counting
- 02Klein Bottle — Closed surfaces that can\'t be embedded without self-intersection
- 03Quaternion Rotations — The double cover of SO(3) by SU(2)
- 04Real Projective Plane — Boy\'s surface and antipodal identification
- 054D Immersions — Tesseract stereographic projection
- 06Closed Curves — Fundamental groups and winding numbers on the torus
Technology
All visualizations are built with Three.js for real-time 3D rendering and Next.js for the application framework. Interactive controls use OrbitControls for mouse drag/zoom/rotate. The parametric surfaces are generated from their mathematical definitions using custom buffer geometry builders.