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param. surface
Tip: Enter z = f(x,y) for surfaces, or x(t), y(t), z(t) for parametric curves. Use u,v for parametric surfaces.
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Klein Bottle 3D Graph Calculator
Interactive 3D Parametric Surfaces Visualization
Explore the Klein bottle in 3D — a non-orientable surface with no inside or outside. Free interactive parametric visualization. A famous object in topology and algebraic geometry.
Mathematical expression: (2 + cos(u/2)*sin(v) - sin(u/2)*sin(2*v))*cos(u), (2 + cos(u/2)*sin(v) - sin(u/2)*sin(2*v))*sin(u), sin(u/2)*sin(v) + cos(u/2)*sin(2*v)
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All 3D Graph Presets
- Paraboloid — Upward-opening paraboloid
- Saddle — Hyperbolic paraboloid (saddle shape)
- Sine Surface — Product of sine and cosine
- Ripple — Circular ripple pattern
- Gaussian — Gaussian bell curve in 3D
- Wave Interference — Two perpendicular wave interference
- Mexican Hat — Ricker wavelet (Mexican hat function)
- Egg Carton — Egg carton surface pattern
- Monkey Saddle — A saddle with three dips
- Cone — Circular cone
- Helix — A standard helix spiraling upward
- Toroidal Spiral — Spiral wrapped around a torus
- Trefoil Knot — A trefoil knot in 3D
- Lissajous 3D — 3D Lissajous figure
- Viviani's Curve — Intersection of a sphere and cylinder
- Sphere — A sphere of radius 2
- Torus — A donut-shaped torus
- Möbius Strip — A one-sided Möbius band
- Klein Bottle — A non-orientable Klein bottle
- Helicoid — A ruled surface resembling a spiral staircase
- Intersecting Planes — Three intersecting planes at the origin
- Shell & Plane — Ripple surface clipped by a horizontal plane