List of mathematical shapes
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It has been suggested that this article or section be merged into List of geometric shapes. (Discuss) Proposed since August 2010. |
Following is a list of some mathematically well-defined shapes. See also list of geometric shapes, list of polygons, polyhedra and polytopes, and list of curves.
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[edit] 0D with no surface
[edit] 1D with 0D surface
[edit] 2D with 1D surface
- Bézier curve: (As + Bt)n | 0 ≤ s ≤ 1 ∧ 0 ≤ t ≤ 1 ∧ s + t = 1, An, An − 1B, ..., Bn are vectors
- circle: x2 + y2 = r2
- ellipse
- parabola
- hyperbola
- plane
- polygon
[edit] 3D with 1D surface
- helix: x = sin(z) ∧ y = cos(z)
[edit] 3D with 2D surface
- Bézier triangle: (As + Bt + Cu)n | 0 ≤ s ≤ 1 ∧ 0 ≤ t ≤ 1 ∧ 0 ≤ u ≤ 1 ∧ s + t + u = 1, ApBqCr vectors if p + q + r = n and p, q, r are nonnegative integers
- cylinder
- hyperplane
- möbius strip
- platonic solid
- torus (doughnut)
- quadric
[edit] 4D with 3D surface
[edit] 5D with 4D surfaces
- regular 5-polytopes:
- 5-dimensional simplex
- 5-dimensional cross-polytope
- 5-dimensional hypercube (5-measure polytope)
[edit] Fractals
- Apollonian gasket
- Cantor set
- Dragon curve
- Koch snowflake
- Lévy C curve
- Lyapunov fractal
- Mandelbrot set
- Sierpinski carpet
- Peano curve
- Sierpinski triangle
