List Of Mathematical Shapes

no D with no surface

• empty set

0D with no surface

• point

1D with 0D surface

• interval
• line

2D with 1D surface

• Bzier curve: (As+Bt)ⁿ | 0≤s≤1 ∧ 0≤t≤1 ∧ s+t=1, Aⁿ, A^n-1B, ..., Bⁿ are vectors
• circle: x²+y²=r²
• ellipse
• parabola
• hyperbola
• plane
• polygon
• chiliagon
• decagon
• enneagon
• googolgon
• hectagon
• heptagon
• hendecagon
• hexagon
• myriagon
• octagon
• pentagon
• quadrilateral
• triangle
• y=f(x): y=f(x)

3D with 1D surface

• helix: x=sin(z) ∧ y=cos(z)
• lorenz attractor

3D with 2D surface

• Bzier triangle: (As+Bt+Cu)ⁿ | 0≤s≤1 ∧ 0≤t≤1 ∧ 0≤u≤1 ∧ s+t+u=1, A^pB^qC^r vectors if p+q+r=n and p, q, r are nonnegative integers
• cylinder
• hyperplane
• mbius strip
• platonic solid
• dodecahedron
• hexahedron (cube)
• icosahedron
• octahedron
• tetrahedron
• torus
• quadric
• cone
• cylinder
• ellipsoid
• spheroid
• sphere
• hyperboloid
• paraboloid
• sphere

4D with 2D surface

• klein bottle

4D with 3D surface

• hypersphere
• polychoron
• hecatonicosachoron
• hexacosichoron
• hexadecachoron
• icositetrachoron
• pentachoron (simplex)
• tesseract

5D

6D

7D

8+ D

Fractals

• Apollonian gasket
• Cantor set
• Dragon curve
• Koch snowflake
• Lvy C curve
• Lyapunov fractal
• Mandelbrot set
• Sierpinski carpet
• Peano curve
• Sierpinski triangle

Esoteric spaces

• Don't know if this has a name: $\backslash int\_\{-\backslash infin\}^\{\backslash infin\}f^\{2\}(x)dx=r^2$
• wormhole

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