Other Geometries

John Golden

Good portrayals of non-2D or non-Euclidean Geometries.

Table of Contents

  1. 3D
    1. All solids of Platon rotate
    2. Parallelepiped
    3. Perfect Pour
    4. Kaercher-Rubik's Flexagon Template
    5. 3-D Solids
    6. Bertoia Rectangles
    7. The projections of spherical trochoid
    8. Dodecahedron Rotation
    9. Hyperbolic Paraboloid Cake
    10. Geodesic
    11. The projected image sees its dimension decrease
  2. Higher Dimensions
    1. Turning a Tesseract
    2. Basic Tesseract
    3. Build a Hypercube
    4. Hypercube
    5. Hipercubo 4D
  3. Non-Euclidean
    1. Taxicab Conic Sections
    2. Spider Geometry
    3. L^p Distances
    4. Klein Disk
    5. Klein's Quartic
    6. Projections
    7. Euclidian vs Spherical geometry
    8. Koch-like Fractal Time Waster

1.

3D

  • 1. All solids of Platon rotate
  • 2. Parallelepiped
  • 3. Perfect Pour
  • 4. Kaercher-Rubik's Flexagon Template
  • 5. 3-D Solids
  • 6. Bertoia Rectangles
  • 7. The projections of spherical trochoid
  • 8. Dodecahedron Rotation
  • 9. Hyperbolic Paraboloid Cake
  • 10. Geodesic
  • 11. The projected image sees its dimension decrease

1.1.

All solids of Platon rotate

– uStas

1.2.

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1.3.

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1.4.

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1.5.

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1.6.

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1.7.

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1.8.

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1.9.

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1.10.

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1.11.

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2.

Higher Dimensions

  • 1. Turning a Tesseract
  • 2. Basic Tesseract
  • 3. Build a Hypercube
  • 4. Hypercube
  • 5. Hipercubo 4D

2.1.

Turning a Tesseract

This uses dilation as the 4th coordinate, and lets you see the effect of rotation on a hypercube in any of the six possible coordinate planes. [br][br]A little funky, but you can try to compose rotations as well.
– John Golden

2.2.

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2.3.

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2.4.

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2.5.

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3.

Non-Euclidean

  • 1. Taxicab Conic Sections
  • 2. Spider Geometry
  • 3. L^p Distances
  • 4. Klein Disk
  • 5. Klein's Quartic
  • 6. Projections
  • 7. Euclidian vs Spherical geometry
  • 8. Koch-like Fractal Time Waster

3.1.

Taxicab Conic Sections

Just occurred to me I could make this![br][br]Using the locus definitions of conic sections, here's what they look like in taxicab geometry.
– John Golden

3.2.

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3.3.

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3.4.

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3.5.

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3.6.

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3.7.

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3.8.

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