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Drawing the Hypercube
J. Scott Carter
University of South Alabama
July 2012ICME, Seoul, Korea
Acknowledgement
This talk was supported by the Ministry ofEducation Science and Technology (MEST) andthe Korean Federation of Science and TechnologySocieties (KOFST).
Outline
• A Cube
• Projections and Matrices
• Step-by-Step Hypercube
• Pascal’s Triangle
• The Hypercube in Art
Outline
• A Cube
• Projections and Matrices
• Step-by-Step Hypercube
• Pascal’s Triangle
• The Hypercube in Art
Outline
• A Cube
• Projections and Matrices
• Step-by-Step Hypercube
• Pascal’s Triangle
• The Hypercube in Art
Outline
• A Cube
• Projections and Matrices
• Step-by-Step Hypercube
• Pascal’s Triangle
• The Hypercube in Art
Outline
• A Cube
• Projections and Matrices
• Step-by-Step Hypercube
• Pascal’s Triangle
• The Hypercube in Art
Captain Kangaroo
graph paper
Drawing a Cube
Drawing a Cube
Drawing a Cube
Drawing a Cube
x
y
z
Drawing a Cube
x
y
z
Drawing a Cube
x
y
z
Drawing a Cube
x
y
z
Drawing a Cube
x
y
z
Drawing a Cube
x
y
z
Drawing a Cube
x
y
z
Drawing a Cube
x
y
z
Drawing a Cube
x
y
z
Drawing a Cube
x
y
z
Drawing a Cube
x
y
z
Drawing a Cube
x
y
z
Projection Matrix
P =
[−1 3 0−2 0 3
]
[−1 3 0−2 0 3
]·
3/21/21
=
[00
]
Projection Matrix
P =
[−1 3 0−2 0 3
]
[−1 3 0−2 0 3
]·
3/21/21
=
[00
]
The Null Space
Drawing the Hypercube
Drawing the Hypercube
1000
Drawing the Hypercube
1000
0100
Drawing the Hypercube
1000
0100
0010
Drawing the Hypercube
1000
0100
0010
0001
Drawing the Hypercube
1000
0100
0010
0001
Drawing the Hypercube
1000
0100
0010
0001
1100 1110
1111
0011
0111
Drawing the Hypercube
1000
0100
0010
0001
1100 1110
1111
0011
0111
Drawing the Hypercube
1000
0100
0010
0001
1100 1110
1111
0011
0111
Drawing the Hypercube
1000
0100
0010
0001
1100 1110
1111
0011
0111
Drawing the Hypercube
1000
0100
0010
0001
1100 1110
1111
0011
0111
Drawing the Hypercube
1000
0100
0010
0001
1100 1110
1111
0011
0111
Drawing the Hypercube
1000
0100
0010
0001
1100 1110
1111
0011
0111
Drawing the Hypercube
1000
0100
0010
0001
1100 1110
1111
0011
0111
Drawing the Hypercube
1000
0100
0010
0001
1100 1110
1111
0011
0111
Drawing the Hypercube
1000
0100
0010
0001
1100 1110
1111
0011
0111
Drawing the Hypercube
1000
0100
0010
0001
1100
0011
1010
1001
0110
0101 0111
1110
1101
1011
1111
0000
Drawing the Hypercube
1000
0100
0010
0001
1100 1110
1111
0011
0111
Drawing the Hypercube
1000
0100
0010
0001
1100
0011
1010
1001
0110
0101 0111
1110
1101
1011
1111
0000
Drawing the Hypercube
1000
0100
0010
0001
1100
0011
1010
1001
0110
0101 0111
1110
1101
1011
1111
0000
Drawing the Hypercube
1000
0100
0010
0001
1100
0011
1010
1001
0110
0101 0111
1110
1101
1011
1111
0000
