Abstract
According to classic geometry, parallel lines do not meet. In projective geometry however, parallel lines are thought of as meeting at an 'ideal point'. In perspective drawing these points are called vanishing points, and in 3-dimensional space they lie on an 'ideal plane'.
The sequence of four models depict a cube in a projective setting, and show how the ideal plane, and the vanishing points on it, can be brought into view. In the final stage, the three ideal points are positioned around the center of the model, and the center of the original cube is at infinity. This transition corresponds to the rotation of a 4-dimensional polytope called the 24-cell, and the subsequent change in appearance of its projections in Euclidean 3-space.
The sequence of four models depict a cube in a projective setting, and show how the ideal plane, and the vanishing points on it, can be brought into view. In the final stage, the three ideal points are positioned around the center of the model, and the center of the original cube is at infinity. This transition corresponds to the rotation of a 4-dimensional polytope called the 24-cell, and the subsequent change in appearance of its projections in Euclidean 3-space.
| Original language | English |
|---|---|
| Publisher | Bridges Organization |
| Publication status | Published - 2016 |
| MoE publication type | F2 Partial implementation of a work of art or performance |
| Event | Bridges Finland: Mathematics, Music, Art, Architecture, Education, Culture - University of Jyväskylä, Jyväskylä, Finland Duration: 9 Aug 2016 → 13 Aug 2016 http://bridgesmathart.org/bridges-2016/ |