Mathematicians have discovered a shape with a pattern that never repeats, a breakthrough that has eluded experts for decades. This polygon, known as the “einstein tile,” is a 13-sided figure that can fill an infinite surface with an always original pattern. Unlike previous tilings, which eventually repeated themselves, this shape does not have translational symmetry. The discovery has astonished mathematicians and is expected to be supported by further investigation. The implications of this finding extend beyond mathematics, as it could lead to advancements in materials science and inspire new decorative designs or art.
| Signal | Change | 10y horizon | Driving force |
|---|---|---|---|
| Mathematicians discover shape with non-repeating pattern | Discovery | Increased understanding of tiling patterns | Curiosity and desire for new knowledge |
| Shape can fill an infinite surface with an always original pattern | Innovation | Development of unique tiling patterns | Innovation and creativity |
| Shape does not have translational symmetry | Breakthrough | New understanding of symmetry in tiling | Advancement in mathematical theories |
| Shape identified by a retired printing technician | Collaboration | Increased collaboration between professionals and nonprofessionals | Cross-disciplinary collaboration |
| Shape may lead to materials science investigations and creative inspiration | Application | Advancements in materials science and art | Practical applications and creative pursuits |