Articles and videos
-
Friezes
- Classification des frises - Micmaths by (March 24th, 2014) ► A description of frieze classification and why there are seven groups.
- [AVENT MATHS] : 7 groupes de frise🚫 by (December 7th, 2020) ► A short description of the seven frieze groups.
-
Tiling
- A Tile with Surround Number 2 by (April 2002) ► A tile that can be fully surrounded by two copies of itself.
- Historic 'Tile' Discovery Gives Math World A Big Jolt — It's the first such find in 30 years. by (August 19th, 2015) ► A 15th pentagon which can tile a plane has been discovered using a computer program.
- J'ai toujours rêvé d'être pentocarreleur by (September 13th, 2015) ► The different types of pentagon tiles.
- Deux (deux ?) minutes pour... classer les pavages ! by (September 19th, 2017) ► The title says it all.
- Heesch Numbers and Tiling - Numberphile by (February 21st, 2019) ► Heesch’s tiling problem and Einstein problem.
- ↪Heesch Numbers (extra footage) - Numberphile by (February 23rd, 2019) ► The continuation of the previous video.
- Fabrique ton pavage quasi-périodique - Les petites découvertes - Épisode 91 by (August 18th, 2020) ► A short presentation of quasiperiodic tilings.
- [AVENT MATHS] : 15 pavages pentagonaux🚫 by (December 15th, 2020) ► A short history of the finding of the 15 tilings possible with a convex pentagon.
- ‘Nasty’ Geometry Breaks Decades-Old Tiling Conjecture — Mathematicians predicted that if they imposed enough restrictions on how a shape might tile space, they could force a periodic pattern to emerge. But they were wrong. by (December 15th, 2022) ► and built a counter-exanple of the periodic tiling conjecture.
- Les pavages du plan (⧉) by (June 10th, 2023) ► A very classical presentation of tilings.
- Le 18e problème de Hilbert - Micmaths⇈ by (November 28th, 2023) ► The history of the 2D and 3D anisohedral tilings.
- Sur les traces du sphinx et des reptuiles impairs - Micmaths by (January 18th, 2024) ► The problem of rep-tiles having with an odd number of sides greater than 3: only the "sphinx" is known.
-
Penrose tiles
- QuasiTiler 3.0 by (1998) ► This is a short description of an algorithm generating Penrose tilings. An online demo is available to play with.
- How to construct Penrose tilings by (April 12th, 2011) ► The title says it all.
- 5 and Penrose Tiling - Numberphile↑ by (March 21st, 2012) ► Tilings with regular polygons, Penrose tiling, and the fact that we cannot understand something if we do not have the proper mathematical tools for it.
- Impossible Cookware and Other Triumphs of the Penrose Tile — Infinite patterns that never repeat have moved from fantasy to reality. by (May 1st, 2014) ► Penrose tiles and quasicrystals.
- The Infinite Pattern That Never Repeats by (October 1st, 2020) ► describes some facts about Penrose tiling which are not so well-known.
- Why Penrose Tiles Never Repeat by (December 1st, 2022) ► The relationship between Penrose tiles and a pentagrid.
-
Einstein
- Un motif apériodique ! by (April 26th, 2023) ► discovered an einstein.
- La première tuile apériodique de l'histoire! The Hat - Passe-science #53 by (May 3rd, 2023) ► The same, but with a more technical description.
- A New Tile in Newtyle - Numberphile by (June 26th, 2023) ► Yet another video on the hat.
- ↪A New Tile (extra) - Numberphile by (June 26th, 2023) ► The continuation of the previous video.
- Une nouvelle tuile apériodique: le spectre! - Passe-science #54 by (July 5th, 2023) ► A presentation of the spectre.
- What Can Tiling Patterns Teach Us? — If you cover a surface with tiles, repetitive patterns always emerge — or do they? In this week’s episode, mathematician Natalie Priebe Frank and co-host Janna Levin discuss how recent breakthroughs in tiling can unlock structural secrets in the natural world. by and (July 3rd, 2024) ► The classical story of the hunt for an einstein and the discovery of quasicrystals.