Golden ratio | Aperiodic tilings | Discrete geometry | Mathematics and art
A Penrose tiling is an example of an aperiodic tiling. Here, a tiling is a covering of the plane by non-overlapping polygons or other shapes, and aperiodic means that shifting any tiling with these shapes by any finite distance, without rotation, cannot produce the same tiling. However, despite their lack of translational symmetry, Penrose tilings may have both reflection symmetry and fivefold rotational symmetry. Penrose tilings are named after mathematician and physicist Roger Penrose, who investigated them in the 1970s. There are several different variations of Penrose tilings with different tile shapes. The original form of Penrose tiling used tiles of four different shapes, but this was later reduced to only two shapes: either two different rhombi, or two different quadrilaterals called kites and darts. The Penrose tilings are obtained by constraining the ways in which these shapes are allowed to fit together in a way that avoids periodic tiling. This may be done in several different ways, including matching rules, substitution tiling or finite subdivision rules, cut and project schemes, and coverings. Even constrained in this manner, each variation yields infinitely many different Penrose tilings. Penrose tilings are self-similar: they may be converted to equivalent Penrose tilings with different sizes of tiles, using processes called inflation and deflation. The pattern represented by every finite patch of tiles in a Penrose tiling occurs infinitely many times throughout the tiling. They are quasicrystals: implemented as a physical structure a Penrose tiling will produce diffraction patterns with Bragg peaks and five-fold symmetry, revealing the repeated patterns and fixed orientations of its tiles. The study of these tilings has been important in the understanding of physical materials that also form quasicrystals. Penrose tilings have also been applied in architecture and decoration, as in the floor tiling shown. (Wikipedia).
MAKING AN INTERACTIVE PENROSE TILING | Math in Dreams (PS4) | ND
The Penrose Tiling has always been a mathematical tiling that I have struggled to wrap my brain around, but I realized I might be able to build the Penrose Tiling in Dreams (PS4) instead of attempting to draw it by hand. With a bit of tinkering and after realizing building it by hand was g
From playlist The New CHALKboard
A time-lapse film of the laying of Roger Penrose's specially designed tiling outside the Andrew Wiles Building. The paving is constructed from just two different diamond-shaped granite tiles, each adorned identically with stainless steel circular arcs. There are various ways of covering th
From playlist The Roger Penrose Playlist
Debora Coombs - Raising Penrose - G4G13 Apr 2018
Raising Penrose tiling into a dimension of somewhere between two and five dimensions.
From playlist G4G13 Videos
Alexandre Muniz - Colorings of Pentomino Tilings - G4G12 April 2016
Pentomino tiling problems can be made more interesting by seeking map colorings with special properties. Three such properties of colorings are 3-colorability, strict colorability, and color balance. Two particular pentomino tilings of the 6 by 10 rectangle with uniquely fortunate and unfo
From playlist G4G12 Videos
This video was filmed in https://www.roblox.com/games/8157896225/Tessell-Tunes-metauni as part of a series of seminars and events happening every Thursday AEDT. See https://www.metauni.org for more details.
From playlist Metauni
Work in progress, join us on Thursday the 4th of November AEDT as we discuss how to make music out of Penrose tiles. See https://metauni.org for the schedule and instructions on how to join. This video was recorded in Tessell Tunes https://www.roblox.com/games/8157896225/Tessell-Tunes-met
From playlist Metauni
Roger Penrose: Forbidden crystal symmetry - Event Q&A
The event question and answer session from an Ri event with Sir Roger Penrose in October 2013. The famous mathematician provides a unique insight into the "forbidden symmetry" of his famous penrose tiles and the use of non-repeating patterns in design and architecture. It is a rigorous
From playlist Celebrating Crystallography
Why Did The Mathematician Cross The Road? - with Roger Penrose
Sir Roger Penrose is one of the biggest names in mathematics AND physics. Here he talks about sibling rivalry, Stephen Hawking, having ideas, and toilet paper. Roger Penrose Wikipedia - https://en.wikipedia.org/wiki/Roger_Penrose Roger Penrose books - Amazon - https://amzn.to/2XIpNBo Th
From playlist The Numberphile Podcast
~Visit www.EdwardChing.artistwebsites.com to see artwork, shop, ... This video is instructional on how to make quill pens. You'll see step by step: how to convert a feather into an iconic drawing tool. There's also info on actually drawing with a quill and using inks of different colors.
From playlist Quill Pen
The Search for Natural Quasicrystals - Paul Steinhardt
Paul Steinhardt Center for Theoretical Science, Princeton University March 7, 2012 For more videos, visit http://video.ias.edu
From playlist Mathematics
Mercredi 23 novembre 2022 : Inauguration de la partition artistique réalisée au Cirm en collaboration avec l'école des beaux-arts - INSEAMM Wednesday, November 23, 2022 Inauguration of the artwork realized at Cirm in collaboration with l'Ecole des Beaux-Arts - INSEAMM 1981-2021 : Le CIRM
From playlist OUTREACH - GRAND PUBLIC
Robert Fathauer - Tessellations: Mathematics, Art, and Recreation - CoM Apr 2021
A tessellation, also known as a tiling, is a collection of shapes (tiles) that fit together without gaps or overlaps. Tessellations are a topic of mathematics research as well as having many practical applications, the most obvious being the tiling of floors and other surfaces. There are n
From playlist Celebration of Mind 2021
Oxford Mathematics Public Lectures : Roger Penrose - Eschermatics Roger Penrose's relationship with the artist M.C. Escher was not just one of mutual admiration. Roger's thinking was consistently influenced by Escher, from the famous Penrose tiling to his groundbreaking work in cosmology.
From playlist The Roger Penrose Playlist
Red Deupree - Tetraflexagons / Coloring the Penrose Pattern - G4G14 Apr 2022
Tetraflexagons are the third cousin to Martin Gardner's original hexaflexagons, and I am presenting my tetraflexagon classification system.
From playlist G4G14 Videos
Margaret Kepner - The Zen of the Z-Pentomino - G4G12 April 2016
There are many puzzles involving tiling with the pentominoes. One problem is to find ways to tile the plane (with no overlaps or gaps) using copies of just one of the pentominoes. It turns out that 10 of the 12 pentominoes can tile the plane in an infinite number of ways. However, one, the
From playlist G4G12 Videos
Roger Penrose - Forbidden crystal symmetry in mathematics and architecture
Sir Roger Penrose provides a unique insight into the "forbidden symmetry" of his famous penrose tiles and the use of non-repeating patterns in design and architecture. It is a rigorous mathematical theorem that the only crystallographic symmetries are 2-fold, 3-fold, 4-fold, and 6-fold s
From playlist Mathematics