The Royal Institution
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 symmetries.
Yet, since the 1970s 5-fold, 8-fold, 10-fold and 12-fold “almost” symmetric patterns have been exhibited, showing that such crystallographically “forbidden symmetries” are mathematically possible and deviate from exact symmetry by an arbitrarily small amount. Such patterns are often beautiful to behold and designs based on these arrangements have now been used in many buildings throughout the world.
In this Ri event Sir Roger Penrose reveals the mathematical underpinnings and origins of these “forbidden symmetries” and other related patterns. His talk is illustrated with numerous examples of their use in architectural design including a novel version of “Penrose tiling” that appears in the approach to the main entrance of the new Mathematics Institute in Oxford, officially opened in late 2013 (http://www.maths.ox.ac.uk/new-building).
The tiling is constructed from several thousand diamond-shaped granite tiles of just two different shapes, decorated simply with circular arcs of stainless steel. The matching of the tiles forces them into an overall pattern which never repeats itself and exhibits remarkable aspects of 5-fold and 10-fold symmetry.
Similar features have been found also in the atomic structures of quasi-crystalline materials. The initial discovery of such material earned Dan Shectman the 2011 Nobel Prize for chemistry, his work having launched a completely novel area of crystallography.
Images of the completed Mathematics Institute in Oxford courtesy of Vanesa Penrose.
The filming and production of this event was supported by the Science and Technology Facilities Council: http://www.stfc.ac.uk. Production by Edward Prosser. Additional camera operation by Mark Billy Svensson.
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The Moiré effect is particularly interesting.
What a wonderful and enlightening presentation. One feels that there are more applications as yet unknown, for this.
Just love the Royal Institute! Penrose, Dawkins, going to sleep with geniuses!
From Faraday and keeping the standard high. Makes you proud. For everyone, even dummies like me can enjoy it. Love it, keep it up!
Roger Penrose stumped by modern technology! How ironic!
its amazing how much hate this lecture gets. truth hurts, eh?
Never fall in love with a girl name Crystal.
Listening to Sir Roger Penrose discuss his non-periodic tiling is like attending a presentation given by Winnie-the-Pooh …
This was good for me. It gave me my third universal choice.
To explain so far. 1. You can either choose to know the location of a particle or is speed.
2. You can either know the diameter or the circumference of a circle.
3. You can either know the infinity or the single shape that makes it up.
Looking for my number 4…
I love scrolling down and seeing intelligent comments. I guess I can go on living another day.
look up Eshers art. great patterns.
M,C Escher mathematically repeatingly brilliant patterns.
Diferantiality=harmony?
5 minutes of watching this and that was enough pain in my life.
Meta Magical Themas, by Douglas R Hoffstadtler, an abstract description of why it is forbidden is a bose einstien condensate process moment. In ,geometry in contrast to relativity, a radius in a process that generates two virtual radius, is the maximum value. three radius rebounds in growth back towards one radius. It never reaches four radius which stops the pattern needed to be crystalline. the equivalence of too much information needed to define system.
Brittish people are dull af…
Very cool, thank you.
Nice combover…
29:11 Dan Shechtman smiles
DOES IT STRIKE ANYONE AS ODD THAT THE PENROSE STRUCTURE WAS DISCOVERED
IN NATURE SOON AFTER HE THOUGHT IT UP AND WE STARTED LOOKING?
I DONT KNOW WHAT EXACTLY IM SUGGESTING BUT ITS POSSIBLY RELATED
TO THE MANDELA EFFECT
Delightful lecture?❣?
18:03 That would be one spectrum of the sri yantra lotus with others un drawn
Does this remind anybody else of the "Glass Shatter" Final Fantasy Random Battle Splash Screens?
He definitely has time on his hands!
Love his hand drawn and written overhead slides, no one does it anymore
Formidable symmetry or forbidden symmetry. I thing the former tittle is preferable.
Roger is an absolutely wonderful human being top quality that one haha
wonderful time passed on this Oxford courtesy
whoa. this is amazing
all my life I've searched for an asymmetric yet infinite grid. it's a basic unity that allows individuality by being infinite. a universe that is designed for both free will and determined fate– a paradox. I understand why this kind of symmetry is forbidden. it undermines the orderly conformity that people find so comforting these days.
Those granite and stainless steel tiles at the end are beautiful
44:05 Dr, Penrose,
please do not say "wobbles around" regarding any architectural feature in san francisco!