Roger Penrose - Forbidden crystal symmetry in mathematics and architecture
Δημοσιεύτηκε στις 16 Ιαν 2014
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.
The Ri is on Twitter: http://twitter.com/ri_science
and Facebook: http://www.facebook.com/royalinstitution
Subscribe for the latest science videos: http://richannel.org/newsletter / Our editorial policy: http://richannel.org/home/editorial-p...
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.
The Ri is on Twitter: http://twitter.com/ri_science
and Facebook: http://www.facebook.com/royalinstitution
Subscribe for the latest science videos: http://richannel.org/newsletter / Our editorial policy: http://richannel.org/home/editorial-p...
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