Tag Archives: symmetry

Penrose tiling

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Sir Roger Penrose is a mathematical physicist best known for his work on theories of general relativity and cosmology. He won the Wolf Prize in 1988 with Stephen Hawking for his work on singularities and black holes; the Institute of Physics’s Paul Dirac Medal and Prize in 1989; and the Royal Society’s Copley Medal in 2008 for “his beautiful and original insights into many areas of mathematics and mathematical physics.”

He is also the inventor of Penrose Tiling, a unique tiling pattern with five-fold symmetry, so I was delighted to discover this building as part of the Greenwich Peninsula complex outside the O2 Millenium Dome.

Almost the entire surface of the Ravensbourne College of Design and Communication building is covered with a Penrose-inspired pattern. Penrose previously sued Kleenex for using his tiling pattern on their quilted toilet paper, but I imagine that Ravensbourne’s architects, Foreign Office, checked with him first.

A public service announcement regarding paper snowflakes

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As Christmas draws nearer decorations are starting to appear in windows, and some of those decorations are paper snowflakes. The problem is that most paper snowflakes are wrong.

Real snowflakes demonstrate hexagonal (sixfold) symmetry; each snowflake is composed of one part, repeated six times, with a separation angle of 60°.

The “standard” method of creating paper snowflakes, folding a piece of paper in half and then in half again, creates snowflakes with tetragonal (fourfold) symmetry, each piece separated by 90°.

How to Make A Genuine Paper Snowflake

1.) Get a square piece of paper and fold it in half diagonally twice, across both sets of corners.

2.) Using the centre of the piece of paper as a marker, fold the paper into equal thirds, and trim off the top to create an equilateral or isoceles triangle.

4.) You should now have a folded triangle of paper. Cut your pattern into the paper, making sure that it is symmetric (if it’s not symmetric you’ll end up with three-fold symmetry). If you cut off the edges of the triangle but not the centre you’ll end up with the desired “spokey” effect.