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### Penrose Tiling Quilt

Diameter: approximately 60"
This updated photograph was taken November 13, 2005.
The quilt now hangs on the wall in Mark's computer room.
It's almost too big for the wall.
That's a bookshelf on the left, and a closet door on the right.
The top point almost touches the ceiling.
Hanging the quilt was tricky (details below).

Here's the original picture that was on this web page:

Photographed March 8, 1996 on a snow pile in our back yard.

The pattern is an area selected from a Penrose tiling.
Mark designed the quilt by computer and Serena made it.
This was before Serena knew about "paper piecing".
The 6 colors were chosen to produce a 3-D effect.
The Golden Ratio appears in the relative lengths of the triangle sides.

There are only two kinds of pieces: a 72-36-72 degree triangle and a 36-36-108 degree triangle.

Penrose Tiling:
Several aperiodic tilings discovered by the British mathematician/physicist Roger Penrose.
Tiling:
A way of precisely covering an infinite plane with a fixed set of shapes.
Aperiodic:
Non-repeating. There is no way you can rotate and/or shift the infinite pattern so that the rotated/shifted pattern is the same as the original pattern. (This is not apparent from the quilt because the quilt is not the entire infinite pattern. In fact, we chose a particularly symmetrical part of the infinite pattern.)

Correction/clarification by Dave Green (August 1, 1998):

• The phrase "the infinite pattern" is misleading, since there are an infinite number of different infinite patterns.
• There are two Penrose tilings with five-fold rotational symmetry -- they can be created by radially extending the two implied Penrose tilings in your quilt around a single point (the center of your quilt).

### Hanging the Quilt:

This quilt spent many years in a dresser drawer because we didn't have a way to hang it.
Then Mark got industrious and found a source of hoops on the web.
These fiberglass hoops are made for use in fishing nets (I guess they hold the net open).
They're sturdy and very nearly circular.
The Penrose Tiling quilt required a 4-foot diameter hoop.
Here's the hoop in our doorway:

Here's a closeup:

It's splintery and will make your hand itch if you touch it.
So we wrapped the hoop in duct tape.

The quilt is attached to the hoop with loops of fabric.
For now, they're just pinned on.
Lengths of coat-hanger wire keep the topmost points from flopping.