📄️ Ammann-Beenker tiles
Most tilings we see around us are periodic tesselations. They are tesselations because there are no gaps, and periodic because they repeat like wallpaper. In fact, until the 1960s, people thought that any finite set of tile shapes that could tesselate could be used to tesselate periodically. Then researchers discovered tiles that only tesselate non-periodically. Such tiles are called aperiodic.
📄️ Archimedes' Puzzling Dissection
From 1998 to 2008, a team of researchers worked to unravel the secrets of a document first written in Byzantine Greek over 1000 years ago (check out this TED talk by the lead researcher, William Noel). Over the centuries, monks periodically cleaned off the markings on the document, and wrote fresh text, thus
📄️ Celtic knots
To artists and mathematicians, knots can be beautiful, interesting structures. Until recently, I hadn't explored them much from either perspective. Then my mother-in-law gave me a copy of George Bain's
📄️ Cipra City
We've been captivated by the Cipra Loops tiles, so we added another Barry Cipra invention to our lineup. Cipra again found inspiration in the work of Sol Lewitt, who often explored the possible combinations of a graphic idea. For these tiles, that graphic idea is vertical, horizontal, and diagonal lines on a square, and Cipra created a tile for each unique combination. The tiles are oriented. In the image below, the orientation is indicated by the blue arrow. All blue arrows will point in the same direction when composing the 16 tiles. Can you convince yourself that all possible combinations of lines are represented?