![]() The two shapes are both parallelograms and the tessellation is often referred to as "Kites and Darts" :Īlthough there are small repeated sections, there is no single unit which can be copied to fill the plane. Amazingly, he managed to reduce this to only six, then just two. Using only pencil and paper, Penrose found such an arrangement but it contained many different shapes. This kind of tessellation became known as quasi-periodic, in other words at first glance there appears to be a repeating pattern, but in fact He began by investigating combinations of shapes which would produce a repeating unit, but this led on to a search for a pattern with no repetition. While studying for his PhD at Cambridge, Penrose became fascinated by the geometry of covering a plane. ![]() Octagons and squares can be arranged to form a semi-regular pattern: The image that we are likely to think of is known as a regular tessellation, where all the shapes are regular and of the same type, for example:Ī semi-regular tessellation is made up of two different regular shapes and each vertex (i.e. Traditionally, the pattern formed by a tessellation is repetitive. Two people have principally been responsible for investigating and developing tessellations: Roger Penrose, an eminent mathematician, and the artist, M.C.Escher. Tessellations are a common feature of decorative art and occur in the Presumably this is an indication of the fact that tiles of this shape are the easiest to interlock. The word tessellation itself derives from the Greek tessera, which is associated with four, square and tile. Tessellation is a system of shapes which are fitted together to cover a plane, without any gaps or overlapping. And of course, there is so much maths involved! It seems a golden opportunity to link art with maths, allowing the creative side of your children to take over. There is so much scope for practical exploration of tessellations both For many, this is their preferred method of learning and, in general, it engages pupils more effectively. So often in the classroom we try to make activities more enjoyable for the children by varying our teaching to include a more tactile or "hands on" approach. You want to bend a fish once, twice, or three times? It's OK the fish still looks comfortable.Ĭan people bend like that? Mostly, no, but there are exceptions like circus people, magicians' assistants, and my ex-girlfriend Zelda.'Why tessellation?' you may well be asking. Like gym socks and monsters, fish are twisty-bendy flexible. Nobody is thinking "Dang, why is that big fin on the shark's nose?! Thaaaaat's not riiiight, mmmkay?" It should be on his back, not his nose!!!ģ0 minutes into the movie "Jaws", the audience is listening to the shark hunter's story. That big triangle-shaped fin shouldn't be there! Yet, in the middle of the movie an old pro shark hunter drew a really weird picture of a shark. Nobody who saw Jaws ever said "Hey, great movie, but that drawing of a shark was totally dumb." Did you ever see that famous shark movie, Jaws? ![]() That's not what a fish looks like." Unless the artist says this fish is a specific species, the artisthas incredible freedom to play with that shape. The artist can add a few extra fins and change the shape of the head and tail, but we won't say "hey, that's not right. Because that's true, we tolerate all kinds of liberties taken by the artist. Like monsters, fish come in so many forms. Isn't it amazing? Of one kind of fish alone, there are 800 species: there's the cleaner wrasse, as small as your smallest finger there's also the Napoleon wrasse, larger than the largest basketball player. ![]() Fish can look like almost any basic shape: long, short, big, small, soft, hard, baseball or bat, spiky or flat. If you have the time, visit Google Images and search for pictures of an eel, a butterfly fish, a porcupine fish, a mimic octopus, a seahorse, a napoleon wrasse, a ray, a frogfish, a flying gurnard, a trumpet fish, a razor fish, a moamoa, a forceps fish, a batfish, a jack, and a jellyfish. It's easy to tessellate fish because their appearance is so variable and their bodies are so flexible. How to Make an Asian Chop (stone stamp). ![]()
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