https://peda.net/id/8e734a86010 2018-01-24T15:00:30+02:00 https://peda.net/:static/537/peda.net.logo.bg.svg <div class="license">Tämän sivun lisenssi <a rel="license" href="https://peda.net/info">Peda.net-yleislisenssi</a></div> https://peda.net/id/48fb8ed8010 2018-01-24T15:37:32+02:00 In this exercise, you get to design your own tiles. <em>Tessellation</em> and <em>tiling</em> are words used to describe flat, planar patterns consisting of a limited set of tiles, not unlike those embedded in your bathroom walls.<br/> <br/> Mathematicians are interested in tessellations for several reasons:<br/> <ul> <li>How many colours do you need to paint a tessallation without using the same colour for adjacent tiles?</li> <li>Is it possible to create infinitely repeating patterns by using a set of tiles?</li> </ul> A special kind of tessellation, called the Penrose tessallation, is featured beside this text. It can also be found decorating Keskuskatu in Helsinki, next to Svenska Teatern and Stockmann.<br/> <br/> What makes the Penrose tiling so special? It is one of few tessallations with <em>no repeating patterns</em>. As in the figure, there are some repeating flower-like structures, but it is impossible to combine several of these indefinitely.<br/> <ol> <li>How many colours do you need to paint this Penrose tiling without two tiles of the same colour touching?</li> <li>Design a blueprint for a Penrose tiling whose tiles are of side length 2 cm.</li> </ol> 2018-01-24T15:27:12+02:00