…………………………………………… …………………………………………… Oops! Not exactly perfect, but Mathspig was using paper and scissors! …………………………………………… We aren’t going to write a computer program, but rather think what we might want the program to do. It involves equilateral triangles repeated. This Leaf Tessellation came from almostunschoolers blog Look at the pattern. Rotating Tessellation A tessellation is a repeating pattern with no gaps like floor tiles. So my little Sweeties, we’re going to use some of these maths skills to build up your maths brain. Wow! Sometimes mathspiggies, teachers forget how important these visualising exercises can be in the development of maths thinking skills. The maths involved here includes: Symmetry …………………………………………… 2D patterns ……………………………………………ĢD & 3D mirror images …………………………………………… 3D Rotations …………………………………………… Algorithms You will find these fab world maps BLDG BLOG, which uses an algorithm to map the 3D world into different 2D shapes, which can then be reconstructed into 3D objects. It is vital that architects can walk around inside an imaginary building in their heads, that engineers can see in their imagination where the support columns need to be placed in a building/bridge, that chemists can visualise 3D mirror images of molecules, that fashion designers can see the axis of symmetry and also invert an item of clothing inside out (because that is how clothes are sewn), that designers can rotate objects in their imagination (not just to look pretty, but to make sure the object can stand up) and it is important that computer programmers can see patterns to write their repeating algorithms (More later). Now, my Sweeties, I want you to understand something important about the way people, who use maths, think. Nancy Clark, 11, of London, made an Einstein’s Hat hat. Garnet Frost, 70, of London made a 24-foot frieze with 1,500 ceramic tiles. Here are some of the submissions highlighted in an article by Siobhan Roberts in the New York Times ( What Can You Do With an Einstein?,):Įvan Brock, 31, Product Designer from Toronto took out one prize with his Einstein’s Hat Ravioli. A panel of judges assessed 245 submissions from 32 countries. Meanwhile, the National Museum of Mathematics ( MoMath) in New York and the United Kingdom Mathematics Trust ( UKMT) in London became so excited about this discovery, they ran a competition asking members of the public to submit creations using Einstein’s Hat. Obviously, it should be called Einstein’s Hat. The monotile is called ‘the hat’ or ‘the Einstein’. This could be the simplest example ever discovered. Mathematicians know a lot about periodic monotiles and the patterns produced by tessellating shapes such as squares on a chessboard or hexagons in a patchwork quilt (below).īut an ‘aperiodic monotile’ producing a non-repeating pattern is rare. The Red tile above shows why he called it ‘the hat’. Its mathematical name is ‘an aperiodic monotile’.ĭavid Smith, a maths hobbyist, discovered it this year, and named it ‘the Hat’. It is an asymmetrical shape that can cover any flat area in a non-repeating pattern. This one also displays strong anisotropy: it can be folded flat when squeezed in one direction but offers a lot of resistance in the perpendicular direction.The Einstein or the Einstein Tile was discovered this year. My new iso-area origami corrugation which I called Shark Teeth due to the sharp triangular molecules of which it is composed. In albums: Models with Pictures of Precreased Sheets, Showcase, Tessellation Examples Images are licensed under the Creative Commons Attribution-NonCommercial 4.0 International License (implies: abstract corrugation, abstract tessellation, abstract, corrugation, geometric, pattern, abstract periodic tessellation, non-recursive periodic tessellation, periodic tessellation, tessellation) Other folds and variants: Shark Teeth Corrugation (blue Elephant Hide)
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