Other common types of pattern are semi-regular tessellations, which allow more than one type of regular polygon as tiles, or monohedral tessellations, which only use congruent tiles. This is because these are the only regular polygons with internal angles that are a factor of 360 degrees. From the fact that angles around a point must sum to 360 degrees, it is easy to infer mathematically that there are only three types of regular polygons which can make up these tessellations – equilateral triangles, squares, and regular hexagons. These are monohedral tilings (where every single tile is congruent) of regular polygons (all having equal sides and angles). The simplest types of tessellation are referred to as regular tessellations. As an art form, tessellation is particularly rich in mathematics, with ties to geometry, topology and group theory. They have even made their name in popular culture, from tiling puzzles and the tangram to the video game Tetris, where the aim is to create tessellations as best you can from a set of falling tetrominoes.Ī tessellation is defined a repeating pattern made of one or more shapes, without the formation of gaps or overlaps.
Tessellation triangle green windows#
Tessellations can be found everywhere: in the periodic arrangement of hexagons in honeycomb, stained-glass windows and mosaic tilings, and the striking artwork of M.C.
Tessellation triangle green series#
From my favourite book as a child Penrose the Mathematical Cat to the video series Doodling in Math Class by Vihart in teenage years, the beauty in this form of mathematics has always fascinated me. For me, this beauty is found in tessellation. But it is much more than this – ask a mathematician which part of maths they find the most intrinsically beautiful and you’ll receive a wide variety of answers, each very individual to the person. At first, it can just seem like they’re referring to the perfection of a nice proof when it comes to its conclusion. You will often hear mathematicians say that maths is beautiful. However, many don’t realise that this beauty is in fact mathematics. Have you ever noticed patterns in the brickwork of the pavement as you’re walking into town? Or in the wallpaper at your grandparents’ house? Or in the quilt on your bed? Most people have at some point in their lives noticed the beauty of the patterns in the world around them.
“Triangles are my favourite shape, three points where two lines meet … let’s tessellate” Harriet Wood – student winner of the 2020 Teddy Rocks Maths Essay Competition Notes on honeycomb and M.C.
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