This means that there is a different effect on every snowflake and how the crystals form. The bonds maximise attractive forces and reduce repulsive forces, allowing the snowflake to form its hexagonal shape (Life Facts, 2015). Isn’t it amazing how no two snowflakes are identical yet every snowflake is completely symmetrical? I wondered how this could happen and Life Facts (2015) gave me an answer- As no two snowflakes fall from the sky at the exact same time, they experience unique atmospheric conditions such as wind and humidity. Snowflakes are made entirely of water molecules which have solidified and crystallised to form weak hydrogen bonds with other water molecules. Snowflakes are another example of maths in nature. They exhibit six-fold radial symmetry, with elaborate, identical patterns on each arm. The following video explains what we did in class (Graff, 2014). We looked into this a bit further with Anna Robb by dividing the length of our rectangles for the golden spiral by the width which came to a number very close to Phi (1.618…). This is very common across a lot of plants and flowers and is actually why finding a four-leaf clover is considered so lucky as there are so few! Scientists believe that flowers form this way as it is the most efficient way to do so- they can “pack in the maximum number of seeds if each seed is separated by an irrational-numbered angle” such as Phi or the golden ratio (Life Facts, 2015). Some scientists and keen beans on flowers have counted the seed spirals in a sunflower to confirm that it was indeed made up of the Fibonacci sequence. This is a sequence made up of numbers where each number is determined by adding together the previous two numbers. The Fibonacci sequence has a huge part to play in the formation of sunflowers. It has inspired me to think of an activity for younger pupils where they can stick pieces of fabric onto paper to create their own tessellations. I would consider this idea for an upper years class due to the materials required. It would be a good cross-curricular link. This would be something for children to be proud of and they could feel a sense of achievement once completed. Not only is it creative and involves maths but is something that the children could make a mini version of to take home or make as an entire class for a display. Interestingly, a family friend of mine is very involved with training teachers in mathematics and has created a course about learning mathematics through patchwork (Brown, 2017). Furthermore, in Spain there are many examples of art in tiling such Park Güell in Barcelona. A lot of Islamic art uses tessellations of equilateral triangles, squares and hexagons. The word monohedral literally means ‘one’ – mono and ‘shape’ – hedral. Regular tessellations are made up of only one regular shape repeated, whilst semi-regular tessellations are made up of two or more regular shapes tiled to create a repeating pattern. Tessellations of congruent shapes, such as above, are called monohedral tessellations. These congruent, irregular shapes make the monohedral tessellations (Valentine, 2017). These shapes are, however, congruent, which means they are the same size. All triangles and quadrilaterals also tile but they are not ‘regular’ shapes and you often have to rotate them to make them fit together. you cannot use a pentagon by itself. The regular shapes that do tessellate are: squares, hexagons and equilateral triangles. As the shapes need to fit perfectly together with no gaps or overlaps, you must consider the shapes you use e.g. With Eddie, we looked at the art of a tessellation and the level of maths required to produce one. Have you ever looked around at the beauty of creation and thought just how wonderful it is how everything comes together? How each hexagonal structure in honeycomb is so perfect and they all fit together? Or how symmetrical a butterflies wings are? How about the enormous amount of detail in a sunflower? A huge amount of maths is within this. I live near the Giant’s Causeway and have visited it too many times to count yet without fail every time I go I am always mesmerised by how the hexagonal rocks all fit together to form such a beautiful tourist spot. It is all around us- in nature, music and photography. It is not just something we do in a textbook to pass time, it can be applied to the real world and is the “building block” in all we do (Hom, 2013). Hom (2013) describes maths as “the science that deals with the logic of shape, quantity and arrangement”. We don’t take time to consider just how complex and essential this subject is. I personally believe that often in today’s world we can limit the idea of maths to calculations, equations and many hours of working things out.
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