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![]() Explore and use art-making conventions, applying knowledge of elements and selected principles through the use of materials and processes.Investigate the purpose of objects and images from past and present cultures and identify the contexts in which they were or are made, viewed, and valued. ![]() Main resource: Creating Escher-Type Drawings. The idea of this unit is for students to develop their understanding of the mathematical concepts that underlie the creation of Escher type tessellations and apply this to the creation of an art piece. You might use the ideas from Measuring Angles, Level 3 for this purpose. Note that this unit does not include explicit teaching around angles, although this could be included as an additional point of learning. Either the corners of the basic shape all fit together to make 360°, or the corners of some basic shapes fit together along the side of another to again make 360°. This requires the vertices to fit together. The same figure (or group of figures) come together to completely cover a wall or floor or some other plane. The key features of tessellations are that there are no gaps or overlaps. These tessellations provide a strong structure for their two different purposes. The brick wall provides a tessellation with rectangles and the honeycomb is a tessellation of regular hexagons. Bees use a basic hexagonal shape to manufacture their honeycombs. Brick walls are made of the same shaped brick repeatedly laid in rows. They also provide a nice application of some of the basic properties of polygons. Tessellations are a neat and symmetric form of decoration. Occasionally you can see them in the living room as the basis of the pattern on carpets and in parquetry wooden floors. Tessellations are found all over the place but especially in the kitchen and bathroom on tiles and lino. You rotate, translate, or reflect them, do a combination of transformations and you would get a repeating pattern.Īs explained at the beginning, in order to use one regular polygon to make a tessellation, there are only three possible polygons to use: triangles, hexagons and squares.The unit of work is based on the work of the Dutch artist Escher who utilised mathematical concepts, including tessellation, to create mathematically pieces of artwork. A tessellation can be created by starting with one or several figures. Staying true to these boundaries, you are able to create a pattern that can go on into infinity. Geometrical objects can’t have holes in the pattern and they must never overlap. Meaning the effect of a reflection combined with any translation is a glide reflection, with this special case just a reflection. A so called glide reflection cannot be reduced like that. In a line and a translation in a perpendicular direction the combination of this reflection is a reflection in a parallel line. ![]() Sometimes objects or shapes have more than one line of symmetry. Reflectional symmetry occurs when a line is used to split an object or shape in halves so that each half reflects the other half. You can only rotate the figure up to 360 degrees. The number of times you can rotate the geometric figure so it looks exactly the same as the original figure is called rotation symmetry. This symmetry results from moving a figure a certain distance in a certain direction which is also called translating (moving) by a vector (length and direction) ![]() It has a translation symmetry if an image can be divided into a sequence of identical figures by straight lines. As explained in symmetry research: Translation Symmetry
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