The tessellations shown here are from Suad, Alim, Mohamed, Ruhan and Era. In geometry, the triangular tiling or triangular tessellation is one of the three regular tilings of the Euclidean plane, and is the only such tiling where the constituent shapes are not parallelogons.Because the internal angle of the equilateral triangle is 60 degrees, six triangles at a point occupy a full 360 degrees. At the end of the inquiry, I displayed some of the tessellations under a visualiser, which elicited an intriguing question from one of the students who had noticed the angles chosen for the quadrilaterals were all less than 180 o : "Would it work if the quadrilateral has a reflex angle?" I encouraged students to write in the angles that met at a point to verify that they summed to 360 o.
#A TRIANGULAR TESSELLATION DEFINITION HOW TO#
They had to think carefully about how to transform the shape. The quadrilaterals presented a challenge even to the students with the highest prior attainment, particularly when the size of the angles were similar.
Īs our time was limited, I directed the students to cut out a triangle or quadrilateral from card and, after measuring and noting down the interior angles, tessellate their shape on paper. I have a triangular tessellation like the one shown in the figure. To tessellate is to cover a surface with a pattern of repeated shapes, especially polygons, that fit together closely without gaps or overlapping. We compared their ideas with a formal definition (below) and agreed that they were consistent. Will it work with all the types of triangles?Īfter showing them pictures of tessellations, the students began to construct an understanding of the concept: They had no prior knowledge of tessellations and, unsurprisingly, that was their first question about the prompt:ĭoes it mean that triangles fit into quadrilaterals? Do they "perfectly overlap"?ĭo triangles and quadrilaterals do it in the same way? From there, tessellation became a part of the culture of many civilizations, from Egyptians to Greeks, from Byzantines to Chinese.
The number of 3’s is determined by the number of shapes that meet at the vertex (in this case, there are six triangles). The prompt gave them an opportunity to see angle facts in a new context. This regular tessellation with regular triangular tiling has a vertex configuration of 3.3.3.3.3.3. Andrew Blair reports on how the inquiry progressed: A year 7 mixed attainment class at Haverstock school (Camden, UK) inquired into the prompt during a 50-minute lesson.
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