![]() ![]() Only triangles, squares, and hexagons, which are the only shapes with equal sides and angles, can make a tessellation on their own. When two or even more polygons meet at a point in a tessellation, or when two or even more polygons meet at a certain vertex, the inner angles should add up to 360°. ![]() You can give a name to a tessellation by focusing on the vertex and noting the side of all the structures that converge at the vertex at the same time. The point where two shapes meet, also known as the corner point, is referred to as the vertex. It follows that there are only three distinct types of regular tessellations: those constructed from squares, equilateral triangles, and hexagons. They are used rather frequently in works of art, patterns for clothing, designs for pottery, and blown glass windows. These days, tessellations are employed for the floors, walls, and ceilings that are found inside buildings. In addition, the tessellations that are used in architecture may be seen at Fatehpur Sikri. The Alhambra Palace in Granada, which is in the southern region of Spain, is an example of a Muslim edifice that hints at the presence of tessellations. Tessellations, which are miniature quadrilaterals used in computer games and in the construction of mosaics, were exploited by the ancient Greeks. Tessellations had been tracked all the way back to the ancient civilizations, where they were first discovered (around 4000 BC). They frequently exhibit certain qualities that are tied to their place of origin in some way. There is evidence that tessellations were used in a variety of ancient cultures across the world. The word “tessellation” originates from the Latin verb tessellate, which translates to “to pave,” or the word “ tessella,” which refers to a little, rectangular stone. ![]() The only rule is that all of the sides must fit together perfectly, with no empty spaces or overlap. But you can also make them by mixing different geometric shapes (e.g., hexagons and squares), to make tessellating patterns. As shown in the figure above, triangles can be used to make a tessellated pattern. Here's a nice article that may give some ideas that students could look into to understand the purpose of tessellations in our natural world. As for the honey bees an interesting thing to look into is why do honey bees use regular hexagons rather than other regular polygon that tessellates- it has to do with optimizing the amount of honey a regular hexagon stores. I'm still thinking about how to move forward on this though. I am thinking about how I could create certain parameters in which the students will have to fill a finite plane of some shape and they will have to make some sort of prediction. I feel something is missing in my project that requires them to take it further than just designing their own. Although it is true that tessellations can be found both in the natural world as well as in more synthetic (man-made) products/ art/architecture. ![]() I am stuck in how to make this project more authentic to the students though. This entails an understanding in transformations, interior angles of a polygon and I differentiated by creating different roles: some students had to design a mutated figure that would tessellate with an equilateral triangle, square, regular hexagon, irregular triangle, and irregular quadrilateral. I am an 11th Grade math teacher and I have done a larger project with my students in which they have to design their own tessellation using Geometer's Sketchpad. I agree with John Golden, in that you could extend the idea to have student think about the "so what". I really like the idea of using pattern blocks to work with semi-regular tessellations. ![]()
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