![]() WolframMathworld (click here!) has pictures of several types of regular tessellations. These are just a few examples of tessellations - repeated patterns of identical shapes with no gaps or spaces. Picture a tiled bathroom floor, or the honeycomb in a beehive, or the pattern on a soccer ball. Find out more in this Bitesize Primary KS2 Maths guide. You have definitely seen tessellations before. Tessellation is when shapes fit together in a pattern with no gaps or overlaps. Snowflakes have a hexagonal (6 sided) base, which happens to be one of the best shapes for tessellations! What is a tessellation? Here are a variety of basic geometric shapes that can tessellate from this same pattern, including a hexagon, triangle, square, trapezoid, parallelogram, pentagon (irregular), rhombus (diamond), and rectangle:Ĭopyright © 2014 Chris McMullen, author of the Improve Your Math Fluency series of math workbooksĬlick to view my Goodreads author page.Last week we talked about symmetry, specifically as seen in snowflakes. The same pattern can make a tessellation with stars and hexagons: The lattice structure below can be shaded in several different ways to create simple geometric patterns that tessellate:įor example, here is a tessellation composed of hexagons: Some of the more extreme examples of this can be seen in M.C. Even arrangements of curved objects can tessellate. 1 Early Greek philosophers studied pattern, with Plato. ![]() ![]() From there, tessellation became a part of the culture of many civilizations, from. The origin of tessellation is dated back to 4,000 years BCE, when Sumerians used clay tiles for the walls of their homes and temples. Natural patterns include symmetries, trees, spirals, meanders, waves, foams, tessellations, cracks and stripes. Tessellation is the science and art of covering an infinite plane with shapes without any gaps or overlaps. For example, equilateral triangles tessellate like this: Lets think about other triangles which tessellate: You can print off some square dotty paper, or some isometric dotty paper, and try drawing different triangles on it. These patterns recur in different contexts and can sometimes be modelled mathematically. We say that a shape tessellates if we can use lots of copies of it to cover a flat surface without leaving any gaps. There are many other shapes that tessellate, such as stars combined with other shapes. Patterns in nature are visible regularities of form found in the natural world. (Quadrilaterals are polygons with four sides.) Although regular pentagons don’t tessellate, some irregular polygons can (such as the pentagon made by placing an isosceles triangles on a square, as children often do to draw a simple picture of a house). (A regular polygon is one with equal sides and angles.) All quadrilaterals can form tessellations. Tessellations can also be made from irregular polygons. For example, it won’t work with pentagons. Notice the hexagon (cubes, first tessellation) and the quadrilaterals fit together perfectly. The following pictures are also examples of tessellations. Not any regular polygon will work, however. There are many types of tessellations, all of which can be classified as those that repeat, are non-periodic, quasi-periodic, and those that are fractals. Examples of a tessellation are: a tile floor, a brick or block wall, a checker or chess board, and a fabric pattern. Equilateral triangles have angles of (60circ). Simple tessellations can be made by creating a two-dimensional lattice out of regular geometric shapes, like equilateral triangles, squares, and hexagons. Regular polygons will tessellate if the size of the angle is a factor of (360circ). A tessellation is a repeated two-dimensional geometric pattern, with tiles arranged together without any space or overlap.
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