By: 8B (23) Lee Pak Long
So, what is “Tessellation? According to the dictionary, Tessellation is the process of creating a pattern using the repetition of a shape with no overlaps and no gaps at all, which the word “tessellate” comes from the Greek word “Tesseres” ,which means “4”.

Otherwise, comprehending in a simpler manner, a way to tile a floor. Also, the puzzle you did last time is also a tessellation actually. Since primary school, we have learnt about 2D tessellation, which can also be found in our mother nature. When basaltic lava flows they mostly have cracks on them caused by contraction forces, creating columns of harden lava which resembles the tessellation of regular hexagons. One of the most famous example, the Giant’s Causeway in Northern Ireland. Tessellations can also found in daily life. For example, the tilings on the floor, toilets etc. For regular tessellation mentioned before, there are actually only 3 types of regular polygons which can be tessellated by themselves, which is : 1. Triangles

2. Squares

3. Hexagons

Only three regular tessellations exist, because there are only three polygons whose interior angles divide evenly into 360 degrees: the triangle (60 degrees) the square (90 degrees) and the hexagon (120 degrees). Of the regular polygons, only triangles, squares, hexagons, octagons, and dodecagons can be used for tiling around a common vertex - again because of the angle value, and 14 such combinations exist! The combination is :

Combination of Polygons| Combination of Angles|
6 triangles| 6X 60 = 360|
4 squares| 4 X 90 = 360|
3 hexagons| 3 X 120 = 360|
3 triangles and 2 squares| (3 X 60) + (2 X 90) = 360|
3 triangles and 2 squares - another formation| (3 X 60) + (2 X 90) = 360| 2 hexagons and 2 triangles| (2 X 120) + (2 X 60) = 360|
2 hexagons and 2 triangles - another formation| (2 X 120) + (2 X 60) = 360| 1 hexagon, 2 squares,...

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Tessellation Patterns
MTH/157
Tessellation Patterns
Tessellation Patterns are a way to express creativeness. A tessellation is a repeating pattern of shapes covering a plane without any gaps or overlaps. Choosing a pattern with triangles that are black and white was a way to express a pattern. There are so many different ways to create a tessellation pattern and use of transformation. Normally, tessellations are created using polygons, this one was created using triangles.
Reflections occur across a line called the axis. To reflect a shape across an axis is to plot a special corresponding point for every point in the original shape. Specifically, the corresponding point is the point that is the same distance from the axis as is the original point. You determine the distance from a point to a line by drawing a line perpendicular to the original line and that passes through the point.
Working with simple lines of symmetry will make this pattern clean and simple with black and white colored triangles for the pattern. This pattern is a reflection of itself so when that it is folded in half either way the reflection will show on the other side as the same. Working with many patterns and colors to make different designs can be quiet confusing in the way they turn out.
There are so many ways to work with a tessellation, one can use squares, triangles...

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What is a tessellation? A tessellation is the creation of a two dimensional plane with the use of a geometric shape repeatedly and leaving no gaps. Tessellations can be found everywhere in our daily life and also in nature. For example of tessellations that can be seen anywhere is the sidewalks that you walk on, even though it’s a simple tessellation it is still a tessellation. Another example of a tessellation that can be seen in nature is a beehives comb, the pattern in side is a tessellation made of octagons which stores honey.
The word “tessellation” got its name from the latin word “tessella” which mean small cube. The history is of tessellations are actually very short. In 1619 Johannes Kepler one of the first people to make record of tessellation when he wrote about regular and semiregular tessellation, which are coverings of a plane with regular polygons. In 1891 a Russian crystallographer Yevgraf Fyodorov proved that every periodic tiling of the plane features one of seventeen different groups of isometries.(source taken from Wikipedia)
M.C Escher a famous dutch artist who uses tessellations in all of his art work. M.C Escher is not only just an artist but a math major. In every artwork of Escher is has many...

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Tessellation Patterns
Sheela Lewis
MTH 214- Mathematics for Elementary Educations II
December 16, 2013
Roland Garbe
Tessellation Patterns
A tessellation is “the filling of a plane with repetitions of figures in such a way that no figures overlap and that there are no gaps” (Billstein, Libeskind, & Lott, 2010) . Tessellations can be created with a variety of figures, including triangles, squares, trapezoids, parallelograms, or hexagons. Tessellations use forms of transformations to show the repetitions of the figures. The transformations can includes translations, rotations, reflections or glided reflections. Any student would be able to create their own original tessellation by piecing together a variety of geometric shapes in a repetitive pattern by a transformation, either by hand or on a computer.
The tessellation that I have created includes hexagons, squares, and triangles. I placed the squares and triangles around the hexagon to fill in the open spaces; this is to ensure that it is a complete tessellation. I did that because I found it to be very eye catching and adding the colors makes it a visually stimulating piece. This tessellation has the transformation of translation. Each shape is moved from one point to another in a straight line. The line can either be up or down, left to right, or even diagonally, but the shape...

...TessellationTessellation is the process of repeating geometric shapes to form a pattern. These patterns do not contain any gaps, or overlaps of the geometric shape. Tessellation in everyday life can be seen in mosaics, tiling, art, and even in nature. A bee hive or honeycomb is a great example of the natural tessellation.
When I first saw the assignment for this week, I assumed it would be easy to do. However, the actual process of making the pattern was harder than expected. The concept seems easy enough; the application is where I struggled. I also found using the paint application harder because the image is not easily formatted to fit on a piece of paper. I had to adjust and readjust the image multiple times in order for it to be seen properly.
The type of transformation used in this tessellation is the flip transformation. I used one image and reverse it back and forth to form a pattern. I chose the figure because it was an easy shape to draw and manipulate. I found as I tried to create a pattern the more intricate the figure, the harder it is to form a coherent pattern. By using a simple pattern I was able to manipulate it with flipping to form an interesting and intricate pattern.
In all, this is a great activity for students, but I think I would help simplify the method for younger children by having cutouts of different shapes for them to use. This would enable my students to use...