Tessellation is the process of creating a repeating pattern using shapes. This can be done with any type of shape, but polygons are the most commonly used. Tessellations are found in nature and in man-made objects. Some examples of tessellations in nature are honeycombs, turtle shells, and fish scales. Man-made examples of tessellations include floor tiles, mosaics, and quilts.

To create a tessellation, the shapes must fit together perfectly so that there are no gaps and no overlapping. This can be a challenge to do without planning ahead. However, by understanding a few principles of geometry, you can create your own tessellations!

One way to create a tessellation is to use regular polygons. A regular polygon is a shape with all sides the same length and all angles the same size. The most common regular polygons are triangles, squares, and hexagons.

To create a tessellation with regular polygons, you will need to start with a basic unit. This is one of the shapes that you will be using to create the tessellation. For example, if you are using triangles, your basic unit could be an equilateral triangle (a triangle with all sides equal in length).

Once you have your basic unit, you can begin creating your tessellation by repeating the unit over and over again. To do this, you will need to connect the vertices (corners) of the shapes together. When you are done, you should have a repeating pattern that covers the entire plane!

As you can see, tessellations can be created using a variety of shapes. By understanding some basic principles of geometry, you can create your own tessellations! Try experimenting with different shapes and see what patterns you can create.

A tessellation is “the filling of a plane with repetitions of figures in such a way that no figures overlap and there are no gaps” (Billstein, Libeskind, & Lott, 2010) . Teseellations may be made out of triangles, squares, trapezoids, parallelograms, or hexagons. Tessellations employ geometric transformations to demonstrate the figure’s duplication.

There are three forms of transformations, translation, glide reflection, and rotation. A translation is a “slide” along a surface without turning or flipping the figure” (Billstein et al., 2010) . A glide reflection is a “slide and flip” transformation, which the figure is turned over after it is slid along the surface. The last transformation is a rotation; this is when a figure is turned around a fixed point. These transformations can be done in any combination to create interesting and complex patterns.

Tessellations are found in nature as well as created by man. Snowflakes are an example of tessellations in nature. Snowflakes form when water vapor turns into ice crystals in the cold atmosphere. The ice crystals start out as simple hexagonal shapes, but as they grow larger, they begin to branch out and form more complex patterns.

Tessellations are also found in architecture and design. Islamic art frequently uses tessellations in their mosaics and patterns. M. C. Escher was a Dutch artist who is well-known for his use of tessellations in his artwork. He used a variety of figures to create detailed and intricate designs.

Tessellations can be used for problem solving in mathematics. They can be used to cover an area without gaps or overlaps, or to fill a space with a limited number of shapes. Tessellations can also be used to create 3-dimensional shapes.

Translation, rotation, reflection, and glided reflections are all examples of transformations. A student may construct their own unique tessellation by combining a variety of geometric forms in a repetitive pattern using a transformation, whether manually or on a computer.

Many everyday objects can be found in tessellations. For example, floor tiles, checkerboard, and the hexagonal cells of a honeycomb are all examples of tessellations. Other less obvious examples include the patterns on a lizard’s skin, a butterfly’s wing, and even the pattern of mountain ranges seen from space!

Tessellations are found in nature because they provide an efficient way to cover a surface with minimal waste. Many animals have adapted their camouflage to match the tessellated patterns found in their environments.

While most tessellations are based on regular polygons, it is possible to create tessellations using other shapes as well. One famous example is M. C. Escher’s “Square Limit,” which uses both squares and devils to create a never-ending tessellation.

Creating your own tessellation can be a fun and challenging problem-solving activity. To get started, try experimenting with different shapes and transformations. With a little practice, you’ll be creating tessellations of your own in no time!

The tessellation I made is made up of hexagons, squares, and triangles. The open areas around the hexagon were filled in with squares and triangles; this was done to ensure that the tessellation was fully completed. That’s why I did it because it looks very attractive when it’s colored in and adds color to make it a more visually stimulating work.

I also found it to be more difficult than just filling in the spaces with one shape. Tessellations can be found in everyday life and sometimes we don’t even realize it. Examining the world around us, we can see tessellations everywhere; from the tiles on the floor or in a mosaic, to the hexagons on a honeycomb, and even the scales on a fish.

When creating my tessellation, I was inspired by some of these real-life examples. I wanted to create something that would be both visually interesting and have some meaning behind it. I think that tessellations are often overlooked as being just “pretty patterns,” but there is so much more to them than that. They are actually a fascinating mathematical concept that can be applied to problem solving in many different ways.

I hope that you enjoy my tessellation and that it inspires you to look for tessellations in the world around you. Thank you for taking the time to view my work!