Tessellations Coloring Book

Tessellations, also known as "mosaicking" or "surface division," refer to geometry and the art of creating patterns or figures by repeating one or more elements in such a way that there are no gaps between them and the surface is filled in a regular and uninterrupted manner. Tessellations have many applications in mathematics, art, architecture and design.

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1. Types of tessellation: There are three basic types of tessellation, which differ in the arrangement of elements:
   • Homogeneous tessellations: all elements are the same and fit together perfectly, forming a regular pattern.
   • Semi-uniform tessellations: the pattern consists of two or more types of elements, but each type fits together.
   • Heterogeneous tessellations: the pattern consists of elements that do not fit together, creating a more chaotic pattern.
2. Mathematical aspects: In mathematics, tessellations are related to geometry, especially the theory of planes and geometric figures. Mathematicians study which plane figures can be used to create regular tessellations and under what conditions.
3. Art and design: Tessellations have been used in various works of art and design over the centuries. They are present in mosaics, stained glass, ceramics, textiles and other artistic fields.
4. Escher and tessellations: Dutch artist M.C. Escher is known for creating complex artworks using tessellations. His works often explore unimaginable geometric arrangements that seemingly merge into infinity.
5. Examples in nature: Many examples of tessellation can be found in nature, such as the arrangement of pineapple peels, the pattern of hexagons in a bee's honeycomb, or the arrangement of bark in certain types of trees.
6. Patterns on floors: Many structures and buildings around the world have floors decorated with tessellations, giving them a unique and artistic look.
7. Applications in architecture: In architecture, tessellations can be used to design patterns on building facades, mosaics, floors or roofs.
8. Education: Tessellations are often used in mathematics education as a way to introduce concepts of geometry, patterns and symmetry.
9. Create your own designs: Modern graphic tools allow you to create your own tessellation patterns. All you have to do is select elements and arrange them accordingly, creating interesting compositions.

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1. Tessellations in nature: Many organisms in nature use tessellations to make optimal use of space. For example, in bees you can see regular hexagonal patterns in their honeycombs.
2. M.C. Escher - master of tessellation: M.C. Escher, a famous Dutch graphic artist, is one of the best-known artists using tessellations in his art. His works, such as "Metamorphoses" and "Up and Down," explore unimaginable geometric arrangements.
3. Mandalas and tessellations: In Hinduism and Buddhism, mandalas, or geometric patterns with circular symmetry, are a type of tessellation. They are used as a meditative and artistic tool.
4. Tessellations on roofs: In Islamic architecture, tessellations can be seen on the roofs of mosques and other buildings. These patterns are one form of Islamic art, and their intricate arrangement is both aesthetic and symbolic.
5. Penrose tessellations: British mathematician and physicist Roger Penrose created the famous "Penrose Tessellations," which are inhomogeneous tessellations, i.e., they form patterns in which the traditional repeating arrangement does not occur.
6. Tessellation contests: There are competitions and art events in which artists compete in creating original tessellation designs. Such events help promote creative thinking and develop artistic skills.
7. Interactive applications: Many interactive apps and online tools allow people to create their own tessellation patterns. It's a great opportunity to explore geometry and creative design.
8. Application in design: Tessellations are used in many design fields, such as textile design, ceramics, graphic design and interior design.
9. Tessellations as learning and fun: Teachers often use tessellations as an educational tool to teach about symmetry, patterns and geometry. At the same time, making tessellations can also be a great form of creative fun.
10. Three-dimensional tessellations: In addition to two-dimensional tessellations, there are also three-dimensional tessellations, which create repeating patterns in three dimensions. This is an advanced area of geometry and mathematics.