Why do we teach tessellation?

Why do we teach tessellation?

Tessellation is an important topic in Mathematics, specifically in the study of 2D shapes. It involves learning about patterns and shapes that fit together perfectly without any gaps or overlaps. Tessellations have a wide range of applications and can be found in various areas of life, including art, architecture, and even hobbies. Understanding tessellation helps develop critical thinking, spatial reasoning, and problem-solving skills.

Key points about tessellation:

1. Tessellated shapes: Tessellated shapes are 2D shapes that fit exactly together. These shapes can be different from each other.
2. Real-life relevance: Tessellations can be found in many aspects of our everyday surroundings. Examples include oriental carpets, quilts, origami, Islamic architecture, and the artwork of M.C. Escher.
3. Understanding tessellation: Tessellation is the process of arranging shapes to create a pattern without any gaps or overlaps. While squares can be tessellated, circles cannot be tessellated as there will always be gaps between them.
4. Tessellation explained for kids: Square tessellation is a common example where squares are arranged in a pattern. The squares meet edge to edge without any gaps or overlapping, similar to a checkerboard.
5. Mathematical relation: In a tessellation, whenever two or more polygons meet at a point (or vertex), the internal angles must add up to 360°. Only three regular polygons – triangles, squares, and hexagons – can form tessellations by themselves.
6. Tessellations as art and math: Tessellations are considered both art and math. They are not just limited to artwork and architecture but also studied as a part of Euclidean geometry in mathematics.
7. Regular tessellations: A regular tessellation involves the repeat of only one shape throughout the pattern. There are three regular polygons that can be repeated without any gaps or overlaps: equilateral triangles, squares, and regular hexagons.
8. Examples in real life: Tessellations can be seen in various real-life scenarios, such as tile floors, brick or block walls, checker or chess boards, and fabric patterns.
9. Tessellation in art: Tessellations play an important role in art and architecture. They provide decorative aesthetics and have been used to cover walls, pavements, and ceilings in many facilities.
10. Tessellation and mathematics: A tessellation or tiling is the covering of a surface, often a plane, using geometric shapes called tiles. The tiles must have no overlaps or gaps. Tessellation can be generalized to higher dimensions and different geometries in mathematics.

Questions about tessellation:

1. What is tessellation and why is it important?

   Tessellation refers to the process of fitting shapes together to create a pattern without any gaps. It is important as it helps develop critical thinking, spatial reasoning, and problem-solving skills.

2. How are tessellations relevant to real life?

   Tessellations can be found in various areas of life, including art, architecture, and hobbies like quilting or origami. Examples include oriental carpets, Islamic architecture, and the artwork of M.C. Escher.

3. What can we learn about tessellation?

   Tessellation is the process of arranging shapes to create a pattern without any gaps or overlaps. It helps understand the concept of space, shapes, and patterns.

4. What is tessellation explained for kids?

   Tessellation for kids can be explained as arranging squares in a pattern where they meet edge to edge without any gaps or overlaps.

5. How does tessellation relate to math?

   Tessellation is related to math as in a tessellation, whenever two or more polygons meet at a point, the internal angles must add up to 360°. Only certain polygons can form tessellations by themselves, such as triangles, squares, and hexagons.

6. Is tessellation math or art? Why?

   Tessellations are both math and art. While they are used in artwork and architecture, they are also studied as a part of Euclidean geometry in mathematics.

7. How do tessellations relate to math?

   In a tessellation, whenever two or more polygons meet at a point, the internal angles must add up to 360°. Only certain polygons can form tessellations by themselves.

8. What is an example of tessellations in real life?

   Examples of tessellations in real life can be seen in tile floors, brick walls, checker or chess boards, and fabric patterns.

9. Why is tessellation important in art?

   Tessellations are important in art because they provide decorative aesthetics and have been used to cover walls, pavements, and ceilings in various facilities.

10. How is tessellation related to math?

    Tessellation involves covering surfaces, often planes, with geometric shapes called tiles without any overlaps or gaps. It can be generalized to higher dimensions and different geometries in mathematics.