We often marvel at the significance of mathematical patterns in nature: the hexagonal chambers in a honeycomb, the fascinating layout of tiles in our bathroom, or the captivating design of a pinecone. These patterns, where shapes fit snugly with no overlaps or gaps, are examples of tessellations. So, what is tessellation? Let’s dive in and explore, making the complex simple for our little ones!
What is tessellation?
Tessellation is an intricate and fascinating concept in both art and mathematics. It refers to a collection of shapes that interlock and fit together without any gaps or overlaps. To visualise this, think about a jigsaw puzzle. Even though every piece of the puzzle is distinct, when put together, they fit seamlessly, leaving no empty spaces. This seamless fitting of shapes embodies the principle of tessellation. Historically, tessellations have been utilised in various cultures for decorative purposes in architecture, ceramics, and textiles. In mathematics, tessellations provide insights into spatial arrangements and geometric patterns.
What shapes will tessellate?
Understanding which shapes can tessellate is crucial. Basic shapes that naturally tessellate include:
Squares: A classic example is a chessboard where squares fit together without any gaps.
Equilateral Triangles: Triangles that have equal sides and angles. When you position six such triangles, they converge at a point seamlessly.
Hexagons: The design of a honeycomb is a testament to the tessellation capabilities of hexagons.
Rectangles: Often used in flooring, rectangular tiles, even though they seem like stretched squares, can tessellate effectively.
However, it’s worth noting that not every shape can tessellate on its own. Circles, for example, can’t tessellate independently. Regardless of their placement, there will always be void spaces between them. But with some creativity, a combination or alteration of different shapes can lead to new tessellating patterns.
Types of tessellations
Having read about the various shapes, you must be wondering about the various types of tessellations. Tessellations can be categorised based on the shapes involved:
Regular Tessellations: These involve only one type of regular polygon, like hexagons in a honeycomb or equilateral triangles fitting together.
Semi-Regular Tessellations: Here, two or more types of regular polygons come together to tessellate. The polygons fit together just as snugly as in regular tessellations.
Irregular Tessellations: Not relying on regular polygons, these tessellations might seem chaotic, but the shapes still interlock perfectly, akin to a jigsaw puzzle.
How to Make a Tessellation
Crafting tessellations can be a delightful activity for kids. Here’s a step-by-step guide on how to make a tessellation:
Materials Needed: Cardstock, scissors, coloured pencils, transparent tape.
Step 1: Start by cutting a small rectangle out of the cardstock.
Step 2: Cut a wavy line, not overly intricate, from one end of the rectangle to the other.
Step 3: Shift the piece you’ve cut to the opposite side of the rectangle and secure it with tape.
Step 4: Replicate the previous step but for the top or bottom side of the rectangle.
Step 5: Your tessellating shape is ready! Trace it multiple times on paper, ensuring they fit snugly.
Step 6: Let the creativity flow! Colour in the patterns and bring the tessellation to life.
Pro-tip: Encourage kids to play around with different designs. This exploration nurtures their creativity and offers a tangible understanding of tessellations.
Introducing Tessellations to Kids
Instilling the concept of tessellations in kids can be both fun and educational:
Start Simple: Initiate the learning with recognizable tessellations, like a tiled floor or a chessboard.
Nature Walk: Nature offers numerous tessellation examples. A simple walk can expose kids to patterns in honeycombs, pinecones, and more.
Interactive Games: The digital world has numerous games and applications where kids can design their tessellations, enhancing their understanding.
Art Projects: Incorporate tessellations into art projects. Let them create beautiful patterns, helping them admire both the beauty and structure of tessellations.
Books: Many children’s books delve into tessellations, seamlessly integrating the concept into captivating narratives.
Historical Importance of Tessellations
Tessellations have a rich history that spans across various cultures and epochs. Ancient civilizations like the Romans and Greeks employed tessellations in their mosaics and architecture, showcasing intricate geometric patterns. In Islamic art, tessellations became an expression of spiritual beliefs as intricate geometric designs adorned mosques and palaces, signifying the infinite nature of God. Renowned artists like M.C. Escher further popularised tessellations in modern times with their mind-bending artworks. Understanding the historical context of tessellations can instil a deeper appreciation for the patterns and help recognise their influence in various art forms and cultures.
Applications of Tessellations in Modern Times
Today, tessellations find applications beyond art and decoration. In science, the study of tessellations aids in understanding molecular structures and crystal formations. In technology, tessellations are used in computer graphics to simplify complex models and reduce the computational load. Urban planning and architecture also utilise tessellation principles to maximise space usage and create efficient designs. For instance, tessellated patterns can be seen in the planning of certain residential complexes or public spaces to ensure optimal space utilisation. By recognising these applications, one can truly appreciate the omnipresence of tessellations in our everyday lives.
Tessellations in Mathematics Education
In the realm of education, tessellations hold a prominent spot, especially within mathematics. They offer an interactive and visual approach to understanding geometric principles, symmetry, and spatial reasoning. When students engage with tessellations, they’re not only appreciating an art form but also developing critical thinking skills. Educators often employ tessellations to introduce concepts like angles, polygons, and transformations. By manipulating and creating tessellated patterns, students can physically see and comprehend abstract mathematical ideas, making learning both engaging and effective.
Tessellations are all around us, weaving magic in nature and art. Introducing children to this concept not only enhances their mathematical understanding but also amplifies their appreciation of the world’s intricate designs.
Speaking of nurturing curious minds, at EuroKids, we believe in fueling children’s imagination and curiosity. Our learning modules are designed to make complex ideas simple and engaging. If you’re seeking a holistic learning environment for your child, look no further. Join the EuroKids family today. If you want to get a first hand experience of life at EuroKids, do visit the EuroKids centre nearest to your house today!