Tessellations: A Visual Feast
Tessellations are repeating patterns of geometric shapes that fit together perfectly without gaps or overlaps. Here are some examples, ranging from everyday to artistic:
Everyday Tessellations:
* Brick walls: Classic rectangular bricks tessellate to create sturdy walls.
* Honeycomb: Hexagonal cells of a honeycomb tessellate to maximize storage space and strength.
* Floor tiles: Square, rectangular, or even hexagonal tiles tessellate in countless patterns for various flooring.
* Checkerboard: Alternating squares of two colors form a simple yet visually appealing tessellation.
Artistic Tessellations:
* Islamic art: Intricate geometric patterns, often using tessellations of polygons and stars, are prominent in mosques and other Islamic architecture.
* M.C. Escher's work: This Dutch artist famously used tessellations to create captivating and impossible optical illusions, like his "Reptiles" and "Metamorphosis" works.
* Modern art: Contemporary artists use tessellations to explore themes of repetition, pattern, and space. Some artists even create their own unique tessellation designs.
Beyond the Basics:
* Penrose tiling: This unique tessellation uses two shapes, a kite and a dart, that can only be arranged in a non-periodic pattern.
* Tiling with fractals: Complex shapes like the Sierpinski triangle can be used to create intricate and visually stunning tessellations.
Try it Yourself:
* Paper cutting: Experiment with cutting shapes from paper and arranging them to create your own tessellations.
* Digital art: Use programs like Photoshop or Illustrator to create tessellations digitally.
* Origami: Some origami patterns, like the "dragon" or "modular units," utilize tessellations.
Tessellations are a fascinating aspect of geometry, blending mathematics and art. With a bit of creativity, you can discover the beauty and complexity of these repeating patterns yourself.