Tessellation

Definition

Tessellation is the covering of a surface using one or more geometric shapes, called tiles, with no overlaps and no gaps. This artistic and mathematical concept is closely related to patterns, symmetry, and geometric abstraction, showcasing how shapes can interact and fill a space in a cohesive manner while maintaining aesthetic appeal.

5 Must Know Facts For Your Next Test

1. Tessellations can be created using regular polygons like triangles, squares, and hexagons, as well as irregular shapes.
2. The concept of tessellation is deeply rooted in both mathematics and art, bridging the gap between these two disciplines through visual patterns.
3. Tessellations have historical significance, being used in ancient architecture and art across different cultures, from Islamic tile work to modern abstract art.
4. In geometric abstraction, artists explore the visual properties of shapes through tessellation, allowing for infinite variations while maintaining a structured composition.
5. The study of tessellations relates to concepts in topology and geometry, where researchers analyze how spaces can be tiled efficiently without gaps or overlaps.

Review Questions

• How do tessellations exemplify the relationship between mathematics and art?
  • Tessellations serve as a perfect example of how mathematics and art intersect because they rely on geometric principles to create visually engaging patterns. Artists use mathematical concepts to arrange shapes in a way that fills a surface completely without gaps or overlaps. This interplay allows for a structured exploration of form while showcasing creativity through variations in design and color.
• Discuss the influence of M.C. Escher on the understanding of tessellation in geometric abstraction.
  • M.C. Escher had a profound impact on the perception of tessellation within the realm of geometric abstraction by pushing the boundaries of traditional tiling techniques. His work often transformed simple geometric shapes into complex images that challenged viewers' perceptions of reality. Escher's intricate designs not only highlighted the aesthetic potential of tessellations but also emphasized their mathematical foundations, inspiring artists and mathematicians alike to explore this dynamic relationship further.
• Evaluate how tessellations can reflect cultural significance in various artistic traditions and movements.
  • Tessellations reflect cultural significance by showcasing how different societies utilize geometric patterns in their artistic expressions. For instance, Islamic art is famous for its intricate tile work that features complex tessellations symbolizing infinity and unity. Similarly, modern abstract artists draw on these traditions to develop new interpretations that resonate with contemporary themes. By evaluating these connections, one can see how tessellations not only serve aesthetic purposes but also embody cultural narratives and mathematical principles that transcend time and place.

Related terms

M.C. Escher: A Dutch graphic artist known for his mathematically inspired artwork that often features impossible constructions, explorations of infinity, and intricate tessellations.

Geometric Patterns: Repeated arrangements of shapes that create visual designs, often used in art and architecture to enhance the aesthetic quality of a surface.

Symmetry: A balance and proportion between the parts of an object, often seen in tessellations where shapes mirror or rotate around a central point or axis.