Art, Ancestors, and Algorithms
Traditional MÄori art is more than just decoration; it is a visual language rich with meaning, history, and mathematics. The intricate patterns found in kÅwhaiwhai (painted rafters), tukutuku (woven panels), and tÄniko (weaving) are beautiful examples of geometric principles like translation, rotation, reflection, and symmetry. These patterns were carefully constructed, following rules and algorithms passed down through generations of artists and mathematicians.
Core Geometric Patterns
KÅwhaiwhai: Translation and Reflection
KÅwhaiwhai patterns, often seen on the rafters of a marae, are a perfect example of translation (sliding a pattern along a line) and reflection (flipping a pattern). The repeating patterns often represent the genealogy of the iwi, with each element flowing from the last.
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Translation
Tukutuku: Symmetry and Tessellation
Tukutuku panels are woven with flax and other materials to create geometric patterns that often have rotational symmetry. The patterns, such as pÄtiki (flounder) or kaokao (armpit), are tessellated (repeated to fill a space without gaps or overlaps) across the panel.
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Tessellation
Deconstructing a Pattern: The PÄtiki
The pÄtiki (flounder) pattern is a common design in tukutuku panels. It represents hospitality and abundance. Mathematically, it is a simple yet elegant example of rotational symmetry. The basic diamond shape is rotated around a central point to create the final design.
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Critical Thinking & Design Challenge
1. Choose one of the geometric principles (translation, rotation, reflection, symmetry). Where do you see examples of this principle in your everyday life?
2. On the grid below, use the principles of translation and reflection to create your own simple kÅwhaiwhai-inspired pattern.