Final answer:
Micro-architecture carries sacred geometry into three dimensions through hierarchically arranged spaces and symmetrical design, illustrated by Byzantine domed churches as cosmos representations and Neo-Platonistic compositional elements in artwork and architecture.
Step-by-step explanation:
The micro-architecture principle is used to express sacred geometry by arranging and carving space to reflect the cosmic order and spiritual concepts in three-dimensional structures. As Byzantine texts describe, the domed church serves as a microcosm, linking the heavens above with the earth below, often in a hierarchical fashion.
This concept finds physical expression in works such as the frescoes and mosaics in Byzantine churches, where holy figures are set against a gold background, creating spatial icons that appear to share the churchgoers' physical space. The use of symmetry, like that seen in the Gateway Arch and Richard Serra's Tilted Spheres, exemplifies sacred geometry in three-dimensional forms, showcasing balance and echoing organic structures.
Similarly, the composition in works such as Masaccio's Holy Trinity relies on geometrical forms like triangles and circles, anchoring the artworks in Neo-Platonism and creating the sense that they are reflections of the divine order. In the case of Gothic architecture, elements like the archivolts, tympanum, and meticulously calculated column ratios also display the use of sacred geometry to structure space in a way that communicates religious symbolism and mathematical harmony.