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Beauty, Form & Function: An Exploration of Symmetry

Nanyang Technological University via Coursera


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Symmetry is everywhere. In the grand scheme of things it is the blueprint by which the universe operates. We see symmetry in nature, art, architecture, science and engineering. This course explores the Beauty, Form and Function of Symmetry in common objects, then progresses to investigate tiling and tessellation, with the extension of these concepts to the atomic structure of crystals. To amplify these ideas, you will undertake field-exercises and be introduced to specialists – botanists, artists, geomancers, historians, scientists and engineers - that work with symmetry, and who will provide their personal insights into its ‘magic’ and impact on their disciplines.


  • Concepts in Symmetry I
    • These lectures will refresh your intuitive appreciation of symmetry in common objects and introduce the mathematical and symbolic descriptors of point symmetry.
  • Concepts in Symmetry II
    • Some of the most beautiful examples of symmetry appear in flowers. These lectures use flowers as exemplars of the application of point symmetry to concisely describe the presence of mirror lines and rotation points.
  • Concepts in Symmetry III
    • The key concepts in plane symmetry are illustrated by examining tessellations in architecture. The important concept of the asymmetric unit is also introduced. The practical importance of symmetry is illustrated through a discussion of chirality and its impact on drug design and efficacy.
  • Concepts in Symmetry IV
    • The formal mathematical nomenclature of point symmetry is introduced, including the relationship between symmetrically linked objects.
  • Plane and Space Symmetry I
    • Plane Groups that describe symmetry operations in 2 dimensions are illustrated using the art of Escher. The 2D Bravais Lattices that capture all tiling permutations are covered together with the difference between ‘primitive’ and ‘centred’ unit cells.
  • Plane and Space Symmetry II
    • The 17 Plane Groups are formally introduced and their representation in the International Tables of Crystallography explained. By mastering the plane group diagrams and figures, all common tessellations can be deconstructed into their symmetric components.
  • Plane and Space Symmetry III
    • These lectures examine the role of symmetry in Islamic architecture and history in the context of regular and irregular networks. The transition to 3D or Space Symmetry is via the five Platonic Solids. The 2D symmetry operators (rotation, reflection, glide) are expanded to include screw axes and axial glide in 3D symmetry.
  • Plane and Space Symmetry IV
    • The 3D Bravais Lattices are the basis for describing the atomic relationships found in many crystalline materials. The way in which Space Symmetry determines not only the atomic locations but also the chemical composition of crystals is explained.

Taught by

Tim White and Jiang Shuo


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