Beauty, Form & Function: An Exploration of Symmetry

Overview

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This course is for anyone interested in the fundamental principles of symmetry across various fields, including art, architecture, science, and engineering. By the end of this course, you will be able to: - Analyze symmetry in natural forms, art, and architectural designs. - Apply tiling and tessellation concepts to design and crystal structures. - Understand the mathematical descriptors of point and space symmetry. - Connect symmetry principles to real-world applications in science and engineering. To be successful, a general interest in science and design is helpful. No specific software is required. You will learn from specialists in botany, art, history, science, and engineering, gaining insights into symmetry's impact on their disciplines.

Syllabus

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.

Formal Point Symmetry: Nomenclature and Relationships

The formal mathematical nomenclature of point symmetry is introduced, including the relationship between symmetrically linked objects.

2D Space Symmetry: Escher and Bravais Lattices

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.

3D Space Symmetry: Architecture and Platonic Solids

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.