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An Exploration of Symmetry (Eligible for NTU Credit)

Nanyang Technological University via Coursera

This course may be unavailable.


Nanyang Technological University and Coursera are proud to offer Beauty, Form & Function: An Exploration of Symmetry that caters to both non-specialists via a non-academic credit on-demand version ( and specialists through this academic credit fixed-session version.  Below can be found the:

Syllabus • Grading Scheme • Recommended Readings •

Required Background Essential Resources Student Responsibility • FAQs

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, gems and crystals, and finally its indispensable role in technology.  Symmetry and asymmetry are also key factors that ensure the successful reproduction of plants and animals. For example, the bilateral symmetry of orchids is widely admired and this geometry is essential for insects to pollinate these flowers.

Duration: 8 weeks

Time Commitment: 7-10 hours per week

Target Group: Scientists and Engineers (current and prospective NTU students)

Recognition: Verified Certificate through Signature Track enrollment

NTU Academic Units: Verified Certificate Students earn 3 Academic Units

NTU Course Type:  Unrestricted Elective or General Elective

This course gives you the means to address several fundamental questions.

  • What tags do we recognize in decorative arrangements?
  • What guidelines shape the patterns in the world around us?
  • What functions do these symmetrical patterns serve?
  • How are drug and materials design engineered through atomic scale symmetry?
  • How is the internal arrangement of atoms reflected by crystal faceting?
  • How does symmetry manipulation create polytypes, polymorphs and polysomes?

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.

The option of earning AUs is open to all students. It is not necessary to be already enrolled at NTU.  Once earned, the AUs remain valid for 3 years.

Course Difficulty

This is a challenging course with 65% of students rating the material as Difficult to Very Difficult, but many find the subject matter stimulating.


The course content is released in two week blocks and consists of approximately 1 hr of lectures and tutorials per week. There are specific windows for uploading homework and undertaking peer-to-peer marking. These are detailed in the downloadable course timetable.

Part I: Basic Concepts of Symmetry

  • Week 1: ‘A World of Symmetry’ will refresh your intuitive appreciation of symmetry in furniture, botany and common objects and introduce the mathematics of point symmetry.

  • Week 2: ‘Tiling and the Asymmetric Unit’ begins by examining tessellations in architecture that will illustrate key concepts in plane symmetry including the asymmetric unit.  ‘Chirality’ discusses this key concept in symmetry and its impact on drug design and delivery.

Part II: Plane (2D) and Space (3D) Symmetry

  • Week 3: ‘Escher and Graphic Design’ introduces symmetry operations in 2 dimensions and the difference between ‘primitive’ and ‘centered’ unit cells are illustrated using the art of Escher. ‘Nets’ examines the role of symmetry in Islamic architecture and history in the context of regular networks.

  • Week 4: ‘Space Symmetry’ expands the symmetry operations to include 3 dimensional motion.  The methodology for reading and using the symmetry diagrams of the 17 plane groups and 230 space groups is introduced.

Part III: Symmetry in Crystals

  • Week 5: ‘Crystal Forms and the Beauty of Minerals’ looks the external shape of mineral crystals and we learn about crystal power by visiting a geomancer. The manner in which crystal faceting reflects the internal atomic arrangements is described. ‘Planes, Directions and Unit Cell’ introduces the mathematics for describing perfect crystal structures.

  • Week 6: ‘Platonic Solids and Atomic Bonding’ shows that regular geometrical shapes can be derived from folding plane nets into polyhedra that often describe atomic clustering and also the appearance of defects or asymmetry that are important aesthetically and technologically.  A laboratory tour will show the experiments used to extract crystallographic information.

Part IV: Symmetry and Technology

  • Week 7: ‘Tailoring Crystals for Technology’ brings together chemistry and crystallography, shows how they are inter-related, and how they are adapted to engineer designer technological materials.  A clean room fabrication facility provides real world context for exploiting chemically- and physically-driven symmetry.

  • Week 8:  ‘Looking for Broken Symmetry - Atomic Scale Imaging’ looks beyond 3 dimensional symmetry to higher dimensional repetitions found in incommensurate crystal structures. ‘Deceptive Perception - Symmetry & Furniture Design’ returns to the everyday appearance of symmetry that can now be explored analytically.

At the conclusion of this study, you will possess the tools and the motivation to look at symmetry with even greater delight, wonder and appreciation!

Taught by

Tim White


3.4 rating, based on 7 Class Central reviews

Start your review of An Exploration of Symmetry (Eligible for NTU Credit)

  • Anonymous
    This is absurdly difficult and I have no idea what that guy is saying. Gotta rewatch the videos several times to understand + do your own research.

    Way too difficult!
  • Anonymous
    The module is ridiculously difficult. The jump from the 2nd part to the 3rd part is too huge and a writing exercise is actually expected of us.
  • Anonymous
    I did not have the time to continue with the course beyond the first module but the lectures were extremely interesting.
  • Claude Lambert
    This was an excellent course, I found that it transformed the way I looked at nature and architecture. It disappeared from Coursera at my great regret, because I wanted to go back and check a few things.
  • Anonymous
    Was a difficult course, but really interesting and informative!
    If you are no math genius then you might need extra time to make everything clear for yourself.
  • Anonymous
  • Revathidevi Allu

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