Beauty, Form & Function: An Exploration of Symmetry
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Course Date: 11 August 2014 to 06 October 2014 (8 weeks)
Learn how to identify symmetrical forms and appreciate their importance in nature, art, architecture, crystallography and technology. Understand symmetry quantitatively, recognize its role in beauty and design, and appreciate its function in our everyday life. The level of difficulty is intermediate-to-hard depending on the Track chosen.
Workload: 4-6 hrs/week for Track 1 (5 weeks - Statement of Accomplishment); 7-10 hrs/week for Track 2 (8 weeks - Statement of Accomplishment with Distinction). This MOOC is for credit and students who obtain a Verified Certificate and complete Track 2 with an overall mark of more than 60% earn 3 Academic Units (AU) that can be directed towards either an Unrestricted Elective (UE) or General Elective (GE-STS) subject at NTU. For Verified Certificate students the usual NTU examination procedure requires student identification through webcam plus keystroke patterning for each assignment submission. It is not necessary to be enrolled at NTU to be awarded 3 AU and once received the AU remain valid 3 years. Because this is a for-credit course students must join the Signature Track stream within the first 2 week add-drop period (up to 26 January 2015, 2359 hrs) in accordance with NTU rules.
Tim White is a
Professor of Materials Science at Nanyang Technological University where he teaches crystallography,
electron microscopy and X-ray diffraction to undergraduate and graduate
students. His research encompasses mineralogy, clean
energy materials, environmental remediation, nuclear waste disposal and
catalysis, where synchrotron X-ray and neutron scattering methods probe atomic-scale
symmetry. In 2006,
he introduced a suite of teaching modules for materials scientists called On-line Micro- and Nano-characterisation Instruction (OMNI) that were extended by the Australian Learning
and Teaching Council to create MyScope, a national curriculum for
blended learning in microscopy and imaging (http://www.ammrf.org.au/myscope/ ).
Tim developed the first comprehensive
on-line course at NTU called Symmetry and Crystals from which this MOOC on Beauty,
Form and Function: An Exploration of Symmetry evolved.
Nanyang Technological University
and Coursera are proud to offer Beauty, Form & Function: An Exploration of
Symmetry as the first dual-track MOOC that caters to both specialists and
non-specialists, and can lead to full academic credits.
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
Track 1 Overview (PARTS I and II)
Duration: 5 weeks
Time Commitment: 4-6 hours per
Target Group: Teachers, artists, architects
and anyone with a passion for symmetry
Recognition: Certificate of
This Track gives you the means to
address several fundamental questions.
What tags do we recognize in
What guidelines shape the
patterns in the world around us?
What functions do these
symmetrical patterns serve?
Track 2 Overview (PARTS I, II, III and IV)
Duration: 8 weeks
Time Commitment: 7-10 hours per
Target Group: Scientists and
Engineers (existing and prospective NTU students)
Recognition: Certificate of Accomplishment
NTU Academic Units: Verified
Certificate Students earn 3 Academic Units
NTU Course Type: Unrestricted Elective or General Elective
This Track explores the impact of
symmetry in technology through:
Describing crystals at the
atomic scale to understand drug and materials design
Understanding how the internal
arrangement of atoms is reflected by crystal faceting
Appreciating symmetry modification
through polytypism, polymorphism and polysomatism.
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.
Successful completion as a Verified Certificate student earns 3 academic
units (AUs) for an Unrestricted Elective or General Elective subject at NTU.
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
Will I get a Statement of Accomplishment
after completing this class? Yes. Students who successfully complete the class will
receive a Statement of Accomplishment from Coursera.
What resources will I need for this class? A Smartphone or a digital camera, and the time to read, write, and discuss, with your peers.
What is the coolest thing I'll learn if I
take this class? The world will never look the same again! Your eyes will be opened to the wonders and beauty of symmetry in ways you cannot imagine.
The entire course content is
available from the course opening 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.
Part I: Basic Concepts of Symmetry
(Track 1 and Track 2)
Week 1: ‘Recognizing Symmetry Around Us’ will refresh your intuitive
appreciation of symmetry in furniture, botany and common objects and introduce
the mathematics of point symmetry.
Week 2: ‘Understanding the Unit Cell’ begins by examining tessellations
in architecture that will illustrate key concepts in plane symmetry including
the asymmetric unit. ‘Nature of
Chirality’ discusses this key concept in symmetry and its impact on drug design
Part II: Plane (2D) and Space (3D)
Symmetry (Track 1 and Track 2)
Week 3: ‘Plane Groups’ describes the symmetry operations in 2 dimensions
and the difference between ‘primitive’ and ‘centered’ unit cells illustrated
using the art of Escher. ‘Nets’ examines the role of symmetry in Islamic
architecture and history in the context of regular and irregular networks.
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
Part III: Symmetry in Crystals
Week 5: ‘Atoms in Crystal Structures’ looks the external shape of
mineral crystals by visiting a geomancer. The manner in which crystal faceting
reflects the internal atomic arrangements is described. ‘Polyhedral Properties’
shows that regular geometrical shapes can be derived from folding plane nets to
create Platonic and Archimedean solids that often describe atomic clustering.
Week 6: ‘Planes, Directions and Unit Cell’ introduces the mathematics
for describing perfect crystal structures 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: ‘Trends and Substitutions’ brings together chemistry and
crystallography, shows how they are inter-related and provide the means to
engineer designer technological materials.
A clean room fabrication facility provides real world context for
exploiting chemically-driven symmetry.
Week 8: ‘Building Complex
Structures’ looks beyond 3 dimensional symmetry to higher dimensional
repetitions found in incommensurate crystal structures. ‘Technological and Design
Implications’ returns to the everyday appearance of symmetry that can now be
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!
The class is divided into 4 major Parts and will consist of:
videos about 9 - 15 minutes in length. These contain 1-2 in video quiz
questions as part of self assessment. This will not be graded.
Multiple Choice Question (MCQ) Quizzes at the
end of each Part which will be graded.
3 open - ended assignment which will involve peer to peer assessment.
1 learning log
TRACK 1: Certificate of Accomplishment (PARTS I & II only)
• 2 MCQ quizzes
• 2 peer-graded assignments
• 1 learning log
TRACK 2: Certificate of Accomplishment with Distinction or Verified Certificate (PARTS I, II, III & IV, equivalent 3AU NTU)
• 4 MCQ quizzes
• 3 peer-graded assignments
• 2 learning log
For both Tracks, you have to obtain >= 60% of the maximum possible score.
In a topic
as broad as Symmetry no single text can
do justice to the field. Therefore, the
notes and supplementary materials provided in this course strive to be
self-contained. There are also many web
resources to access.
Video book reviews are provided to get a sense of the breadth of
who wish to study conventionally the following texts, that are widely available in
public libraries, are recommended.
Track 1: Visual Symmetry, by Magdolna Hargittai and István
Hargittai ISBN 978-981-283-531-4
Symmetry is as simple or as
complicated as we are ready to absorb it in everything around us. From flowers
to bridges, buildings, coke machines, and snowflakes; from molecules to
walnuts, fences, pine cones, and sunflowers; from music to children's drawings;
from hubcaps to bank logos, propellers, wallpaper decorations, and pavements,
we recognize it if we walk around with open eyes and an open mind. This book
provides aesthetic pleasure and covert education, immersing the reader in both
the familiar and the unknown and leading always to unexpected discoveries. The authors, world-renowned
scientists, have already produced a dozen books on symmetry for professionals
as well as lay persons, for grownups as well as children, in English, Russian,
German, Hungarian, and Swedish languages. They provide this attractive account
of symmetry in few words and many, as many as 650, images in full color from
the most diverse corners of our globe. An encounter with this book will open up
a whole new experience for the reader, who will never look at the world with
the same eyes as before.
and Crystal Structures byRichard J. D. Tilley ISBN: 978-0-470-01820-0
Crystals and Crystal Structures is an
introductory text for students and others who need to understand the subject
without necessarily becoming crystallographers. Using the book will enable
students to read scientific papers and articles describing a crystal structure
or use crystallographic databases with confidence and understanding. Reflecting the interdisciplinary nature of
the subject the book includes a variety of applications as diverse as the
relationship between physical properties and symmetry, and molecular and
protein crystallography. As well as covering the basics the book contains an
introduction to areas of crystallography, such as modulated structures and
quasicrystals, and protein crystallography, which are the subject of important
and active research.