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Beauty, Form & Function

An Exploration of Symmetry

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Tim White and Jiang Shuo

Tim White and Jiang Shuo

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.

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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.

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What's inside

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.

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Traffic lights

Read about what's good

what should give you pause

and possible dealbreakers

Teaches learners about the foundational importance of symmetry in industries such as art and architecture

Teaches learners about the role of symmetry in the atomic structure of crystals

Emphasizes the application of symmetry in various disciplines

Course format could potentially be enhanced to include interactive exercises, hands-on labs, or simulations to improve comprehension

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Reviews summary

Interdisciplinary symmetry exploration

According to learners, this course offers a largely positive and captivating journey into symmetry, masterfully blending its presence in art, nature, and various scientific disciplines. Many found the instructor, Professor Phang, exceptionally engaging and skilled at making complex concepts accessible, leading to a newfound appreciation for patterns in the world. Unique elements like field exercises and specialist interviews are highlighted as enriching additions. However, students note a significant shift in difficulty, with later modules delving into rigorous mathematical and crystallographic concepts, which may not align with expectations for those seeking a purely aesthetic or general interest exploration. This can lead to a divided experience for learners with different backgrounds.

Features like field exercises and specialist interviews enrich learning.

"The field exercises were a brilliant touch, though I wish there were more hands-on assignments."

"The interview segments with specialists were a unique and enriching addition. It truly showed the pervasive nature of symmetry."

"The field exercises were fun, but not graded, so less incentive to do them."

Professor Phang makes complex ideas accessible and inspires.

"Professor Phang does an excellent job of making complex ideas accessible."

"Prof. Phang's enthusiasm is infectious. ... connected abstract mathematical concepts to real-world examples."

"Professor Phang is a phenomenal educator, clear, concise, and passionate."

Blends art, nature, and science for a holistic view of symmetry.

"This course masterfully blends art, nature, and science. ... opened my eyes to symmetry everywhere."

"It's rare to find a subject taught with such interdisciplinary flair. ... showed the pervasive nature of symmetry across different fields."

"I appreciated the interdisciplinary approach... This course redefined how I see the world."

Some older reviews mentioned dated video quality or audio issues.

"The production quality felt a bit dated in parts, especially some of the older video lectures."

"Some of the videos felt a bit low resolution or had audio issues occasionally."

"Content is good but the structure needs work. ... the presentation could be refined."

Starts accessible but becomes mathematically rigorous later.

"Some of the later modules, especially on Bravais Lattices, felt a bit dense and would benefit from more practical examples."

"I signed up hoping for more art and design application, and less pure science. The sudden shift was jarring."

"The early parts are fantastic for beginners, but the later parts assume a bit more mathematical comfort."

"It felt like two different courses combined, one for general interest, another for a more scientific audience."

Activities

Be better prepared before your course. Deepen your understanding during and after it. Supplement your coursework and achieve mastery of the topics covered in Beauty, Form & Function: An Exploration of Symmetry with these activities:

Review high school geometry

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Strengthen your understanding of basic geometric concepts for a stronger foundation in symmetry

Browse courses on Geometry

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Review notes or textbooks from a high school geometry course
Focus on topics related to shapes, transformations, and symmetry
Practice solving geometry problems to improve your problem-solving skills

Read 'Symmetry: A Unifying Concept'

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Expand your understanding of symmetry with a comprehensive theoretical perspective

View Symmetry (Princeton Science Library) on Amazon

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Obtain a copy of the book
Read the book thoroughly, taking notes and highlighting key concepts
Complete the exercises and problems at the end of each chapter

Identify symmetry in real-world objects

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Identify examples of symmetry in everyday objects to develop observation skills

Browse courses on Symmetry

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Look for objects around you that exhibit symmetry
Determine the type of symmetry present (e.g., bilateral, rotational)
Create a collection of images or sketches of objects with different types of symmetry

Five other activities

Expand to see all activities and additional details

Show all eight activities

Symmetry resource collection

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Gather external resources on symmetry to expand your understanding of the topic

Browse courses on Symmetry

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Find articles and videos on symmetry in nature, art, and architecture
Compile a list of experts in the field of symmetry and their contact information
Identify relevant books, conferences, and workshops on symmetry
Create a digital or physical folder to store your collection

Practice symmetry transformations

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Complete tutorials on symmetry transformations to solidify understanding of these concepts

Browse courses on Symmetry

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Search for online tutorials on symmetry transformations
Follow the steps outlined in the tutorials to practice applying symmetry transformations
Work through practice problems to test your understanding

Design a tessellated pattern

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Create your own tessellated pattern to demonstrate your grasp of symmetry principles

Browse courses on Symmetry

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Choose a shape or motif for your tessellation
Experiment with different symmetry transformations to create a repeating pattern
Transfer your design onto a physical medium (e.g., paper, fabric)

Attend a workshop on symmetry in design

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Attend a workshop to learn about practical applications of symmetry in design

Browse courses on Symmetry

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Research and identify workshops on symmetry in design
Register for and attend the chosen workshop
Actively participate in the workshop activities

Connect with professionals in symmetry-related fields

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Expand your professional network and learn about career opportunities in symmetry-related fields

Browse courses on Symmetry

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Attend industry events or conferences focused on symmetry
Join professional organizations related to symmetry
Reach out to professionals in symmetry-related fields on LinkedIn

Career center

Learners who complete Beauty, Form & Function: An Exploration of Symmetry will develop knowledge and skills that may be useful to these careers:

Architect

Architects design and oversee the construction of buildings and other structures. They use their knowledge of engineering, mathematics, and aesthetics to create functional and visually appealing spaces. This course can help you develop the skills and knowledge you need to succeed as an architect. You will learn about the principles of symmetry, which are essential for creating balanced and harmonious designs. You will also learn about the different types of building materials and construction techniques, and how to use them to create sustainable and efficient structures.

See salaries and explore the career path for Architect

Landscape Architect

Landscape architects design and create outdoor spaces, such as parks, gardens, and campuses. They use their knowledge of plants, soil, and water to create functional and visually appealing landscapes. This course can help you develop the skills and knowledge you need to succeed as a landscape architect. You will learn about the principles of symmetry, which are essential for creating balanced and harmonious designs. You will also learn about the different types of plants and how to use them to create sustainable and resilient landscapes.

See salaries and explore the career path for Landscape Architect

Urban Planner

Urban planners develop plans for the development and use of land in urban areas. They use their knowledge of architecture, engineering, and economics to create plans that meet the needs of the community. This course can help you develop the skills and knowledge you need to succeed as an urban planner. You will learn about the principles of symmetry, which are essential for creating balanced and harmonious designs. You will also learn about the different types of land use planning tools and how to use them to create sustainable and equitable communities.

See salaries and explore the career path for Urban Planner

Interior designer

Interior designers create the interior spaces of buildings, including homes, offices, and public spaces. They use their knowledge of color, texture, and furniture to create functional and aesthetically pleasing environments. This course can help you develop the skills and knowledge you need to succeed as an interior designer. You will learn about the principles of symmetry, which are essential for creating balanced and harmonious designs. You will also learn about the different types of interior design styles, and how to use them to create spaces that meet the needs of your clients.

See salaries and explore the career path for Interior designer

Product Designer

Product designers create and develop new products. They use their knowledge of engineering, design, and marketing to create products that are functional, aesthetically pleasing, and commercially viable. This course can help you develop the skills and knowledge you need to succeed as a product designer. You will learn about the principles of symmetry, which are essential for creating balanced and harmonious designs. You will also learn about the different types of product design materials and manufacturing techniques, and how to use them to create products that meet the needs of your customers.

See salaries and explore the career path for Product Designer

Graphic Designer

Graphic designers create visual concepts, using computer software or by hand, to communicate ideas that inspire, inform, and captivate consumers. They develop the overall layout and production design for applications such as brochures, magazines, and corporate reports. This course can help you develop the skills and knowledge you need to succeed as a graphic designer. You will learn about the principles of symmetry, which are essential for creating balanced and harmonious designs. You will also learn about the different types of graphic design software and techniques, and how to use them to create effective and visually appealing designs.

See salaries and explore the career path for Graphic Designer

Fashion Designer

Fashion designers create clothing and accessories. They use their knowledge of fabrics, textiles, and design to create garments that are both stylish and functional. This course can help you develop the skills and knowledge you need to succeed as a fashion designer. You will learn about the principles of symmetry, which are essential for creating balanced and harmonious designs. You will also learn about the different types of fabrics and textiles, and how to use them to create garments that are both beautiful and durable.

See salaries and explore the career path for Fashion Designer

Jeweler

Jewelers create and repair jewelry. They use their knowledge of metals, gemstones, and design to create beautiful and valuable pieces. This course can help you develop the skills and knowledge you need to succeed as a jeweler. You will learn about the principles of symmetry, which are essential for creating balanced and harmonious designs. You will also learn about the different types of metals and gemstones, and how to use them to create jewelry that is both beautiful and durable.

See salaries and explore the career path for Jeweler

Ceramicist

Ceramicists create functional and decorative objects from clay. They use their knowledge of clay, glazes, and firing techniques to create pieces that are both beautiful and durable. This course can help you develop the skills and knowledge you need to succeed as a ceramicist. You will learn about the principles of symmetry, which are essential for creating balanced and harmonious designs. You will also learn about the different types of clay and glazes, and how to use them to create ceramics that are both beautiful and durable.

See salaries and explore the career path for Ceramicist

Sculptor

Sculptors create three-dimensional works of art from a variety of materials, including clay, metal, wood, and stone. They use their knowledge of anatomy, perspective, and design to create sculptures that are both beautiful and meaningful. This course can help you develop the skills and knowledge you need to succeed as a sculptor. You will learn about the principles of symmetry, which are essential for creating balanced and harmonious designs. You will also learn about the different types of sculpting materials and techniques, and how to use them to create sculptures that are both beautiful and durable.

See salaries and explore the career path for Sculptor

Painter

Painters create two-dimensional works of art using paint, canvas, and other materials. They use their knowledge of color, composition, and perspective to create paintings that are both beautiful and meaningful. This course can help you develop the skills and knowledge you need to succeed as a painter. You will learn about the principles of symmetry, which are essential for creating balanced and harmonious designs. You will also learn about the different types of paints and brushes, and how to use them to create paintings that are both beautiful and durable.

See salaries and explore the career path for Painter

Photographer

Photographers capture images of people, places, and things using a camera. They use their knowledge of composition, lighting, and exposure to create photographs that are both beautiful and informative. This course can help you develop the skills and knowledge you need to succeed as a photographer. You will learn about the principles of symmetry, which are essential for creating balanced and harmonious compositions. You will also learn about the different types of cameras and lenses, and how to use them to capture stunning images.

See salaries and explore the career path for Photographer

Writer

Writers create written works, such as novels, short stories, poems, and plays. They use their knowledge of language, grammar, and storytelling to create works that are both entertaining and informative. This course can help you develop the skills and knowledge you need to succeed as a writer. You will learn about the principles of symmetry, which can be used to create balanced and harmonious plots and characters.

See salaries and explore the career path for Writer

Musician

Musicians create and perform music using instruments or their voices. They use their knowledge of rhythm, melody, and harmony to create music that is both beautiful and meaningful. This course can help you develop the skills and knowledge you need to succeed as a musician. You will learn about the principles of symmetry, which can be used to create balanced and harmonious melodies and rhythms.

See salaries and explore the career path for Musician

Dancer

Dancers create and perform dance movements using their bodies. They use their knowledge of rhythm, coordination, and expression to create dances that are both beautiful and meaningful. This course can help you develop the skills and knowledge you need to succeed as a dancer. You will learn about the principles of symmetry, which can be used to create balanced and harmonious dance movements.

See salaries and explore the career path for Dancer

Reading list

We've selected seven books that we think will supplement your learning. Use these to develop background knowledge, enrich your coursework, and gain a deeper understanding of the topics covered in Beauty, Form & Function: An Exploration of Symmetry.

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The Topology of Chaos

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Good starting point to understand symmetry across disciplines. It is intended as a textbook at the college sophomore level.

The Topology of Chaos: Alice in Stretch and...

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Materials Engineering

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Good reference for understanding the applications of symmetry to mechanical engineering.

Materials Engineering: Bonding, Structure, and...

Materials Engineering: Bonding, Structure, and...

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The Forgotten Revolution

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Provides an excellent review of the mathematics behind symmetry.

The Forgotten Revolution: How Science Was Born in...

The Forgotten Revolution: How Science Was Born in...

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Fractional Calculus

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Good starting point for understanding the concept of symmetry breaking and its applications in a broad variety of disciplines.

Fractional Calculus: An Introduction for Physicists

FRACTIONAL CALCULUS: AN INTRODUCTION FOR PHYSICISTS...

Fractional Calculus: An Introduction For Physicists...

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Infinity: A Very Short Introduction

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Very short (less than 100 pages) accessible overview of symmetry.

Infinity: A Very Short Introduction

Infinity: A Very Short Introduction

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The Symmetries of Things

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This accessible book uses clear and concise language to explain the basic mathematical concepts behind symmetry.

The Symmetries of Things

The Symmetries of Things (AK Peters/CRC...

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Mathematics in Western Culture

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Provides an excellent survey of how symmetry has impacted both science and the humanities.

Mathematics in Western Culture

Mathematics in Western Culture

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Level

Introductory

Via

Coursera

Institution

Nanyang Technological University, Singapore

Instructors

Tim White

Jiang Shuo

Language

English

Transcripts

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Traffic lights

Read about what's good

what should give you pause

and possible dealbreakers

Teaches learners about the foundational importance of symmetry in industries such as art and architecture

Teaches learners about the role of symmetry in the atomic structure of crystals

Emphasizes the application of symmetry in various disciplines

Course format could potentially be enhanced to include interactive exercises, hands-on labs, or simulations to improve comprehension

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