Topology of Movement : Exploring Spatial Rotations and the Quaternion numbers


Last date of Registration : 17th January, 2024

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SKU: 20th January, 2024 Categories: ,



Session Date : 20th January, 2024


Timings : 

Session 1 : 10:00 a.m. – 01:00 p.m.

Session 2 : 02:00 p.m. – 04:00 p.m.

Course Description

We explore the collection of rotations of three dimensional space.  In particular, we use a spherical puppet to start physically exploring SO(3), the set of spatial rotations. It quickly becomes clear that the larger shape of this space is very strange – and yet also somehow known to the human body intuitively and viscerally. In order to build a more logical intuition for this space, students will construct a spherical puppet of their own, which they use to solve a series of movement challenges, culminating in proof of the strangest property of SO(3), known as orientation entanglement: namely, that a 360 degree rotation will tangle up a set of strings, and yet a 720 degree rotation loops mysteriously brings everything back to its initial state. Even professional mathematicians can gain a newfound understanding of this phenomenon by personally going through these physical movement exercises. Finally, we introduce the algebra of the Quaternion numbers, which allows us to translate our movement-based discoveries into mathematically precise, formal statements that computers and robots can easily understand.

About the Instructor

Prof. Vijay Ravikumar recently joined the faculty at Azim Premji University in Bangalore. He is interested in math communication and outreach, as well as visual art and puppetry. He was an Assistant Professor at the Chennai Mathematical Institute from 2016 to 2020. He received his PhD from Rutgers University in 2013.

Intended Audience

Students graduating in Mathematics, Physics, and Engineering discipline

Eligibility & Fees

Some familiarity with complex numbers & a first course in linear algebra is helpful

Fees :

Rs. 354 (Rs. 300 + 18% GST)

Learning Outcomes

Concepts Covered :

Spatial Rotations, Quaternions

Learning Outcomes:

Ability to work with spatial rotations and understand the topology of the collection of all spatial rotations.


Short MCQ quiz at the end; intermediate movement challenges with puppet throughout, for which participation is mandatory

Attendance, participation in the movement challenges and final quiz is the criteria for certificate


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