The Arithmetic of Symmetry

This is a 10-week workshop that begins on September 25th, 2017.

Moderator:             John Armstrong
Day and Time:      Monday 10:00AM – Noon
Format:                    Seminar
Location:                Smith College, Dewey Hall Common
(parking permit required; provided to participants by moderator)


To deepen appreciation for symmetry in nature, art, and mathematics. For a definition of symmetry appropriate to this seminar, see

Symmetry is common in art and ubiquitous in nature; mathematics embodies symmetry at every turn. We will explore symmetry in familiar, but also in unexpected places. Symmetry is present in biology, crystals, geometric figures, and in fractals. In many cases one’s understanding and appreciation are enlarged by the use of ‘augmented arithmetic’: X times Y need not equal Y times X. This is true already regarding the symmetries of the familiar equilateral triangle! While this arithmetic approach will not be required, it is hoped participants will make the modest effort to learn it.

Role of participants:
Choose a topic from a list provided by the moderator, make a presentation, and lead a discussion. The list provided will include relevant web resources, but participants will be free to choose their own topic concerning symmetry.

Participants will be expected to be able to use the internet for finding relevant materials.


A good overview of the multiple areas in which symmetry plays a role is given in

About the Moderator:
The moderator has led many LIR seminars on science and technology and has had a lifelong fascination with symmetry in all its forms.

Maximum number of participants: 16

Emeritus/a accepted: yes, up to 2