The human perceptual apparatus seems to make repeated use a few general
principles to make sense of the world. A big one is symmetry. Animal bodies
generally exhibit bilateral symmetry, for example; when they don't (as with
a flounder, for example, or owls' ears) we notice. Everyone will separate a
perfect circle from any less symmetric doodle, and a sphere from any less
symmetric blob.
The concept of symmetry has been clarified and generalized by mathematicians,
perhaps beginning with Plato and his solids. Different types of symmetry are
distinguished from each other and studied using the abstraction captured in
the concept of a "group."
This seminar will consider the phenomenon of symmetry, and how it enters
into art and music as well as mathematics and physics. Students will take
turns leading discussions of a range of topics over the term, using
resources mainly available on the web, and contribute to a document
recording these discussions.

We will scour the web and the MIT library for information about selected
topics arising from unpacking the concept of symmetry, and come together
weekly to discuss what we've discovered. Each week a pair of students will
serve as discussion leaders, in collaboration with the faculty organizer.
We will schedule a time to discuss the material with you beforehand.
No "Psets" and no "Exams"!

But there will be a deliverable: We will create a manuscript together
documenting what we have found, using
Overleaf,
a tool for collaborative creation of documents in LaTex.
Here's
a link to this document, available only to members of the class. I'm very
excited to see how it develops. Many hands make light work!

The regular class meetings will occur on Wednesdays from 3:00 to 5:00 PM
Eastern US time, in 2-255.

** A couple of useful resources:**

**Associate Advisor: **
Paige Dote, paigeb@mit.edu

**Participants:**

Elizabeth Athaide, eathaide@mit.edu

Howard Beck, hbeck@mit.edu

Nico Bulhof, nbulhof@mit.edu

Brandon Chen, branchen@mit.edu

Raul Hernandez, rhern@mit.edu

Isaac Lopez, imlopez@mit.edu

Luis Modes, modes@mit.edu

Syd Robinson, syro@mit.edu

Date | Leaders | Topic | Resources |
---|---|---|---|

Wed Sep 8 | Ensemble | Symmetry, a general discussion | |

Fri Sep 17 | Raul and Luis | Regular polyhedra and polytopes | Symmetries of Platonic solids and 4-dimensional analogues |

Fri Sep 24 | Nico and Syd | Friezes and wallpapers | Frieze patterns and Wallpaper patterns |

Fri Oct 1 | Elizabeth and Isaac | Hyperbolic geometry | Escher, Wikipedia, and Encycla. |

Fri Oct 8 | Howard and Brandon | Hyperbolic isometries | Encycla. |

Fri Oct 15 | Elizabeth | Symmetry in music | |

Fri Oct 22 | Nico and Raul | Hyperbolic polygons | Katok. |

Fri Oct 28 | Luis and Isaac | Hyperbolic tessellations | Joyce , list. |

Fri Nov 5 | Haynes Miller | Homogeneous surfaces: Spherical, Flat, Hyperbolic | |

Fri Nov 12 | Howard and Brandon | Groups | Wikipedia |

Fri Nov 19 | Syd and Elizabeth | Symmetry of roots of polynomials | Galois theory, Abel, Galois |

Fri Dec 3 |

Professor Haynes Miller

Department of Mathematics 2-478

Massachusetts Institute of Technology

Cambridge, MA 02139

Email: hrm@math.mit.edu

Zoom office: https://mit.zoom.us/j/6691725321

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