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& Margalit


Olena Buriakova

- 3rd Year Undergraduate Student

- Computer Science

- Georgia Tech


Dan Margalit

- Faculty

- Low-Dimensional Topology and Geometric Group Theory

- Georgia Tech

Squared Lantern Relation

Medium: Digital


In mathematics and science, braids are used to describe the motion of points in a two-dimensional space - if we trace out the motion of the points over time, we obtain a braid. On paper, we can form braids by crossing any two strands at a time any number of times. Sometimes after performing some number of crossings, if we “pull” the strands outwards, we can get a simplified braid. This is depicted in the painting. The girl on the right has a very long braid, which can also be represented much more simply, like the braid of the girl on the left. Even though the braids look different, they still simplify to the same formula. 


The equality of the two braids depicted in the painting is called the "squared lantern relation."  This equality was discovered by Tara Brendle and Dan Margalit in their work on braid groups. 


The metaphorical meaning of this piece could be interpreted as two sisters who look the same, who come from the same place, yet develop differently in life due to the surrounding environment.

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