Pontificia Universidad Católica de Chile (UC): UC Mathematics joins the global trend of crocheting mathematical corals

A colorful crocheted coral reef is on display in the Hall of the Felipe Villanueva building of the Faculty of Mathematics. The work is part of a global initiative that consists of graphing a mathematical model using crochet reefs.

In October 2021, within the framework of Científica tu Casa +60 of the Vice-Rector for Research, the UC Senior Adult Program, Fundación Más and Travesía 100, the Faculty of Mathematics held online crochet classes given by Sandra Cerda and the talk of hyperbolic geometry dictated by the academic Constanza del Campo.

In addition, to explain the formation of the reefs, the biologist and researcher from the Coastal Marine Research Station (ECIM) Alejandro Pérez contributed.

As a result of this activity, the group of participants, most of them women over 60 years of age, contributed with their mathematical corals, in order to form a hyperbolic reef, inspired by the international experience “The Sydney Hyperbolic Crochet Coral Reef”.

Mariana Milos Montes, Manager of School Projects of the Faculty of Mathematics , explains: “There were approximately 30 weavers who sent their creations from different parts of Chile, gathering to date 155 fabrics of marine beings (corals, snails, jellyfish, fish, etc.)”.

“There were approximately 30 weavers who sent their creations from different parts of Chile, gathering to date 155 fabrics of marine beings (corals, snails, jellyfish, fish, etc.)” – Mariana Milos Montes, manager of school projects at the Faculty of mathematics

Within the framework of Científica tu Casa +60 of the Vice-Rector for Research, the UC Senior Adult Program, Fundación Más and Travesía 100, the Faculty of Mathematics held online crochet classes given by Sandra Cerda and a talk on hyperbolic geometry given by the academic Constanza del Campo. Images: César Cortés and Karina Fuenzalida.
hyperbolic geometry?
When we think of geometry, it is easy for us to think of circles, triangles, and a number of relationships between lines and angles on flat, two-dimensional surfaces. But how would you mathematically describe a coral or sea snail?

Through math and crochet workshops, it was possible to “understand-create” the mathematical logics that explain shapes that are neither flat nor two-dimensional. This is hyperbolic geometry. This concept is not easy to understand, but it was explained to the weavers in a talk on the subject.

Professor Constanza del Campo explains that we all face the study of geometry at some point. Experts or not, we all come up with figures such as triangles, circles and lines. What we were probably never told is that the geometry learned in school, called Euclidean geometry, is just one kind of geometry . There are others, and today we are called hyperbolic geometry .

What does it consist of?

“Draw two points on a sheet of paper and trace with a pencil the segment that joins them with a ruler. Now imagine that an ant is placed on one of these points and a piece of apple is placed on the other point. I assure you that the ant will walk along the path you drew, because this is the shortest path between those two points and the ant intelligently knows this.Understanding that nature is wise and that the ant will inherently walk the shortest path to reach its goal, put the ant to walk now on one of the surfaces of crochet corals.The path that the ant will travel to the food is clearly different from the path traveled on the sheet of paper. One is “super straight” and the other not so much anymore. But in both cases the ant walks along the shortest path between those two points”, clarifies the academic .

Thus, unlike Euclidean geometry, hyperbolic geometry is one in which curves abound.

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