We introduce the connection between geometric figures and abstract algebra by showing how you can associate a group with triangles. The more symmetric the triangle, the larger the group. We illustrate this by finding the group of symmetries for equilateral, isosceles and scalene triangles.
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Abstract Algebra deals with groups, rings, fields, and modules. These are abstract structures which appear in many different branches of mathematics, including geometry, number theory, topology, and more. They even appear in scientific topics such as quantum mechanics.