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Topology is a branch of mathematics. Like geometry, it studies shapes, but it focuses on certain properties of them. For example, length is not a topological property, so to a topologist, a line of length 20 metres and one of length 2 metres are the same. Nor are angles, or curvature, so a topologist would say that triangles and circles are also undistinguishable.

Topology is a branch of mathematics. Like geometry, it studies shapes, but it focuses on certain properties of them. For example, length is not a topological property, so to a topologist, a line of length 20 metres and one of length 2 metres are the same. Nor are angles, or curvature, so a topologist would say that triangles and circles are also undistinguishable.

A way of thinking about topology (albeit a non-rigorous one) is that two shapes are topologically the same, if they can be transformed into one another if one can be turned into the other by stretching it (or parts of it), but there must be no cutting of the shape. If you imagine the objects are made of clay then you can stretch or compress the clay or pull it around, but you cannot tear it at any point.

A way of thinking about topology (albeit a non-rigorous one) is that two shapes are topologically the same, if they can be transformed into one another if one can be turned into the other by stretching it (or parts of it), but there must be no cutting or gluing of the shape. If you imagine the objects are made of clay then you can stretch or compress the clay or pull it around, but you cannot tear it at any point.

[[category:mathematics]][[Category:Topology]]

[[category:mathematics]][[Category:Topology]]