There are many dualities that mathematicians study. In this post, I shall discuss two of them, in order to illustrate some of the ideas involved.

**Line, point duality**

As a simple example of mathematical duality, consider the duality of points and lines in Euclidean geometry. And recall from your school days, that when we talk of a line in Euclidean geometry, we are talking of an infinite straight line extended in both directions. The short “lines” that we actually draw can be called “line segments” so as to distinguish them from the extended lines.

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