Archive for October 13th, 2011

October 13, 2011

Mathematical duality

by Neil Rickert

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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