On the projective plane, if the concepts of point and straight line are reversed in a projective theorem, that is, the point becomes a straight line, the straight line becomes a point, and the * * * line relationship of the point becomes the * * point relationship of the straight line, then the proposition obtained is still valid, which is the so-called duality principle. This can be done by polar coordinate mapping of the central conic.

For example, Deschamps theorem is a theorem about points, straight lines and their connections, and it is a projective theorem. Its duality theorem is its inverse theorem. This principle can also be extended to n-dimensional projective spaces.

In short, duality is the most common structural law in nature, which is distributed in the form of "fractal". Any system can find the structural relationship between the upper and lower dual images, and the two images have completeness, complementarity, unity of opposites, stability, mutual expansion and mutual roots.