Consider the following statement from elementary geometry: “Given any two points, there is a unique line containing them.” Now consider the statement: “Given any two lines, there is a unique point contained in them” (the intersection point). The words “line” and “point” can be interchanged in the the first statement to give the second statement and vice versa. Exchanging the words “point” and “line” in other statements also yields true results. This is called “point-line duality.”

Actually, a pair of parallel lines do not contain a common point, so we have to enlarge our view of geometry to allow parallel lines to meet. Point-line duality will lead us to a new geometry with coordinates that are independent of any scale (“projective geometry”). If time permits, we will look at some examples of point-line duality on spaces with only a finite number of points.

This talk will be accessible to anyone with a high school math background.

USG funded