I was just reading Ars Technica's primer on ECC. Somewhere near the middle of the second page, the author introduces the "dot" operation that takes an elliptic curve and two other known points, giving a third unique point.
However, the author then claims that A dot A equals B. That is, if the two first points are the same, it's possible to come up with a unique third intersecting point. How is this possible? Intuition tells me that there is an infinite number of possible intersections if the two first points are the same.