Tag: infinity

Last week, we have talked about certain situations where the operation performed with points of the elliptic curve does not produce a result which is a valid point of the elliptic curve over real numbers. In this article we present a different approach to explaining the point at infinity using visualizations of the projective plane. Once you can see it, you will find it rather easy to understand.

Setting aside the reasoning why we are building an algebraic system using points of elliptic curves (we will get into that later on), we omitted some bad things that can happen when applying the rules for point addition and doubling. We did this on purpose as it would be too confusing for some readers. But now the time has come and we can look at these problematic cases to find something new: the point at infinity.