Two submanifolds are said to intersect transversally if, along its intersection, the tangent spaces of the two submanifolds span the tangent space of the ambient space.
Can a hypersurface immersed in $R^n$ intersect itself non-transversally? I ask because all the examples I see of immersed surfaces intersecting themselves seem to be transversal intersections and I'm finding it hard to come up with an example of my own where the intersection is non-transversal (I'm relatively new to this way of thinking).