I would like to make sense of this proof for a cardioid as an envelope of a pencil of lines in this Wikipedia article, but I don't recognise most of the notation and equations used in it. So far, I only know:
- The dot syntax refers to a derivative
- The T symbol stands for transpose and means that the normal vector should be treated as a column vector.
However, I am still very confused about:
- How they got the equation of the tangent
- How they got the normal vector form the parametric equations
- Where the two points in the "secant line passing the two points" are
and so on, which I have not been able to find anything about. Could someone please tell me what I would have to learn to fully understand this proof?
