An object is moving counter-clockwise along a circle with the centre at the origin. At \(t=0\) the object is at point \(A(0,5)\) and at \(t=2\pi\) it is back to point \(A\) for the first time.

Below is the graph of a quadratic function, showing where the function is increasing and decreasing. If we draw in the tangents to the curve, you will notice that if the gradient of the tangent is ...

Theorem. Let $V$ be a complex analytic variety irreducible at a point $p \in V$. Given any integer $l$, there exists an analytic curve $C_l$ on $V$ passing through $p ...