I am learning physics theory called Hertz contact theory which considers a small particle contacting a plate. But I have been stuck in the geometry problem. I would like to get $z$ in the figure. When $z$ is very small, the theory assumes $$z(r) = R-\sqrt{R^2-r^2}\approx r^2/2R, \quad if \quad r<<R$$ $R$ is the radius of curvature. How we can make this approximation?
I'm really happy if you could answer these questions.
