I particularly liked the contrast between the algebraic and geometrical views of the world. The simple illustration of a 'singularity' arising from the slope o

I particularly liked the contrast between the algebraic and geometrical views of the world. The simple illustration of a 'singularity' arising from the slope of a vertical line (y = mx+c with m=infinity) compared with the geometrical view where such a line is simply a vertical line which can be transformed into any other line by rotating will be useful in teaching!