Golden ratio.

Without pure mathematics, applied mathematics would essentially be meaningless. That would be bad.

How does your computer cope with non-parallel lines? The screen is made of pixels, which are discrete, which means the lines never have to meet on a computer screen. Ordinarily, you would cope with this with some fairly bulky and slow mathematics, but as it happens you can use an abstract concept instead - if you have an surface divided into infinitely many infinitessimaly small pixels non-parallel lines will always meet. If you use the mathematics from that but replace instances of infinity with a number more like 10000, the graphics can be worked out quickly and easily. I think it was Ian Stewart who pointed out that pure maths is not useless, it is simply years ahead of any other subject.

I'm not sure what you're trying to say here, but I've worked in Computer Graphics for 20 years, and it's not making a lot of sense to me.

Because if there are pixels and the graphics are not much the line would look like a bunch of dots stuck together e.g. when you draw a big line on paint and you see a weird pattern instead of a straight line. If the pixels were more then the line will be more straight. As there is no such thing as a perfectly straight line that is why he was saying that. Hard to explain but simple to understand.