The article describe how the grace, style and athleticism of figure skating depend on basic scientific principles of friction, momentum and Newton's third law.
There is also a video interview with coach Joel Savary:
Here's a transcript of what said:
To make a good skater you have to incorporate style, beauty as well as great athleticism, so it is a very unique sport because you have to be both athletic and showing the artistic side. So if you can incorporate both of those together that will make you a great skater.
There are a lot of different jumps - there's toe jumps, where you use the toe to assist you into the air, such as the toe loop and the flip jump and the lutz jump, and there's edge jumps, which is the salchow and the axel and the loop jump, which do not use the toe to assist you into the air - you just got to take that edge to lift you. And then of course you have the number of rotations you do on each jump, so you can go from single jump all the way up to - people are doing quads now, so there are 4 rotations, and people are really pushing for 4 1/2 in the future.
There are so many spins. People are advancing spins now all the time. We have sit spin, you know classic spins like sit spin, scratch spin, laybacks. We've flying spins, death drops and all these new spins in different positions like the ladies are doing Bielmann spins, where they're grabbing the leg and pulling it to the head. There's just a lot of new spins coming up. Being flexible allows us to more interesting positions in spins.
You pull in to generate the force of spinning faster - and this is in the jumps and this is also in the spins. The tighter position you can get with your legs being as tight as you can and your arms being as tight as you can and being completely straight will get you to rotate much faster.