The thinner skates cause the body weight of the skater to be distributed over a very small surface area. This does two things...first, it reduces friction which makes you slide longer/faster/more effortlessly. Second, it creates a high amount of pressure between blade and ice. This causes a thin line of the ice under the blade to liquefy, further reducing friction. (The freezing point of water is roughly 32 degrees at standard atmospheric pressure...the higher the pressure, the colder the freezing point. This is why snow packs into a snowball when you squeeze it.
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Ice Skates are shaped as curves, so that your can easily move to the back of your skate/to the toe pick. This is essential as when skating, your body must be able to lean back and forth rather than just straight. It is key in many skating moves.
The blades on ice skates are narrow....
by the formula Pressure = Force / Area
narrowness exerts more pressure and due to increase in pressure the melting point of water decreases and so does the freezing point which is why it will remain in the water state for a longer time.
As the skater glides the ice behind reforms as the pressure in that area has been removed.
So that you can balance and skate with accuracy, skates that aren't smooth (unsharpened) can be dangerous when doing jumps etc.
because you have to glide across the ice on the blades and without skates the ice is hard to move on as it's really slippery.