Dyson calls it an "air multiplier", but everywhere you see this, it's called a bladeless fan. A fan with no blades? Where does the air come from? Apparently, it's drawn into the bottom of the gadget, where there is a, yes, a conventional fan with blades (just well hidden). The air is fed up to the big loopy round part (for want of a more descriptive name). Somehow, this process also draws in more air from behind the fan and around the edges of the fan. Which gives you lots of air blowing.
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Dyson (the company that makes the vacuum cleaners) is marketing the Air Multiplier as a pleasant change from a blade fan because of the smoothness of the air flow, compared to the choppiness of fans using blades. Forget that, real people who have used conventional fans will notice two other advantages first and foremost. 1. Your kids won't lose their fingers when they stick them in this fan, and 2. you can clean it. Conventional fans have safety covers to keep little fingers away from spinning blades, but the grills catch dust as much as blades do. By the end of the summer, you need to take your fan outside and shake it, sweep it, and if you are at your wit's end, use a spray hose (not recommended) to get all the nasties out. This won't happen with a bladeless fan.

200_dyson_fanStill, there is the $300 price tag. You can toss out a couple of dozen dirty little conventional fans before you approach that kind of payout. Of course, there's the cachet of having the newest, most expensive, and just plain cool fan to impress your friends. Then on the other hand, if you can afford $300 for a fan, why don't you just get an air conditioner?