Hydroponics is the science of growing plants without using soil. There are a variety of methods and styles of growing crops hydroponically, and most involve having nutrient-rich solutions flow over the exposed roots of the plants, where they take up the nutrients they need, and release waste products out into the flow.
A variation of this method, where nutrient- and oxygen-rich solution is sprayed onto plant roots that are hanging free in the air of a container is called AeroPonics?.
Another variation where fish are raised (MariCulture?) and their wastewater is used to fertilize plants is called AquaPonics?. In aquaponics, the fish help feed the plants, and the plants clean the water for the fish. This models what happens in nature, and makes a much more environmentally friendly system.
You can find more information about hydroponics at http://reality.sculptors.com/hydro
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