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A clockwise motion is one that proceeds 'like the clock's hands': from the top to the right, then down and then to the left, and back to the top. The opposite sense of rotation is anti-clockwise (UK) or counterclockwise (US).
Before clocks were commonplace, the terms 'sunwise' and 'deasil' or 'deosil' (from the Scottish Gaelic deiseil, from the same root as the Latin dexter, "right") were used for clockwise. (Of course, deasil (righthandwards) is only sunwise in the Northern Hemisphere.) 'Widdershins' or 'withershins' (from Middle Low German weddersinnes, "opposite course") was used for anti-clockwise.
Technically, the terms clockwise and anti-clockwise can only be applied to a rotational motion once a side of the rotational plane is specified, from which the rotation is observed. For example, the daily rotation of the Earth is anti-clockwise when viewed from the North Pole, and clockwise when viewed from the South Pole.
Clocks traditionally follow this sense of rotation because of the clock's predecessor: the sundial. Clocks were first built in the Northern Hemisphere, and they were made to work like sundials. In order for the sundial to work (in the north), it must be placed looking southward. Then, when the Sun moves in the sky (east to south to west), the shadow cast by the sundial moves in the opposite direction, that is west to north to east. That's why hours were drawn in sundials in that manner, and that's why modern clocks have their numbers set in the same way.
Occasionally, clocks whose hands revolve anti-clockwise are nowadays sold as a novelty. Historically, some Jewish clocks were built that way, for example in some Synagogue towers in Europe. This was done in accordance with the right-to-left reading direction of Hebrew.
Typically, screws and bolts are loosened anti-clockwise and tightened clockwise. One mnemonic for remembering this is "righty-tighty, lefty-loosey" (right to tighten, left to loosen.)
In trigonometry, and mathematics in general, plane angles are conventionally measured anti-clockwise.
Clockwise and anti-clockwise distinctions occur throughout nature: see
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