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[parent] radian (Definition)

The radian is a measure unit of angle used in the higher mathematics. The magnitude of an angle $ \alpha$ is one radian, if the arc corresponding the angle $ \alpha$ as a central angle of a circle is equally long as the radius of the circle. Thus, a radian is equal to $ \frac{180}{\pi}$ degrees. It is in degrees, minutes and seconds approximately $ 57^{\mathrm{o}}\,17'\,44.80625''.$

In degrees, a circle has 360 degrees, while in radians a circle has $ 2\pi$ radians. In fact, many angles of equilateral polygons are equal to a multiple of $ \pi$ divided by some integer: for example, the interior angle of an equilateral triangle's vertex is $ \frac{\pi}{3}$, while the interior angle of an equilateral pentagon's vertex is $ \frac{3\pi}{5}$.



"radian" is owned by Mravinci. [ full author list (2) | owner history (1) ]
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See Also: solid angle

Other names:  absolute unit of angle

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Cross-references: pentagon's, vertex, triangle's, interior angle, integer, multiple, equilateral polygons, degrees, in degrees, radius, circle, central angle, arc, angle
There are 23 references to this entry.

This is version 4 of radian, born on 2004-11-15, modified 2007-09-20.
Object id is 6476, canonical name is Radian.
Accessed 4714 times total.

Classification:
AMS MSC51M04 (Geometry :: Real and complex geometry :: Elementary problems in Euclidean geometries)

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TODO list for Radian by PrimeFan on 2007-09-20 17:32:48
1. Add a diagram or two illustrating one radian in relation to a circle, triangle or square
2. Add a few more "interesting angles" (such as those involving some neat ratio between pi and integers)
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