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# radian

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 $57^{{\mathrm{o}}}\,17^{{\prime}}\,44.80625^{{\prime\prime}}.$

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 $\frac{3\pi}{5}$.

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51M04*no label found*

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## Comments

## TODO list for Radian

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)