Radians are a unit of measurement for angles.

Most people are familiar with using "degrees" as an measurement of angle, and very confused about why "radians" are at all useful. The idea is that when you measure in radians, the value of the angle (in radians) is equal to the length of the circumference of the unit circle subtended by that angle. If you walk some distance around the unit circle, the angle you've gone through, when measured in radians, is equal to the distance you've walked.

On that basis, if you walk all the way around the circle the distance you've walked is $2\pi,$ because circumference is $2{\pi}R,$ and $R=1$ for the unit circle. That means that 360 degrees is $2\pi$ radians, and so a radian is a little more than $57^o.$

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Local neighbourhood - D3

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