Definition:Angle/Unit/Degree
< Definition:Angle | Unit
Definition
The degree (of arc) is a measurement of plane angles, symbolized by $\degrees$.
\(\displaystyle \) | \(\) | \(\displaystyle 1\) | degree | ||||||||||
\(\displaystyle \) | \(=\) | \(\displaystyle 60\) | minutes | ||||||||||
\(\displaystyle \) | \(=\) | \(\displaystyle 60 \times 60 = 3600\) | seconds | ||||||||||
\(\displaystyle \) | \(=\) | \(\displaystyle \dfrac 1 {360}\) | full angle (by definition) |
Value of Degree in Radians
The value of a degree in radians is given by:
- $1 \degrees = \dfrac {\pi} {180} \radians \approx 0.01745 \ 32925 \ 19943 \ 29576 \ 92 \ldots \radians$
This sequence is A019685 in the On-Line Encyclopedia of Integer Sequences (N. J. A. Sloane (Ed.), 2008).
Historical Note
The division of the circle into $360$ degrees originates from the Babylonians, who used a sexagesimal (base $60$) number system for the purposes of mathematics and astronomy.
Degrees are usually the first way of measuring angles taught to mathematics students, usually at grade school.
Conveniently, the most commonly used angles in geometry (e.g. $30^\circ, 45^\circ, 60^\circ$) are all whole numbers when measured in degrees.
Technical Note
The $\LaTeX$ code for \(\degrees\) is \degrees
.
Sources
- 1986: David Wells: Curious and Interesting Numbers ... (previous) ... (next): $60$
- 1986: David Wells: Curious and Interesting Numbers ... (previous) ... (next): $3600$
- 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $60$
- 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $3600$
- Weisstein, Eric W. "Degree." From MathWorld--A Wolfram Web Resource. http://mathworld.wolfram.com/Degree.html