Definition:Angular Measure/Second
Definition
The second (of angle) is a measurement of plane angles, symbolized by $$.
| \(\ds \) | \(\) | \(\ds 1\) | second | |||||||||||
| \(\ds \) | \(=\) | \(\ds \dfrac 1 {60}\) | minute of angle (by definition) | |||||||||||
| \(\ds \) | \(=\) | \(\ds \dfrac 1 {60 \times 60} = \dfrac 1 {3600}\) | degree of angle |
Also known as
A second of angle is also known as a second of arc, or an arc second.
This term has a specific definition which is subtly different from the concept of a second of angle, and so its use in this context on $\mathsf{Pr} \infty \mathsf{fWiki}$ is discouraged.
Also see
- Results about seconds of angle can be found here.
Historical Note
The division of the degrees into $60$ and $3600$ subdivisions originates from the Babylonians, who used a sexagesimal (base $60$) system for the purposes of mathematics and astronomy.
Linguistic Note
The word second, in the context of the measurement of time and of angle, derives from the fact that it was originally specified as a second minute part of an hour or of a degree of angle.
The minute had already been defined as a minute part of an hour.
The use of the word second in English, in this specific context, started near the end of the $16$th century.
Sources
- 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): angular measure
- 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): angular measure
- 2014: Christopher Clapham and James Nicholson: The Concise Oxford Dictionary of Mathematics (5th ed.) ... (previous) ... (next): second (angular measure)
- Weisstein, Eric W. "Arc Second." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/ArcSecond.html