Definition:Angle/Unit/Second
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Definition
The second (of arc) is a measurement of plane angles, symbolized by $''$.
| \(\ds \) | \(\) | \(\ds 1\) | second | |||||||||||
| \(\ds \) | \(=\) | \(\ds \dfrac 1 {60}\) | minute of arc (by definition) | |||||||||||
| \(\ds \) | \(=\) | \(\ds \dfrac 1 {60 \times 60} = \dfrac 1 {3600}\) | degree of arc |
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 arc.
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
- 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