The helicopter pilot yells **directions** over the radio to guide street police: ‘To your right!’, ‘head east-north-east!’ and ‘at your six (o’clock)!’. He can’t point out the direction, so he is *telling* the direction.

What do all these ways of telling a direction have in common? They are all about splitting a full round into smaller bits.

- We could split it into four bits –
*quarters*– and say ‘one quarter’, ‘two quarters’ and ‘three quarters clockwise’, - into 12 bits such as on a clock,
- or into 16 bits such as on a simple compass with its ‘east’, ‘north-west’, ‘south-south-west’ etc.
^{1}

The more bits we split into, the more precisely can a direction be pointed out.

So why not even more, for example 360 bits? That is in fact the general choice that was made back in history, of some reason,^{2} and still is in use today.

Let’s invent a name for those 360 bits; why not the term **degrees**. We can give it a simple little lifted circle $^\circ$ as a unit symbol.^{3} And the ‘turn’ itself is something we can call an **angle** and give a symbol, say, the letter theta $\theta$ from the Greek alphabet.

Then ‘three o’clock’ and ‘a quarter of a round’ are the same as ‘an **angle** of 90 **degrees’**, in short:

$$\theta=90^\circ$$

85 degrees would be a slightly smaller angle than a quarter of a round, while 1 degree is a very, very small turn, only one three-hundred-and-sixtieth of a full round. 360 degrees would be a full round, and 361 degrees would be *the same* direction as 1 degree, just one round ahead.

Angles in degrees | |
---|---|

$1^\circ$ | One three-hundred-and-sixtieth of a round |

$45^\circ$ | Half of a quarter round |

$90^\circ$ | A quarter of a round |

$180^\circ$ | Half a round |

$270^\circ$ | Three quarters of a round |

$360^\circ$ | A full round |

References:

- ‘
**What is the origin of the fact that a circle has 360 degrees? Why not 720 or 270?**’ (web page, answer to forum post), PhysLink.com, www.physlink.com/education/askexperts/ae373.cfm (accessed May 7th, 2019) - ‘
**Origin of 360 degrees?**’ (web page, answer to forum post), History of Science and Mathematics Stack Exchange, 2015, hsm.stackexchange.com/questions/1884/origin-of-360-degrees (accessed May 7th, 2019)