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# Direction & angle

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:

1. 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)
2. 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)