Compass and/or divider

Device with two arms that are pinned together at one end, the top, such that the free ends at the bottom can be moved and the distance between these ends changed. If the compass is place against a straight edge the distance between the two ends can be marked off against this straight edge. I consider the distance between these marks to be the length.

I appreciate that the above is really quite a circular argument, with length and distance being interchangeable. However I do not want to get held up with esoteric arguments so I am being lazy in my argument.

It is therefore possible to compare the lengths of various items with a compass or divider and determine if the one is less, equal or greater than the other.

A divider has a sharp point at each free end and is used to make measurements. A compass has one sharp point and one drawing point (pen nib or pencil lead) at the other and is used to draw curves which are a constant distance from the sharp point.

Angles

Consider 2 straight lines AB, CD intersecting at O

AO can be rotated about O so that it lies upon CO, occupying the same set of points

The amount of revolution is known as the angle AOC

If AO continues to rotate about O until it once again overlays its original position it will have performed 1 revolution.

One measure divides 1 revolution into 360 degrees, each degree into 60 minutes and each minute into 60 seconds i.e.

1 revolution = 360 degrees = 2,160 minutes = 1,296,000 seconds

(5º is shorthand way of writing 5 degrees)