What is the shape of an angle that shows a half turn?

Answer 1

that depends on what you mean by a 'turn'. I'm going to assume 1 turn is 1 full revolution (after one full turn, you would be facing the same direction you started). Another common definition would hold that one full turn would have you facing the opposite direction you started, completing one half of a revolution, and I will deal with that option later. Assuming one turn is equivalent to one revolution, there are 2π radians or 360 degrees in a turn, so there are π radians or 180 degrees in a half-turn. In mathematics, convention has it that a π or 180 degree angle is depicted by a half circle about the chosen angle vertex on the line formed by the two rays of the angle. This looks like the figure below, except that the bottom line should extend past the edge of the angle marker and the angle marker would, obviously, be much smaller:

Sometimes it is said that the shape formed by this kind of angle is a straight line, but that is not necessarily true on a macroscopic level; the trivial cubic f(x)=x3, for example, has a π angle at (0,0), but the function is not linear over any finite region.

Now we will consider the other common and applicable definition of a turn. It is the case that half of the previous angle constitutes half of one of our new turns, since our old turn in twice the size of our new turn. Thus in the half-turn angle there will be π÷2 radians or 90 degrees. The convention in mathematics, much more widely followed than the above convention, is to represent such an angle (referred to as a right angle) with a square angle indicator, rather than a sector angle indicator. This looks like the figure below:

edit: the figures presented appear to have failed to be displayed. To see visual representations of these angles, or any other angles, it is recommended that you try the link located in the "Sources and related links" section below.