TITLE: Pair of compasses drawing a square (from children's fiction)
QUESTION [12 upvotes]: I have read a children's book where alien race of "square people" used a pair of compasses that drafted a perfect square when used. Now I wanted to explain to the child that it is not possible to have such a pair of compasses, but then I was not really sure. So is it possible to construct a mechanical tool with one fixed point and one moving point that would actually draft a square with one continuous movement?

REPLY [2 votes]: Does the book actually describe its use as "One continuous movement"? 
If not, it seems likely the "pair of compasses" in your book is not referring to any exotic contraption. "Pair of compasses" = "compass" 
Definition courtesy of Wiktionary

pair of compasses (plural pairs of compasses) A tool used to draw
  circles, usually consisting of two arms joined at one end in such a
  way that the arms can be opened and closed; one of the arms is pointed
  at its free end while the other holds a pencil, pencil lead or some
  other implement for making marks.
Synonyms compass

When used correctly, (with a pencil and a straight edge)
you can easily draw a perfect square.
A---B
|   |
C---D

(draw lightly until step 12, most marks will be temporary)  

Draw a line with the pencil and straight edge.
Choose/mark a starting point (Corner A of square).
Set compass to a small radius.
use compass to mare two points
Centered A use the compass to mark the two points it crosses the line.
Increase radius of compass marginally.
Using marks from step 5, draw two arcs so they cross above and below the line.
Using the straight edge and pencil draw a line through the intersection points of the arcs from step 7. This line will be perpendicular to the original and should also cross through your original starting point)
Set compass radius to the desired length for the side of the square.
Use compass centered at A to mark the corner points B and C on the two lines.
Use compass to draw two arcs centered at B and C. The point these arcs intersect is corner point D.
Use the straight edge to draw your line segments BD and CD, and darken AB and AC.
Erase arcs, temporary marks, and lines 

Similar instructions with pictures