That is to make geometric constructions using only the compass.
The problem becomes much mor difficult than with usual compass and straightedge.
Of course only points (and circles) can be constructed, and no staright line segment, but it could be proved
ainsi que des points et aucun segment de droite, mais on peut montrer (théorème de
(Mohr-Mascheroni theorem) taht every point constructible with compass and straightedge
can be constructed with compas only.
Constructions are often very acrobatic.
Midpoint of segment AB
Given only points A and B, line AB not drawn.
Vertices of a square with side AB
Given only points A and B.
Centter of a given circle
This is the "Napoleon problem".
Given a circle without knowing its center, construct the center.