Construct the center of the circle 1 with compass alone.

Solution:
In the figure below, we proceed in 8 steps. Prove that G is the center
of circle 1.

**Mascheroni or Mohr-Mascheroni Construction**
A geometric construction done with a movable compass alone, named after the Italian geometer Lorenzo Mascheroni (1750-1800), who, in his Geometria del compasso (1797), astonished the mathematical world by showing how every compass-and-straightedge construction can be done just using a compass without a ruler.

**Straight line:** it's assumed that two points, obtained by arc intersections, define a straight line.

**Georg Mohr** (1640-1697) proved the same results earlier in his Euclides danicus (1672).

Mascheroni, or Mohr-Mascheroni, constructions are today primarily of
interest to puzzle enthusiasts who try to improve on the older solutions
by finding ones with fewer steps.

See also:

Art
and typography of Mascheroni construction.