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Construct the midpoint M of a line
segment specified by two points A and B with a movable compass
alone. Step by step solution is illustrated
Mascheroni or Mohr-Mascheroni
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.