Home | Problems | Circles | Mascheroni 1 | 2 | 3 | Napoleon's Problem Mascheroni Construction 1: Midpoint of a segment. Level: High School, SAT Prep, College geometry Activate Flash plugin or Javascript and reload to view Mascheroni Construction. Use the Previous and Next buttons above to browse through the 16 steps. 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 above.   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.

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