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 Mascheroni Construction 1: Midpoint of a segment. Level: High School, SAT Prep, College geometry

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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 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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Last updated: August 10, 2007