Every point which can be constructed with a straightedge and compass, and no other points, can be constructed using identical matchsticks (i.e., identical movable line segments). Wells (1991) gives matchstick constructions which bisect a line segment and construct a square.
Matchstick Construction
See also
Geometric Construction, Mascheroni Construction, Neusis Construction, Steiner ConstructionExplore with Wolfram|Alpha
References
Dawson, T. R. "'Match-Stick' Geometry." Math. Gaz. 23, 161-168, 1939.Wells, D. The Penguin Dictionary of Curious and Interesting Geometry. London: Penguin, p. 149, 1991.Referenced on Wolfram|Alpha
Matchstick ConstructionCite this as:
Weisstein, Eric W. "Matchstick Construction." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/MatchstickConstruction.html