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In geometry, a trisectrix is a curve which can be used to trisect an arbitrary angle with ruler and compass and this curve as an additional tool. Such a method falls outside those allowed by compass and straightedge constructions, so they do not contradict the well known theorem which states that an arbitrary angle cannot be trisected with that type of construction. There is a variety of such curves and the methods used to construct an angle trisector differ according to the curve. Examples include:

A related concept is a sectrix, which is a curve which can be used to divide an arbitrary angle by any integer. Examples include:

See also[edit]


  • Loy, Jim "Trisection of an Angle", Part VI
  • Weisstein, Eric W. "Trisectrix". MathWorld.
  • "Sectrix curve" at Encyclopédie des Formes Mathématiques Remarquables (In French)
  •  This article incorporates text from a publication now in the public domainChisholm, Hugh, ed. (1911). "Trisectrix". Encyclopædia Britannica. 27 (11th ed.). Cambridge University Press.