Maclaurin's trisectrix as the locus of the intersection of two rotating lines
In algebraic geometry, the trisectrix of Maclaurin is a cubic plane curve notable for its trisectrix property, meaning it can be used to trisect an angle. It can be defined as locus of the point of intersection of two lines, each rotating at a uniform rate about separate points, so that the ratio of the rates of rotation is 1:3 and the lines initially coincide with the line between the two points. A generalization of this construction is called a sectrix of Maclaurin. The curve is named after Colin Maclaurin who investigated the curve in 1742.
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In algebraic geometry, the trisectrixofMaclaurin is a cubic plane curve notable for its trisectrix property, meaning it can be used to trisect an angle...
Limaçon trisectrix (some sources refer to this curve as simply the trisectrix.) TrisectrixofMaclaurin Equilateral trefoil (a.k.a. Longchamps' Trisectrix) Tschirnhausen...
{2}}(3X^{2}-Y^{2}),} which is the equation of the trisectrixofMaclaurin. "Folium of Descartes". Encyclopedia of Mathematics. June 5, 2020. Retrieved January...
sectrix ofMaclaurin can be defined as a curve whose equation in biangular coordinates is linear. The name is derived from the trisectrixofMaclaurin (named...
of Descartes Cissoid of Diocles Conchoid of de Sluze Cubic with double point Strophoid Semicubical parabola Serpentine curve Trident curve Trisectrix...
Folium of Descartes Cissoid of Diocles Conchoid of de Sluze Right strophoid Semicubical parabola Serpentine curve Trident curve TrisectrixofMaclaurin Tschirnhausen...
Descartes Cissoid of Diocles Conchoid of de Sluze Right strophoid Semicubical parabola Serpentine curve Trident curve TrisectrixofMaclaurin Tschirnhausen...
of Diocles a = −2, right strophoid a = −4, trisectrixofMaclaurin Smith, David Eugene (1958), History of Mathematics, Volume 2, Courier Dover Publications...
This is a broad family of rational cubic curves containing several well-known examples. Specifically: The TrisectrixofMaclaurin given by 2 x ( x 2 + y...
can be used to trisect arbitrary angles. Examples include the trisectrixof Colin Maclaurin, given in Cartesian coordinates by the implicit equation 2 x...
family of curves called the conchoids of de Sluze. This family includes, in addition to the cissoid of Diocles listed above, the trisectrixofMaclaurin (d...
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