Trisectrix of Maclaurin

trisectrix of Maclaurin
Trisectrix of Maclaurin

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This is a curve Colin Maclaurin (1698 to 1746) used to trisect a angle.



The following formula has asymtote at x=1 and loop point at origin:

Polar: r==Sec[t] - 4 Cos[t], -Pi/2 < t < Pi/2.

Parametric: (1-4 Cos[t]^2)*{1, Tan[t]}, -Pi/2 < t < Pi/2.

Parametric: {(-3 + t^2)/(1 + t^2), (t*(-3 + t^2))/(1 + t^2)}, -∞ < t < ∞.

Cartesian: y^2 (1-x) == x^2 (x + 3)

Polar: r==Sec[t/3], -3/2 Pi < t < 3/2 Pi. (vertex at {1,0}, double point at {-2,0})


Relation to Parabola

It is the pedal of parabola with repect to its focus reflect by the directrix.

trisectrix of Maclaurin

Trisecting a Angle

Suppose we have a trisectrix with node at the origin and vertex at point {-3,0}, and let P be any point on the loop of the curve. angle[{-3,0},{-2,0},P] == 3*angle[{-2,0},{0,0},P].

trisectrix of Maclaurin triOfMaclaurin
Moving Point P

Related Web Sites

See: Websites on Plane Curves, Plane Curves Books .

The MacTutor History of Mathematics archive