The Trisectrix as the Locus of Points of Intersection

θ

1.34

show point labels

A trisectrix (red) is the locus of the points of intersection (red point

P

) of a moving horizontal line

L

(blue) and a rotating line

M

(black).

Initially, the line

L

lies along the line

y=1

and the line

M

lies along the line

x=0

. The line

M

rotates clockwise about the origin

O

at 1 radian per time unit, and the line

L

moves toward the

x

axis at a constant rate of

2/π

units per time unit, so that both lines reach the

x

axis at the same time. The line

M

meets the

x

axis at an angle

θ

.