Descartes's Angle Trisection
Descartes's Angle Trisection
Descartes used the intersection of a circle and a parabola to trisect an angle. The equations of the circle and parabola are +-x+4ay=0 and =x, respectively. The coordinates of the intersection satisfy . Since , by taking , the smaller positive root of the last equation is
2
x
2
y
13
4
2
y
1
4
4=3y-a
3
y
4(t)=3sin(t)-sin(3t)
3
sin
a=sin(3t)
sin(t)
.