# 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)

.