Image:Trisected perimeter point 3-4-5.svg

from pyx import canvas,path,color
 
def meet(p,q):
    return [p[i-1]*q[i]-q[i-1]*p[i] for i in [2,0,1]]
 
def sign(p,r,q):
    L = meet(p,q)
    return sum(L[i]*r[i] for i in [0,1,2])
 
A = [0,3,1]
B = [0,0,1]
C = [4,0,1]
 
lo = 0
hi = 3
for i in range(40):
    x = (lo + hi) / 2.0
    AP = [4-x,0,1]
    BP = [4-0.8*(4-x),0.6*(4-x),1]
    CP = [0,x,1]
    if sign(meet(A,AP),meet(B,BP),meet(C,CP)) < 0:
        hi = x
    else:
        lo = x
 
c = canvas.canvas()
 
def line(p,q):
    c.stroke(path.line(p[0],p[1],q[0],q[1]),[color.rgb.black])
 
for p,q in [(A,B),(A,C),(B,C),(A,AP),(B,BP),(C,CP)]:
    line(p,q)
 
c.writePDFfile("Trisected perimeter point 3-4-5")