False perpendicular bisector

asked 2019-10-19 05:55:20 -0500

creyesm1992 gravatar image

Hello, I use the Poincare Disc Model in SAGE and I try to get the perpendicular bisector of a geodesic joining to points in the PD. It gives me a perpendicular geodesic, but it does not pass through the midpoint of my geodesic. I can not upload a screenshot of my situation so it is all I can say. Please help meee

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Comments

Could you please provide the code that leads to the issue ?

tmonteil gravatar imagetmonteil ( 2019-10-19 07:52:42 -0500 )edit

Of course, it is the following

PD=HyperbolicPlane().PD()
M=9
R=N(arccosh((cos(N(pi)/3.))/(sin(N(pi)/M))))
r=N(tanh(R/2))
B=PD.get_point(0+0*I)
C=PD.get_point(r*cos(N(pi)*3/2)+r*sin(N(pi)*3/2)*I)
seg=PD.get_geodesic(B,C)
seg2=seg.perpendicular_bisector()
seg3=seg.perpendicular_bisector()
seg.plot(color='blue')+(seg3).plot(color='red')

The supposed perpendicular bisector of BC is a geodesic which seems to be perpendicular to it, but it does not divide BC by the midpoint, because it cross it outside the segment BC.

creyesm1992 gravatar imagecreyesm1992 ( 2019-10-20 16:22:29 -0500 )edit