# poincare: find the distance between the points

• Dec 13th 2009, 12:59 PM
mandy123
poincare: find the distance between the points
I need some help finding the Poincare distance
I have tried to do this problem, but I know my answer is wrong!

Let Gamma be the interior of the unit disk centered at the origin in the xy-plane, (x^2+y^2 <1). Find the poincare distance between the following pairs of points.
(0,0) and (1/2,0).
• Dec 14th 2009, 03:54 AM
HallsofIvy
Quote:

Originally Posted by mandy123
I need some help finding the Poincare distance
I have tried to do this problem, but I know my answer is wrong!

Let Gamma be the interior of the unit disk centered at the origin in the xy-plane, (x^2+y^2 <1). Find the poincare distance between the following pairs of points.
(0,0) and (1/2,0).

Okay, what have you done to get your "wrong" answer? In particular, what formulas are you using?

I assume you are talking about the Poincare disk model for hyperbolic geometry.
• Dec 14th 2009, 06:56 AM
mandy123
Find A’
· TU is the line x= ½
· T= (½ , (√3)/2)
· U=(½ , - (√3)/2)
· Find the equation of the line tangent to gamma at T (Perpendicular to radius of T)
o The slope of point T is √3
o Slope of the perpendicular to the radius is -1/√3
o Equation of the line: y = -1/√3 x + 2/√3
· A’
o 0= -1/√3 x + 2/√3
o X=2
o A’ =(2,0)
Find midpoint of AA’
· ( 5/4 , 0)
Equation of the perpendicular bisector
· X= 5/4
Midpoint of BA
· (¼ , 0)
Intersection of midpoint and perpendicular bisector
· (5/4, 0)