1. ## Hyperbolic Geometry

I am taking my first class with Hyperbolic Geometry and I need some help with the basics.

I am asked to find the hyperbolic line through $i$ and $2+2i$. I understand that this line is going to be represented in the shape of a Euclidean Circle and I am able to draw this circle but I'm not sure how to express it. Any help would be appreciated.

2. Originally Posted by zebra2147
I am taking my first class with Hyperbolic Geometry and I need some help with the basics.

I am asked to find the hyperbolic line through $i$ and $2+2i$. I understand that this line is going to be represented in the shape of a Euclidean Circle and I am able to draw this circle but I'm not sure how to express it. Any help would be appreciated.

I supose you're working with the Poincare's half (upper) plane model of a dimension 2 hyperbolic geometry,and thus you'd need a

half circle through $1,\,2+2i$ with center on the real axis. There are infinite such circles, of course, but here's a

geometric easy way to choose a "nice" one: find the equation of the perpendicular bisector of the segment determined by

$i,\,2+2i$ , and find its intersection with the real axis, which will be our half circle's center...

Tonio

3. Alright great...That's the process I had started. But then I guess my question is... Am I suppose to use the formula for a euclidean circle?

4. Originally Posted by zebra2147
Alright great...That's the process I had started. But then I guess my question is... Am I suppose to use the formula for a euclidean circle?

Yes, of course...that's what we do in that Poincare's model of hyp. geometry.

Tonio