Conclusion

References

The presented conformal models may be used as a visualization tools for hyperbolic geometry. New way of visualization of specific concept helps to create better intuitive understanding of the concent and to make new discoveries.Conformal mappings of hyperbolic plane seems to show nice properties of the geometry - there is a lot of hyperbolic plane squeezed near the boundary of the Poicare disk and various conformal mappings unwrap this parts of the plane into the visible existence.Different mappings of the same hyperbolic pattern provide strikingly different views, which higlights different properties of the pattern.There are a lot of examples of visualization of the hyperbolic geometry in the disk and upper half plane models. First one were made by Klein and Fricke in. Check it, it is good.As far as I know the band model was mentioned without illustrations in exercises inIt is described with a few nice illustrations inFirst time I have seen the hyperbolic tiling in the band model was in private communication from Anton Sherwood in the summer of 2008. He has a nice example on his web page where he calls it 'Mercator Projection'.