Talk:Hypercycle (geometry)
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An entry from Hypercycle (geometry) appeared on Wikipedia's Main Page in the Did you know? column on October 24, 2006. |
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[edit] List of properties copied?
It seems that the bulleted list of properties were copied directly from http://www.math.uncc.edu/~droyster/math3181/notes/hyprgeom/node68.html, which is referenced in the article. -- SilverStar 05:30, 25 October 2006 (UTC)
I started from that list, but I reformulated the properties, changed the order and added some. The proofs are not taken from there: I did them myself, partially following Martin's book. Eubulide 07:36, 25 October 2006 (UTC)
[edit] Circle Limit III
The text says that the Escher print contains hypercycles, but it doesn't explain why. Where's the straight line that one of those hypercycles is based on, and what defines the distance between them? 171.64.71.123 00:01, 11 January 2007 (UTC)
- In the Poincaré model, a circle represents
- * a circle if it does not meet the horizon;
- * a horocycle if it is tangent to the horizon;
- * a straight line if it cuts the horizon at right angles;
- * a hypercycle if it cuts the horizon at any other angle.
- Since Escher's arcs are not perpendicular to the horizon, they must be hypercycles. The axis of a hypercycle is represented by the perpendicular circle that meets the horizon in the same pair of points. Sorry I can't help more than that. —Tamfang 08:39, 28 February 2007 (UTC)
