Centres
of Circles?
| The points on a Euclidean circle centre O and
radius point M also form a circle in our hyperbolic disc, the definition
being the points equidistant from a fixed centre point.
In this model, since inversions preserve circles in Euclidean space, if we reflect the circle about a d-line, the resulting set of points, which lie on a hyperbolic circle, also a circle to us as observers. However the hyperbolic centre will not coincide with the point that we would use as the centre as the non-Euclidean radius looks shorter on the horizon side of a diameter. A measurement problem can be formulated whereby, given a circle in one geometry we are asked to calculate the coordinates of the centre in the other. |
Length continuedCentres
of Circles?
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