## Annette Ebbers-Baumann, Rolf Klein, Christian Knauer, and Günter
Rote:

# The geometric dilation of three points

*Journal of Computational Geometry* **10**,
no. 1 (2019), 532–549.
doi:10.20382/jocg.v10i1a18
→BibTeX
### Abstract

Given three points in the plane, we construct the plane geometric network of
smallest geometric dilation that connects them. The geometric dilation of a
plane network is defined as the maximum dilation (distance along the network
divided by Euclidean distance) between any two points on its edges. The
optimum network is either a line segment, a Steiner tree, or a curve
consisting of two straight edges and a segment of a logarithmic spiral.

Last update: November 29, 2019.