Are there some outstanding results using some version of Helly's theorem in a totally different area (whatever that means) than convex geometry?



Helly's theorem in other areas of mathematics
* Applications of Helly's theorem to linear programming are discussed
in this [thesis](http://web.cs.ucdavis.edu/~amenta/pubs/ninathesis.pdf).
* Then there are applications to the theory of approximation of
continuous functions by polynomials ([Chebyshev
approximation](http://www.maths.manchester.ac.uk/~khudian/Etudes/Algebra/chebysh2.pdf)).
* [Robotics](http://graphics.stanford.edu/~anguyen/papers/disconnection.pdf) (the discovery of an obstacle-avoiding path) makes use of Helly's theorem.
* [Analysis of Incomplete Data and an Intrinsic-Dimension Helly Theorem](http://www3.cs.stonybrook.edu/~jgao/paper/clustering_lines.pdf) discusses an application in the context of pattern recognition.
* [A Wavelet Approximation to the Helmholtz Equation](http://www.sciencedirect.com/science/article/pii/S0022247X99964065) relies on Helly's theorem.
* Finally, an application to the social sciences appears in the proof of the 
[Agreeable Society Theorem.](http://arxiv.org/abs/0811.3245v1)


