# The Fermat-Steiner Problem

@article{Gueron2002TheFP, title={The Fermat-Steiner Problem}, author={Shay Gueron and Ran Tessler}, journal={The American Mathematical Monthly}, year={2002}, volume={109}, pages={443 - 451} }

The original treatment of the problem considered only triangles with acute angles, for which P must be an interior point. Therefore, a discussion of the relative position of P with respect to the triangle did not emerge. Let us first make some simple observations about this relative position: P cannot lie outside ABC because in this case the “nearest point projection”, call it P ′, gives G(P ′) < G(P). By the convexity of the distance function it follows that if P is inside ABC , it is unique…

## 53 Citations

On the Fermat point of a triangle

- Mathematics
- 2017

For a given triangle △ABC, Pierre de Fermat posed around 1640 the problem of finding a point P minimizing the sum sP of the Euclidean distances from P to the vertices A, B, C. Based on geometrical…

The twist angle of weighted Steiner minimal trees in the three dimensional Euclidean Space

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We find the equations that allow us to compute the position of the two interior nodes (weighted Fermat-Torricelli points) w.r. to the weighted Steiner problem for four points determining a…

Solving a Generalized Gauss Problem

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This work solves a generalized Gauss problem in the Euclidean plane and introduces a new class of generalized Gaussian trees that are absorbed with respect to the sum of the four given weights of the convex quadrilateral.

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- Mathematics
- 2018

We consider the Steiner tree problem in hyperbolic geometry in the context of the AdS/CFT duality between large-c conformal blocks on the boundary and particle motions in the bulk. The Steiner trees…

Perturbative classical conformal blocks as Steiner trees on the hyperbolic disk

- MathematicsJournal of High Energy Physics
- 2019

A bstractWe consider the Steiner tree problem in hyperbolic geometry in the context of the AdS/CFT duality between large-c conformal blocks on the boundary and particle motions in the bulk. The…

Moving a Rectangle around a Corner—Geometrically

- MathematicsAm. Math. Mon.
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The problem of moving a couch around a comer by simple Euclidean geometry is solved, in the same spirit as the author's solution of L'Hospital's Pulley Problem, to stress mathematical concerns whose importance has been made increasingly evident by developments in computer science and engineering.

Euclidean and Minkowski Steiner Trees

- Mathematics
- 2015

This chapter begins with a comprehensive study of the Euclidean Steiner tree problem. This is the most intuitively appealing of the Steiner tree problems and the one with the longest history. The…

Viviani's Theorem and Its Extension

- Mathematics
- 2010

Summary Viviani's theorem states that the sum of distances from any point inside an equilateral triangle to its sides is constant. Here, in an extension of this result, we show, using linear…

ar 2 00 9 On Viviani ’ s Theorem and its Extensions

- Mathematics
- 2009

Viviani’s theorem states that the sum of distances from any point inside an equilateral triangle to its sides is constant. We consider extensions of the theorem and show that any convex polygon can…

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