Journal ArticleDOI
The Fermat-Steiner problem
Shay Gueron,Ran Tessler +1 more
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The sum of the distances of any interior point M from the sides of an equilateral triangle equals the altitude of the triangle, and applying Viviani’s Theorem solves the problem.Abstract:
(2002). The Fermat-Steiner Problem. The American Mathematical Monthly: Vol. 109, No. 5, pp. 443-451.read more
Citations
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Journal ArticleDOI
What is Mathematics
TL;DR: In this article, Courant and Robbins present What is Mathematics? An Elementary Approach to Ideas and Methods, which is a good book which deserves to run through many editions and is not a book on mathematical logic or philosophy: it deals not with the nature of mathematics but with its content.
Proceedings ArticleDOI
Energy Efficient Robot Rendezvous
TL;DR: This work examines the problem of finding a single meeting location for a group of heterogeneous autonomous mobile robots, such that the total system cost of traveling to the rendezvous is minimized, and proposes two algorithms that solve this problem.
Journal ArticleDOI
Analytic Approach to Optimal Routing for Commercial Formation Flight
Thomas E. Kent,Arthur Richards +1 more
TL;DR: In this paper, a weighted extension of the classical Fermat point problem is used to develop a scalable methodology for the formation routing problem, enabling quick calculation of formation costs, and a case study for 210 transatlantic flight routes is presented, with results showing possible average fuel-burn savings against solo flight of around 8.7% for formations of two and 13.1% for up to three.
Journal ArticleDOI
An Old Friend Revisited
TL;DR: The emergence of a sixth-degree equation may be surprising at first, but perhaps less so in retrospect: triangles in ratio chaining form a (discrete) “logarithmic” spiral in which multiplication by m occurs at every stage.
Journal ArticleDOI
Perturbative classical conformal blocks as Steiner trees on the hyperbolic disk
TL;DR: In this article, the authors 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.
References
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Book
Introduction to Geometry
TL;DR: In this paper, the authors describe the topology of surfaces in the Euclidean plane, including the Golden Section and Phyllotaxis, as well as the five Platonic solids.
Journal ArticleDOI
What is Mathematics
TL;DR: In this article, Courant and Robbins present What is Mathematics? An Elementary Approach to Ideas and Methods, which is a good book which deserves to run through many editions and is not a book on mathematical logic or philosophy: it deals not with the nature of mathematics but with its content.