Access the full text.
Sign up today, get DeepDyve free for 14 days.
A. Zachos, Gerasimos Zouzoulas (2009)
The weighted Fermat-Torricelli problem for tetrahedra and an inverse problemJournal of Mathematical Analysis and Applications, 353
Leoni Dalla (2001)
A note on the Fermat-Torricelli point of a d-simplexJournal of Geometry, 70
R. Noda, T. Sakai, M. Morimoto (1991)
Generalized Fermat's ProblemCanadian Mathematical Bulletin, 34
A. Zachos (2010)
A Plasticity Principle of Convex Quadrilaterals on a Convex Surface of Bounded Specific CurvatureActa Applicandae Mathematicae, 129
L. Li︠u︡sternik (1966)
Convex figures and polyhedra
(1997)
Geometric aspects of the generalized Fermat-Torricelli problem
D. Chand, S. Kapur (1970)
On Convex PolyhedraMathematics Magazine, 43
A.D. Alexandrov (2005)
Convex Polyhedra
V. Bolti︠a︡nskiĭ, H. Martini, V. Soltan (1998)
Geometric Methods and Optimization Problems
(2011)
An evolutionary structure of pyramids in the three dimensional Euclidean space
(2008)
An evolutionary structure of convex quadrilaterals
We prove a plasticity principle of closed hexahedra in the three dimensional Euclidean space which states that: Suppose that the closed hexahedron A 1 A 2⋯A 5 has an interior weighted Fermat-Torricelli point A 0 with respects to the weights B i and let α i0j =∠A i A 0 A j . Then these 10 angles are determined completely by 7 of them and considering these five prescribed rays which meet at the weighted Fermat-Torricelli point A 0, such that their endpoints form a closed hexahedron, a decrease on the weights that correspond to the first, third and fourth ray, causes an increase to the weights that correspond to the second and fifth ray, where the fourth endpoint is upper from the plane which is formed from the first ray and second ray and the third and fifth endpoint is under the plane which is formed from the first ray and second ray. By applying the plasticity principle of closed hexahedra to the n-inverse weighted Fermat-Torricelli problem, we derive some new evolutionary structures of closed polyhedra for n>5. Finally, we derive some evolutionary structures of pentagons in the two dimensional Euclidean space from the plasticity of weighted hexahedra as a limiting case.
Acta Applicandae Mathematicae – Springer Journals
Published: Aug 25, 2012
Read and print from thousands of top scholarly journals.
Already have an account? Log in
Bookmark this article. You can see your Bookmarks on your DeepDyve Library.
To save an article, log in first, or sign up for a DeepDyve account if you don’t already have one.
Copy and paste the desired citation format or use the link below to download a file formatted for EndNote
Access the full text.
Sign up today, get DeepDyve free for 14 days.
All DeepDyve websites use cookies to improve your online experience. They were placed on your computer when you launched this website. You can change your cookie settings through your browser.