منابع مشابه
Cubics Associated with Triangles of Equal Areas
The locus of a point X for which the cevian triangle of X and that of its isogonal conjugate have equal areas is a cubic that passes through the 1st and 2nd Brocard points. Generalizing from isogonal conjugate to P -isoconjugate yields a cubic Z(U,P ) passing through U ; if X is on Z(U, P ) then the P isoconjugate of X is on Z(U,P ) and this point is collinear with X and U . A generalized equal...
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We present an improved algorithm for finding all solutions to Goehl’s problem A = mP for triangles, i.e., the problem of finding all Heronian triangles whose area (A) is an integer multiple (m) of the perimeter (P ). The new algorithm does not involve elimination of extraneous rational triangles, and is a true extension of Goehl’s original method.
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It is possible to construct a figure in 3 dimensions which is combinatorially equivalent to a regular icosahedron, and whose faces are all congruent but not equilateral. Such icosamonohedra can be convex or nonconvex, and can be deformed continuously. A scalene triangle can construct precisely zero, one, or two convex icosamonohedra, and each occurs. Demonstrated here are two explicit convex ex...
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Small-world networks are abundant in nature and society, describing such diverse systems as the World Wide Web, communication networks or the neuronal network of the worm C.elegans. In the past ten years, many small-world network models have been proposed in both probabilistic and deterministic fashions. In this letter, we propose a new deterministic small-world model by simply extending triang...
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ژورنال
عنوان ژورنال: Mathematical Inequalities & Applications
سال: 1999
ISSN: 1331-4343
DOI: 10.7153/mia-02-13