منابع مشابه
Heron Quadrilaterals via Elliptic Curves
A Heron quadrilateral is a cyclic quadri lateral whose area and side lengths are rational. In this work, we establish a correspondence between Heron quadri laterals and a family of elliptic curves of the form y2 = 3 2 x + αx2 − n x. This correspondence generalizes the no tions of Goins and Maddox who established a similar connec tion between Heron triangles and elliptic curves. We further s...
متن کاملAn elliptic K3 surface associated to Heron triangles
A rational triangle is a triangle with rational sides and rational area. A Heron triangle is a triangle with integral sides and integral area. In this article we will show that there exist infinitely many rational parametrizations, in terms of s, of rational triangles with perimeter 2s(s + 1) and area s(s − 1). As a corollary, there exist arbitrarily many Heron triangles with all the same area ...
متن کاملOn Heron triangles
There has previously been given a one-parameter family of pairs of Heron triangles with equal perimeter and area. In this note, we find two twoparameter families of such triangle pairs, one of which contains the known one-parameter family as a special case. Second, for an arbitrary integer n > 2 we show how to find a set of n Heron triangles in two parameters such that all triangles have equal ...
متن کاملCounting Heron Triangles with Constraints
Heron triangles have the property that all three of their sides as well as their area are positive integers. In this paper, we give some estimates for the number of Heron triangles with two of their sides fixed. We provide a general bound on this count H(a, b), where the sides a, b are fixed positive integers, and the estimate here is better than the one of Ionascu, Luca and Stănică for the gen...
متن کاملElliptic Curves and Triangles with Three Rational Medians
In his paper Triangles with three rational medians, about the characterization of all rational-sided triangles with three rational medians, Buchholz proves that each such triangle corresponds to a point on a oneparameter family of elliptic curves whose rank is at least 2. We prove that in fact the exact rank of the family in Buchholz paper is 3. We also exhibit a subfamily whose rank is at leas...
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ژورنال
عنوان ژورنال: Rocky Mountain Journal of Mathematics
سال: 2006
ISSN: 0035-7596
DOI: 10.1216/rmjm/1181069379