منابع مشابه
Rational Triangles with Equal Area
We consider the set of triangles in the plane with rational sides and a given area A. We show there are infinitely many such triangles for each possible area A. We also show that infinitely many such triangles may be constructed from a given one, all sharing a side of the original triangle, unless the original is equilateral. There are three families of triangles (including the isosceles ones) ...
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We prove that there are 14 distinct ways to tile the unit square (modulo the symmetries of the square) with 5 triangles such that the 5-tiling is not a subdivision of a tiling using fewer triangles. We then demonstrate how to construct infinitely many rational tilings in each of the 14 configurations. This stands in contrast to a long standing inability to find rational 4-tilings of the unit sq...
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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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In this paper we review the derivation of implicit equations for non-degenerate quadric patches in rational Bézier triangular form. These are the case of Steiner surfaces of degree two. We derive the bilinear forms for such quadrics in a coordinate-free fashion in terms of their control net and their list of weights in a suitable form. Our construction relies on projective geometry and is groun...
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ژورنال
عنوان ژورنال: Časopis pro pěstování matematiky a fysiky
سال: 1877
ISSN: 1802-114X
DOI: 10.21136/cpmf.1877.121692