Polygons Whose Vertex Triangles Have Equal Area

Polygons Whose Vertex Triangles Have Equal Area

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) ...

Determinants Whose Elements Have Equal Norm1

Hence A, B, C equal A', B', C in some order. Each of the 6 orders leads immediately to the proportionality of two rows or columns. The above theorem, in its specialization to minors of Vandermonde determinants composed of gth roots of unity in R*, was used in [l] for the proof of a theorem on power series without terms whose subscript belongs to one of 3 residue classes modulo an arbitrary inte...

Equal Area Polygons in Convex Bodies

In this paper, we consider the problem of packing two or more equal area polygons with disjoint interiors into a convex body K in E such that each of them has at most a given number of sides. We show that for a convex quadrilateral K of area 1, there exist n internally disjoint triangles of equal area such that the sum of their areas is at least 4n 4n+1 . We also prove results for other types o...

Tiling Polygons with Lattice Triangles

Given a simple polygon with rational coordinates having one vertex at the origin and an adjacent vertex on the x-axis, we look at the problem of the location of the vertices for a tiling of the polygon using lattice triangles (i.e., triangles which are congruent to a triangle with the coordinates of the vertices being integer). We show that the coordinate of the vertices in any tiling are ratio...