5 papers
Lattice triangles whose centers are lattice points
Christian Aebi, Grant Cairns
We show that for an integer , there exists an acute integer lattice triangle of lattice perimeter such that its orthocenter is an integer lattice point, if and only if…
The sad life of lattice triangles
Christian Aebi, Grant Cairns
This paper treats triangles in the plane whose vertices lie on the integer lattice, i.e., the vertices have integer coordinates. It shows that apart from trivial examples, the circ…
Equable Parallelograms on the Eisenstein Lattice
Christian Aebi, Grant Cairns
This paper studies equable parallelograms whose vertices lie on the Eisenstein lattice. Using Rosenberger's Theorem on generalised Markov equations, we show that the set of these p…
Less than Equable Triangles on the Eisenstein lattice
Christian Aebi, Grant Cairns
We classify perimeter dominant triangles whose side lengths are in and whose area is in . There is one exceptional example, which is equi…
Equable Triangles on the Eisenstein Lattice
Christian Aebi, Grant Cairns
We show that there are only two equable triangles having vertices on the Eisenstein lattice, up to Euclidean motions.