4 papers
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…
Following in Yiu's Footsteps but on the Eisenstein Lattice
Christian Aebi, Grant Cairns
Paul Yiu proved that all Heron triangles are realizable on the integer lattice. We give an analogous result for triangles with vertices on the Eisenstein lattice.
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.
The Quartic Residues Latin Square
Christian Aebi, Grant Cairns
We establish an elementary, but rather striking pattern concerning the quartic residues of primes that are congruent to 5 modulo 8. Let be a generator of the multiplicative…