11 citations · 23 across the 23 of their papers we have counts for
29 papers
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.
Respectful decompositions of Lie algebras
Grant Cairns, Yuri Nikolayevsky
One of Pierre Molino's principal mathematical achievements was his theory of Riemannian foliations. One of his last papers, published in 2001, showed that his theory could be exten…
A simple sum for simplices
Christian Aebi, Grant Cairns
We give a vector identity for points in . It follows as a corollary that when is odd the sum of the signed volumes of the -simplices is zero, and when …
Lattice Equable Quadrilaterals III: tangential and extangential cases
Christian Aebi, Grant Cairns
A lattice equable quadrilateral is a quadrilateral in the plane whose vertices lie on the integer lattice and which is equable in the sense that its area equals its perimeter. This…
A vector identity for quadrilaterals
Christian Aebi, Grant Cairns
A surprising simple result about quadrilaterals is given as an application of the vector triple product identity.
Lattice equable quadrilaterals II -- kites, trapezoids and cyclic quadrilaterals
Christian Aebi, Grant Cairns
We show that there are 4 infinite families of lattice equable kites, given by corresponding Pell or Pell-like equations, but up to Euclidean motions, there are exactly 5 lattice eq…