6 papers
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 …
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…
Wolstenholme again
Christian Aebi, Grant Cairns
We give an elementary and self-contained proof of the equivalence of a collection of Wolstenholme-type congruences due to Helou and Terjanian.
Morley's other miracle: $\displaystyle 4^{p-1}\equiv\pm (\smallmatrix p-1 \frac{p-1}{2} \endsmallmatrix) \pmod {p^3} $
Christian Aebi, Grant Cairns
Frank Morley is famous for his theorem concerning the angle trisectors of a triangle. This note gives an elementary proof of another result of Morley's, which relates the middle bi…
Wilson Theorems for Double-, Hyper-, Sub- and Super-factorials
Christian Aebi, Grant Cairns
We present generalisations of Wilson's theorem for double factorials, hyperfactorials, subfactorials and superfactorials.