Search
Now showing items 1-8 of 8
A note on two rational invariants for a particular 2 x 2 matrix.
We state and prove the invariance, with respect to matrix power, of both the diagonals and anti-diagonals ratio of a special case 2×2 matrix. The proof methodology is new, contrasting with those deployed previously in establishing anti-diagonals matrix invariants.
On two derivative sequences from scaled geometric mean sequence terms.
The so called geometric mean sequence recurrence, with additional scaling variable, produces a sequence for which the general term has a known closed form. Two types of derivative sequence—comprising products of such sequence terms—are examined. In particular, the general term closed forms formulated are shown to depend strongly on a mix of three existing sequences, from which sequence growth rates are deduced and other results given.
A new non-linear recurrence identity class for Horadam sequence terms.
We state, and prove by a succinct matrix method, a non-linear recurrence identity class for terms of the so called Horadam sequence. A particular instance was established (in equivalent form) over half a century ago by A.F. Horadam, which provides a starting point for the discussion and an introduction to our formulation technique.
A few thoughts on the aesthetics of mathematics in research and teaching.
Mathematical aesthetic, having a variety of forms, is commonly experienced by mathematicians as a genuine reality and is available at every level of study. This short essay in hopefully moving beyond standardised hermeneutic critique attests to its authenticity through the words of some mathematical proponents, and reminds us that it should be promoted to children and students as a phenomenon that is as accessible as it is incontestable.