**Volume 8** ▶ Number 1 ▷ Number 2 ▷ Number 3 ▷ Number 4

**About Tartaglion’s representation of planes**

*Original research paper. Pages 77—84*

Blagoi N. Djokov

Full paper (PDF, 297 Kb) | Abstract

**#!**is considered, but as a special and a new commutative ring. The elements of this ring are called tartaglions. Necessary and sufficient conditions, for a plane in

**#!**to be representated by Cartesian tartaglion’s equation, are estabilished.

**Algebraic and geometric analysis of a Fermat/Cardano cubic**

*Original research paper. Pages 85—94*

J. V. Leyendekkers, A. G. Shannon and C. K. Wong

Full paper (PDF, 463 Kb) | Abstract

**#!**It is shown that the functions R = – x3 + 3(p + q)x2 – 3(p2 + q2)x + (p3 + q3), p,q e Z+, and R = 3×2 – 3(2{p + q ) – \ ) x + (3{p2 + q2) – 3{p + q) + \ ) intersect at a point that is always non-integer, A geometric analysis shows that the cubic crosses the x -axis at a point, xq, that is always non-integer, with xq = N« ( p * q + (2pq)’A), N,n e 2+, where N~ is obtained from the geometry of the curve. These results show that a general parameter associated with the real roots of Fermat/Cardano polynomials is a function of p, q and the geometry of the curve, which in turn yield the link with the geometry of the complex plane.

**Powers as a difference of squares: The effect on triples**

*Original research paper. Pages 95—106*

J. V. Leyendekkers and A. G. Shannon

Full paper (PDF, 519 Kb) | Abstract

**An invariant integrals in the p-adic number fields**

*Original research paper. Pages 107—111*

Lee Chae Jang

Full paper (PDF, 174 Kb) | Abstract

**!#**In this paper we investigate some properties of non-Archimedean integration which is defined by T. Kim, cf. [2]. By using our results in this paper, we can give an answer of the problems which is remained by I.-C. Huang and S-Y. Huang in [ 1: p. 179]

**New variant of a Fibonacci plane**

*Original research paper. Pages 112—115*

Krassimir T. Atanassov and Anthony G. Shannon

Full paper (PDF, 110 Kb)

**On a generalization of identities of Hoggatt and Horadam**

*Original research paper. Page 116*

A. G. Shannon and J. H. Clarke

Full paper (PDF, 45 Kb)