1 citations · 1 across the 15 of their papers we have counts for
15 papers
A Geometric Representation
Nicholas Phat Nguyen
This article provides a geometric representation for the well-known isomorphism between the special orthogonal group of an isotropic quadratic space of dimension 3 and the group of…
Solvable Polynomials over the Gaussian Field Q(i)
Nicholas Phat Nguyen
In this paper, we describe a congruence property of solvable polynomials with coefficients in the Gaussian field Q(i).
A Congruence Property of Solvable Polynomials
Nicholas Phat Nguyen
We describe a congruence property of solvable polynomials over Q, based on the irreducibility of cyclotomic polynomials over number fields that meet certain conditions.
Four Points and a Quadric
Nicholas Phat Nguyen
This paper provides a new simple proof of Hesse's theorem in projective geometry for any dimension.
On Generalizations of the Butterfly Theorem
Nicholas Phat Nguyen
This paper provides a uniform explanation of different extensions and generalizations of the butterfly theorem based on the Desargues involution theorem.
A Generalization of Desargues' Involution Theorem
Nicholas Phat Nguyen
This paper states and proves a generalization of the well-known Desargues involution theorem from plane projective geometry.
The Triangle Altitudes Theorem in Hyperbolic Plane Geometry
Nicholas Phat Nguyen
We provide a new formulation and proof of the triangle altitudes theorem in hyperbolic plane geometry, together with an easily computed discriminant to distinguish between differen…
A Note on Cyclotomic Polynomials
Nicholas Phat Nguyen
We present a more general proof that cyclotomic polynomials are irreducible over Q and other number fields that meet certain conditions. The proof provides a new perspective that t…
An Algebraic Construction of Hyperbolic Planes over a Euclidean Ordered Field
Nicholas Phat Nguyen
Using concepts and techniques of bilinear algebra, we construct hyperbolic planes over a euclidean ordered field that satisfy all the Hilbert axioms of incidence, order and congrue…
Projective Line Revisited
Nicholas Phat Nguyen
This article provides a new perspective on the geometry of a projective line, which helps clarify and illuminate some classical results about projective plane. As part of the same…
Explanation of a Polynomial Identity
Nicholas Phat Nguyen
In this note, we provide a conceptual explanation of a well-known polynomial identity used in algebraic number theory.
A Note on Cyclotomic Integers
Nicholas Phat Nguyen
In this note, we present a new proof that the cyclotomic integers constitute the full ring of integers in the cyclotomic field.
Anisotropic Quadratic Forms and Inversive Geometry
Nicholas Phat Nguyen
We develop an inversive geometry for anisotropic quadradic spaces, in analogy with the classical inversive geometry of a Euclidean plane.
Valuation and Divisibility
Nicholas Phat Nguyen
In this paper, we explain how some basic facts about valuation can help clarify many questions about divisibility in integral domains.
A Note on Graded Rings and Modules
Nicholas Phat Nguyen
In this note, we consider a situation that is generally used as an intermediate technical step in proving the Artin-Rees lemma but otherwise is not much discussed in introductory a…