5 papers · 1 filter
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…
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.
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…
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…