4 papers
math.HO2020
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.
math.HO2020
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.
math.HO2019
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…
math.HO2018
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…