11 citations · 29 across the 14 of their papers we have counts for
8 papers · 1 filter
Generalised vector products and metrical trigonometry of a tetrahedron
Gennady A Notowidigdo, Norman J Wildberger
We study the general rational trigonometry of a tetrahedron, based on quadrances, spreads and solid spreads, using vector products associated to an arbitrary symmetric bilinear for…
Generalised vector products in three-dimensional geometry
Gennady A Notowidigdo, Norman J Wildberger
In three-dimensional Euclidean geometry, the scalar product produces a number associated to two vectors, while the vector product computes a vector perpendicular to them. These are…
Universal Hyperbolic Geometry II: A pictorial overview
N J Wildberger
This article provides a simple pictorial introduction to universal hyperbolic geometry. We explain how to understand the subject using only elementary projective geometry, augmente…
Universal Hyperbolic Geometry I: Trigonometry
N. J. Wildberger
Hyperbolic geometry is developed in a purely algebraic fashion from first principles, without a prior development of differential geometry. The natural connection with the geometry…
The ancient Greeks present: Rational Trigonometry
N. J. Wildberger
Pythagoras' theorem, the area of a triangle as one half the base times the height, and Heron's formula are amongst the most important and useful results of ancient Greek geometry.…
Chromogeometry and relativistic conics
N. J. Wildberger
This paper shows how a recent reformulation of the basics of classical geometry and trigonometry reveals a three-fold symmetry between Euclidean and non-Euclidean (relativistic) pl…