Revisiting Taxicab Apollonius Circles
The existence of excircles and an Apollonius circle for a triangle in taxicab geometry are connected to the concept of inscribed triangles.
math.GM↗
arXiv subjects
Kevin P. Thompson
Publications and source records attributed to Kevin P. Thompson.
Taxicab Calculus: Trig Derivatives
The set of trigonometric functions in taxicab geometry is completed and derivatives of all of the taxicab trigonometric functions are explored.
math.MG↗
An Alternative Computational Approach to the Collatz Conjecture
An alternative computational approach to the Collatz (3n+1) conjecture is presented that may be theoretically capable of confirming the conjecture.
math.NT↗
Arbitrary Sectioning of Angles in Taxicab Geometry
A construction to arbitrarily section a taxicab angle into an equal number of angles in (pure) taxicab geometry is presented.
math.MG↗
The Nature of Length, Area, and Volume in Taxicab Geometry
While the concept of straight-line length is well understood in taxicab geometry, little research has been done into the length of curves or the nature of area and volume in this geometry. This paper sets forth a comprehensive view of the basic dimensional measures in taxicab geometry.
math.MG↗
Taxicab Triangle Incircles and Circumcircles
Inscribed angles are investigated in taxicab geometry with application to the existence and uniqueness of inscribed and circumscribed taxicab circles of triangles.
math.MG↗