The uses of homogeneous barycentric coordinates in plane Euclidean geometry

  title={The uses of homogeneous barycentric coordinates in plane Euclidean geometry},
  author={Paul Yiu},
  journal={International Journal of Mathematical Education in Science and Technology},
  pages={569 - 578}
  • P. Yiu
  • Published 1 July 2000
  • Mathematics
  • International Journal of Mathematical Education in Science and Technology
The notion of homogeneous barycentric coordinates provides a powerful tool for analysing problems in plane geometry. The paper explains the advantages over the traditional use of trilinear coordinates, and illustrates its power in leading to discoveries of new and interesting collinearity relations of points associated with a triangle. 
Euclidean and Hyperbolic Barycentric Coordinates
In Chap. 3, we have seen two important theorems in mechanics. These are Theorem 3.3, p. 69, about the mass and the center of momentum velocity of a particle system in classical mechanics, and Theorem
A Generalization of the Klamkin Inequality
A generalization of a geometric inequality of Klamkin is established by considering the triples of barycentric coordinates of the points from a set which is included in the plane of the fundamental
Inertia tensor of a triangle in barycentric coordinates
We employ the barycentric coordinate system to evaluate the inertia tensor of an arbitrary triangular plate of uniform mass distribution. We find that the physical quantities involving the
In this paper we establish two new geometric inequalities involving an arbitrary point in the plane of a triangle. It is interesting that the equalities in both inequalities hold if and only if the
Isogonal Conjugates in a Tetrahedron
The symmedian point of a tetrahedron is defined and the existence of the symmedian point of a tetrahedron is proved through a geometrical argument. It is also shown that the symmedian point and the
Extensible point location algorithm
  • R. Sundareswara, P. Schrater
  • Computer Science
    2003 International Conference on Geometric Modeling and Graphics, 2003. Proceedings
  • 2003
We present a general walkthrough point location algorithm for use with general polyhedron lattices and polygonal meshes assuming the usage of nothing more than a simple linked list as a data
A Geometric Way to Generate Blundon Type Inequalities
We present a geometric way to generate Blundon type inequalities. Theorem 3.1 gives the formula for cosPOQ in terms of the barycentric coordinates of the points P and Q with respect to a given
Electrostatic potential of a uniformly charged triangle in barycentric coordinates
We compute the electrostatic potential of a uniformly charged triangle. Barycentric coordinates are employed to express the field point, the parametrization of the surface integral, and the gradient
Estimation of center of mass of the object to be held by barycentric coordinate system and polygon parcelling
A novel method based on barycentric coordinates is proposed for calculating the center of mass of an object to determine the contact points for grasping and results obtained are compared against quadrangle/hexagon parcelling algorithms and processing of pixels of the object in image data.
Novel Tools to Determine Hyperbolic Triangle Centers
Recently discovered tools to study analytic hyperbolic geometry in terms of analogies with analytic Euclidean geometry are presented and employed. Special attention is paid to the study of two novel


Linear Algebra and its Applications
Central points and central lines in the plane of a triangle
Triangle geometry ranks among the most enduring topics in all of mathematics. A treasury of triangle lore abounds in Euclid's Elements of 2.3 millenia ago, and still today interesting elementary
Math. Mag
  • Math. Mag
  • 1994
Crux Math
  • Crux Math
  • 1997
Advanced Euclidean Geometry, Dover reprint
  • 1965
Amer. Math. Monthly
  • Amer. Math. Monthly
  • 1999
Congressus Numeratium
  • Congressus Numeratium
  • 1998
Int. J. Math. Educ. Sci. Technol
  • Int. J. Math. Educ. Sci. Technol
  • 1998