Triangle centres and homogeneous coordinates 1

During a course in Euclidean geometry at high school level, a student encounters four classical triangle centres—the circumcentre, the incentre, the orthocentre and the centroid (introduced as the points of concurrence of the perpendicular bisectors of the sides, the bisectors of the angles of the triangle, the altitudes and the medians, respectively). We shall study two alternative ways of describing and characterising these four significant points. They are both known as homogeneous coordinate systems, but we explain the significance of this term later. In part I of the article, we consider the first of these: trilinear coordinates.

18094 registered users
6935 resources