6533b861fe1ef96bd12c57d6
RESEARCH PRODUCT
A Vector Approach to Euler's Line of a Triangle
Jesús Ferrersubject
Discrete mathematicsPlane (geometry)General MathematicsCentroidTopologysymbols.namesakeIdentity (mathematics)Simple (abstract algebra)Line (geometry)Metric (mathematics)Euler's formulasymbolsAffine transformationMathematicsdescription
Among the many interesting properties that triangles possess there is one that quickly attracts our curiosity and stays easily in our mind: The centroid, circumcentre and orthocentre all lie in a common line (Euler's Line). An elementary simple proof can be obtained using metric and affine properties of the points involved, [1]. Our aim here is to illustrate a proof using vectors. We identify points in the plane with their position vectors. It is easy to see that the centroid G of the triangle ABC is given by the identity
| year | journal | country | edition | language |
|---|---|---|---|---|
| 1992-08-01 | The American Mathematical Monthly |