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Volume 26 - Issue 272 - December 1942

Contents

Page 1 of 2

Other

Research Article

  • On Some Geometrical Inequalities

  • D. Pedoe
  • Published online by Cambridge University Press:
    03 November 2016, pp. 202-208

  • In § 1 of this Note we first investigate some geometrical inequalities connecting a set of n unordered points in a plane. An ellipse is associated with the set of points, and use is made of the invariants of this ellipse under rotation of the coordinate axes. Some inequalities, first obtained by Weitzenböck, are derived and extended. A new geometrical entity, which we call the mutual area, is then defined for a set of n and a set of m points with the same centroid. Using the mutual invariants of two ellipses with a common centre under rotations of the coordinate axes, we obtain some inequalities connecting two sets of points with a common centroid.

Other

Research Article

  • Some Homothetic Triangles Related to the Euler Line

  • R. H. Cobb
  • Published online by Cambridge University Press:
    03 November 2016, pp. 209-211

  • In this note the triangle formed by the tangents to the circumcircle at the vertices of a given triangle is called the circumtriangle of the given triangle; the triangle formed by the points of contact of the incircle with the sides of a given triangle is called the intriangle of the given triangle; and the triangle formed by the points of contact of an excircle with the sides of a given triangle is called an extriangle of the given triangle.

Other

Mathematical Notes

Reviews

Page 1 of 2