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.

Hurwitz [6] posed in 1898 the problem of determining, for given integers r and s, the least integer n, denoted by r s, for which there exists an [r, s, n] formula, namely a sums of squares formula of the typewhere are bilinear forms with real coefficients in and . Such an [r, s, n] formula is equivalent to a normed bilinear map satisfying . We shall, therefore, speak of sums of squares formulae and normed bilinear maps interchangeably.

JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of content in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new forms of scholarship. For more information about JSTOR, please contact support@jstor.org.. Mathematical Association of America is collaborating with JSTOR to digitize, preserve and extend access to The American Mathematical Monthly.A Heronian triangle has integer sides and integer area. It is possible to put the vertices of a Heronian triangle at lattice points, provided the triangle has an integer height. There are, however, Heronian triangles with no integer heights. For example, the triangle with sides 25, 34, and 39 has area 420, but none of its heights is an integer [1]. The paper [4] gives a complete charactenrzation, and construction, of such triangles. The Heronian triangle (25, 34, 39; 420) can nevertheless be realized with vertices at the origin and at the lattice points (16, 30), (36, 15). Here is the main result of this note.

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