Abstract

Introduction If we denote the sides of a triangle by (a; b; c) then the area is given by (1) = p s(s a)(s b)(s c) where s = (a + b + c)=2 is the semiperimeter. This formula is usually attributed to Heron of Alexandria circa 100 BC - 100 AD. However, it was already known to Archimedes prior to 212 BC [5, p. 105]. Our investigation is limited to triangles with rational sides. Even with sides of rational length, \Heron's" formula shows that the area need not be rational; any triangle with three rational sides and rational area is called a Heron triangle. The smallest such triangle with integer sides is the familiar (5; 4; 3) right triangle (with area 6) shown in Figure 1. B C a = 5<F

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