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Upper and Lower Bounds for The Area of a Triangle for Whose Sides Two Symmetric Functions are Known
Published online by Cambridge University Press: 20 November 2018
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Improving on inequalities given by Gerretsen (2), Beatty (1) has proved that for the area Δ of any plane triangle with sides a, b, c the following inequalities hold:
(1.1)
where
(1.2);
the signs of equality in (1.1) only apply when the triangle is equilateral. Beatty has also remarked that the second inequality in (1.1) is of no value in case 5H ≥ 3K, since then the lower estimate which it gives for Δ2 is not even positive.
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- Copyright © Canadian Mathematical Society 1957
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