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Inequalities Associated with the Triangle

Published online by Cambridge University Press:  20 November 2018

W. J. Blundon
W. J. Blundon*
Affiliation:
Memorial University of Newfoundland
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Let R, r, s represent respectively the circumradius, the inradius and the semiperimeter of a triangle with sides a, b, c. Let f(R, r) and F(R, r) be homogeneous real functions. Let q(R, r) and Q(R, r) be real quadratic forms. The latter functions are thus a special case of the former. Our main result is to derive the strongest possible inequalities of the form

1

with equality only for the equilateral triangle.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 8 , Issue 5 , October 1965 , pp. 615 - 626
Copyright
Copyright © Canadian Mathematical Society 1965

References

1. Blundon, W. J., On certain polynomials associated with the triangle. Math. Magazine 4 (1963), 247-248.Google Scholar
2. Gerretsen, J. C. H., Ongelijkheden in de driehoek. Nieuw Tijdschr. Wisk. 41 (1953-54), 1-7.Google Scholar
3. Hobson, E. W., A treatise on plane trigonometry. Cambridge University Press, 1925.Google Scholar
4. Leuenberger, F., Einige Driecksungleichungen. Elem. Math. 13 (1958), 121-126.Google Scholar
5. Makowski, A., Inequalities for radii of inscribed, circumscribed and escribed circles. Nieuw Archief voor Wisk. (3),12 (1964), 5-7.Google Scholar
6. Marsh, D. C. B., Solution to Problem E1589. Amer. Math. Monthly 71 (1964), 213-214.Google Scholar
7. Steinig, J., Inequalities concerning the circumradius and inradius of a triangle. Elem. Math. 18 (1963), 127-131.Google Scholar