ISSN:
1420-8903
Keywords:
Primary 26D99
;
51M25
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
Abstract Leta 1,b 1,c 1,A 1 anda 2,b 2,c 2,A 2 be the sides and areas of two triangles. Ifa=(a 1 p +a 2 p )1/p ,b=(b 1 p +b 2 p )1/p ,c=(c 1 p +c 2 p )1/p , and 1≤p≤4, thena, b, c are the sides of a triangle and its area satisfiesA p/2≥A 1 p/2 +A 2 p/2 . If obtuse triangles are excluded,p〉4 is allowed. For convex cyclic quadrilaterals, a similar inequality holds. Also, leta, b, c, A be the sides and area of an acute or right triangle. Iff(x) satisfies certain conditions,f(a),f(b),f(c) are the sides of a triangle having areaA f, which satisfies (4A f/√3)1/2≥f((4A/√3)1/2).
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF02193037
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