In:
Bulletin of the Australian Mathematical Society, Cambridge University Press (CUP), Vol. 30, No. 2 ( 1984-10), p. 161-167
Abstract:
Let A 1 A 2 A 3 A 4 , be a planar convex quadrangle with diagonals A 1 A 3 and A 2 A 4 . Is there a quadrangle B 1 B 2 B 3 B 4 in Euclidean space such that A 1 A 3 〈 B 1 B 3 , A 2 A 4 〈 B 2 B 4 but A i A j 〉 B i B j for other edges? The answer is “no”. It seems to be obvious but the proof is more difficult. In this paper we shall solve similar more complicated problems by using a higher dimensional geometric inequality which is a generalisation of the well-known Pedoe inequality ( Proc. Cambridge Philos. Soc. 38 (1942), 397–398) and an interesting result by L.M. Blumenthal and B.E. Gillam ( Amer. Math. Monthly 50 (1943), 181–185).
Type of Medium:
Online Resource
ISSN:
0004-9727
,
1755-1633
DOI:
10.1017/S0004972700001866
Language:
English
Publisher:
Cambridge University Press (CUP)
Publication Date:
1984
detail.hit.zdb_id:
2268688-5
SSG:
17,1
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