2913. The Nine-Point Conic of a Convex Quadrangle

1960 ◽  
Vol 44 (349) ◽  
pp. 214
Author(s):  
E. H. Neville
Keyword(s):  
Convex Quadrangle

Largest Area Ellipse Inscribing an Arbitrary Convex Quadrangle

2019 ◽  
pp. 239-248
Author(s):  
M. John D. Hayes ◽  
Zachary A. Copeland ◽  
Paul J. Zsombor-Murray ◽  
Anton Gfrerrer
Keyword(s):  
Arbitrary Convex ◽  
Convex Quadrangle

scholarly journals Metric spaces which cannot be isometrically embedded in Hilbert space

1984 ◽  
Vol 30 (2) ◽  
pp. 161-167
Author(s):  
Yang Lu ◽  
Zhang Jing-Zhong
Keyword(s):  
Hilbert Space ◽  
Euclidean Space ◽  
Metric Spaces ◽  
Geometric Inequality ◽  
Cambridge Philos ◽  
Higher Dimensional ◽  
Planar Convex ◽  
Convex Quadrangle

Let A1A2A3A4, be a planar convex quadrangle with diagonals A1A3 and A2A4. Is there a quadrangle B1B2B3B4 in Euclidean space such that A1A3 < B1B3, A2A4 < B2B4 but AiAj > BiBj 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. Monthly50 (1943), 181–185).

Doping-induced evolutions of PbWO4 mesocrystals and their optical properties

RSC Advances ◽  
2014 ◽  
Vol 4 (69) ◽  
pp. 36738-36741 ◽  
Author(s):  
Ying Xiong ◽  
Bing Wang ◽  
Hao Zhuang ◽  
Xin Jiang ◽  
Guohua Ma ◽  
...  
Keyword(s):  
Optical Properties ◽  
Convex Quadrangle

Y-doped PbWO4 mesocrystals with controllable morphologies, from convex quadrangle to concave erythrocyte, are obtained by simply increasing the Y3+ doping concentrations.

Sign in / Sign up

Export Citation Format

Share Document