On a Fixed Value Theorem for Directed Areas in Conic Circumscribed Polygons and Applications

Chinese Quarterly Journal of Mathematics ›› 2009, Vol. 24 ›› Issue (4): 485-490.

On a Fixed Value Theorem for Directed Areas in Conic Circumscribed Polygons and Applications

School of Mathematics and Information Sciences, Nanchang Hangkong University

Received:2007-06-11 Online:2009-12-30 Published:2023-06-16
About author:YU De-sheng(1959-), male, native of Gaoan, Jiangxi, a professor of Nanchang Hangkong University, M.S.D., engages in geometry, computer aided geometric design.
Supported by:
Supported by Natural Science Foundation of China(60675022)；

Abstract

Abstract: Using polar equations for conic sections, we research conic circumscribed n-sided polygons(n≥4) deeply on the basis of papers. We obtain a general fixed value theorem for directed areas of some triangles in conic circumscribed n-sided polygons and derive as many as n(n-3) concurrent points of three lines and some other collinear, equiareal results in conic circumscribed n-sided polygons(n≥4). So the results of papers are unified.

Key words: conic circumscribed polygon, (directed) area, fixed value, concurrent, collinear

CLC Number:

O182.1

YU De-sheng. On a Fixed Value Theorem for Directed Areas in Conic Circumscribed Polygons and Applications[J]. Chinese Quarterly Journal of Mathematics, 2009, 24(4): 485-490.

[1]	LI Ke- dian. The Completeness of Cone Metric Spaces [J]. Chinese Quarterly Journal of Mathematics, 2013, 28(4): 565-572.
[2]	LI Wei-ping, GE Wen-xu, WANG Tian-ze. The Integer Parts of a Nonlinear Form with Integer Variables and Mixed Powers 2 and 4 [J]. Chinese Quarterly Journal of Mathematics, 2013, 28(3): 317-322.
[3]	SHANG Yu, WANG Li-min. On Some Subsemigroups of the 4-cyclic Semigroup-II [J]. Chinese Quarterly Journal of Mathematics, 2013, 28(3): 390-396.
[4]	YANG Ji-hua, LIU Mei. Stability and Bifurcation Analysis of Man-machine System with Time Delay [J]. Chinese Quarterly Journal of Mathematics, 2012, 27(2): 196-203.
[5]	YE Xu-guo, DU Xue-qiao. The Integration of Dual-domain Method for Estimating the Drift Function of Financial Assets [J]. Chinese Quarterly Journal of Mathematics, 2011, 26(2): 190-195.
[6]	LI Shou-wei, ZHU Dong-jin. The Moments of First Entrance Time Distributions of Markov Chains in Random Environments [J]. Chinese Quarterly Journal of Mathematics, 2011, 26(1): 51-55.
[7]	LIU Yu-ji. Picard Boundary Value Problems of Second Order p-Laplacian Diﬀerential Equations [J]. Chinese Quarterly Journal of Mathematics, 2011, 26(1): 77-84.
[8]	WANG Yong, ZHANG Liang-yun, CAI Zhi-min. The Structure Theorem for Module Coalgebras [J]. Chinese Quarterly Journal of Mathematics, 2011, 26(1): 85-92.
[9]	PENG Ting-ting, GUO Xiao-jiang. Factorisable Quasi-adequate Semigroups [J]. Chinese Quarterly Journal of Mathematics, 2011, 26(1): 93-99.
[10]	WU Ming-zhong. The Solvable Lie Algebras with Filiform Rn Nilradicals [J]. Chinese Quarterly Journal of Mathematics, 2011, 26(1): 100-107.
[11]	TAN Cheng-liang, WU Qun-ying, HE Yan-mei. Inequalities of Maximum of Partial Sums and Convergence Rates in the Strong Laws for ρ^--mixing Random Variables [J]. Chinese Quarterly Journal of Mathematics, 2011, 26(1): 114-119.
[12]	WANG Jin-feng, LIU Yang, LI Hong. Error Estimates of H¹-Galerkin Mixed Methods for the Viscoelasticity Wave Equation [J]. Chinese Quarterly Journal of Mathematics, 2011, 26(1): 131-137.
[13]	LIANG Ju-hua, REN Li-shun, ZHAO Zhi-liang. Existence of Solutions for a Multi-point Boundary Value Problems with Three Dimension Kernal at Resonance [J]. Chinese Quarterly Journal of Mathematics, 2011, 26(1): 138-143.
[14]	ZHOU Hong-xian, ZHANG Yan. The Number and Distributions of Limit Cycles of a Cubic Hamiltonian System with Z₂-symmetry Perturbation [J]. Chinese Quarterly Journal of Mathematics, 2011, 26(1): 144-151.
[15]	WANG Zhong-zhi. On Strong Law of Large Numbers for Random Sequence [J]. Chinese Quarterly Journal of Mathematics, 2010, 25(4): 475-480.

On a Fixed Value Theorem for Directed Areas in Conic Circumscribed Polygons and Applications

PDF (PC)

Knowledge

Abstract

Cite this article

share this article

References

Related Articles 15

Recommended Articles

Metrics

Comments