ON THE AREA OF A POLYGON INSCRIBED IN A CIRCLE

被引：0

作者：

Matsumoto, Y. ^{[1
]}

Matsutani, Y. ^{[2
]}

Oda, M. ^{[3
]}

Sakai, T. ^{[4
]}

Shibuya, T. ^{[5
]}

机构：

[1] Gakushuin Univ, Fac Sci, Dept Matemat, Toshima Ku, 1-5-1 Mejiro, Tokyo, 1718588, Japan

[2] 3-21-1 Minamimachi, Kokubunji, Tokyo 1850021, Japan

[3] Tsuda Coll, Kodaira, Tokyo 1878577, Japan

[4] Nihon Univ, Coll Humanities & Sci, Dept Math, Setagaya Ku, Tokyo, 1560045, Japan

[5] 2-19-22-301 Nishiwaseda, Tokyo, 1690051, Japan

来源：

ENSEIGNEMENT MATHEMATIQUE | 2007年 / 53卷 / 1-2期

关键词：

D O I：

暂无

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We prove that if n >= 5, the area of the general cyclic n-gon cannot be calculated from its side lengths, using only arithmetic operations and k-th roots. To prove this, we apply Galois theory.

引用

页码：127 / 153

页数：27

共 50 条

[1] Maximizing the area of an axially symmetric polygon inscribed in a simple polygon
Barequet, Gill
Rogol, Vadim
[J]. COMPUTERS & GRAPHICS-UK, 2007, 31 (01): : 127 - 136
[2] Maximum area of inscribed polygon with constant perimeter
Shu, Yangchun
[J]. Wuhan Gangtie Xueyuan Xuebao/Journal of Wuhan Iron and Steel University, 2000, 23 (01): : 105 - 107
[3] PLANE-CURVES WITH A MOBILE CLOSED POLYGON INSCRIBED IN A CIRCLE
WUNDERLICH, W
[J]. ARCHIV DER MATHEMATIK, 1982, 38 (01) : 18 - 25
[4] With Random Parametric Equation of Circle Inscribed Polygon Generation Algorithm and Analysis
Sun, Yanhai
Song, Laizhong
Shen, Tao
[J]. APPLIED MECHANICS AND MATERIALS I, PTS 1-3, 2013, 275-277 : 2506 - 2510
[5] Triangles inscribed in a circle
Zhou, L
[J]. AMERICAN MATHEMATICAL MONTHLY, 2005, 112 (04): : 369 - 370
[6] Hexagon Inscribed in Circle
Geupel, Oliver
[J]. AMERICAN MATHEMATICAL MONTHLY, 2011, 118 (06): : 559 - 559
[7] INSCRIBED REGULAR POLYGON OF 13 SIDES
GOLDBERG, M
[J]. AMERICAN MATHEMATICAL MONTHLY, 1967, 74 (06): : 720 - &
[8] On the Average Perimeter of the Inscribed Random Polygon
Ya.Yu. Nikitin
T. A. Polevaya
[J]. Vestnik St. Petersburg University, Mathematics, 2020, 53 : 58 - 63
[9] On the Average Perimeter of the Inscribed Random Polygon
Nikitin, Ya. Yu.
Polevaya, T. A.
[J]. VESTNIK ST PETERSBURG UNIVERSITY-MATHEMATICS, 2020, 53 (01) : 58 - 63
[10] AREAS OF POLYGONS INSCRIBED IN A CIRCLE
ROBBINS, DP
[J]. DISCRETE & COMPUTATIONAL GEOMETRY, 1994, 12 (02) : 223 - 236

← 1 2 3 4 5 →