Inscribed Polygons Lead to An Interesting Limit

1979 ◽  
Vol 72 (4) ◽  
pp. 294-295
Author(s):  
Kenneth Kich
Keyword(s):  
Inscribed Polygons

Recently, while working with polygons inscribed in a circle, I had an idea that led to a very interesting limit. The concept that got me started was the notion that the area of an inscribed n-sided polygon approaches the area of a circle as n approaches infinity.

84.55 Perpendiculars and Inscribed Polygons

2000 ◽  
Vol 84 (501) ◽  
pp. 502 ◽  
Author(s):  
Larry Hoehn
Keyword(s):  
Inscribed Polygons

Optimal Inscribed Polygons in Convex Curves

1989 ◽  
Vol 96 (10) ◽  
pp. 886-902 ◽  
Author(s):  
John S. Lew ◽  
Donald A. Quarles
Keyword(s):  
Convex Curves ◽  
Inscribed Polygons

Optimal Inscribed Polygons in Convex Curves

1989 ◽  
Vol 96 (10) ◽  
pp. 886 ◽  
Author(s):  
John S. Lew ◽  
Donald A. Quarles
Keyword(s):  
Convex Curves ◽  
Inscribed Polygons

On the area formulas of inscribed polygons in classical geometry

2020 ◽  
Vol 16 (3) ◽  
pp. 557-572
Author(s):  
Yohei Komori ◽  
Runa Umezawa ◽  
Takuro Yasui
Keyword(s):  
Classical Geometry ◽  
Inscribed Polygons

Certain sequences of inscribed polygons

1973 ◽  
Vol 3 (3-4) ◽  
pp. 255-260 ◽  
Author(s):  
G. Lükő
Keyword(s):  
Inscribed Polygons

scholarly journals Limit theorems for generalized perimeters of random inscribed polygons. I

2020 ◽  
Vol 65 (4) ◽  
pp. 678-687
Author(s):  
Ekaterina N. Simarova ◽  
◽  
Keyword(s):  
Stochastic Geometry ◽  
Limit Theorems ◽  
Extreme Values ◽  
Limiting Behavior ◽  
Limit Distributions ◽  
Random Polygon ◽  
Generalized Perimeter ◽  
Definition Of ◽  
Inscribed Polygons

Lao and Mayer (2008) recently developed the theory of U-max-statistics, where instead of the usual averaging the values of the kernel over subsets, the maximum of the kernel is considered. Such statistics often appear in stochastic geometry. Their limit distributions are related to distributions of extreme values. This is the first article devoted to the study of the generalized perimeter (the sum of side powers) of an inscribed random polygon, and of U-max-statistics associated with it. It describes the limiting behavior for the extreme values of the generalized perimeter. This problem has not been studied in the literature so far. One obtains some limit theorems in the case when the parameter y, arising in the definition of the generalized perimeter does not exceed 1.

Inscribed polygons and Heron polynomials

2003 ◽  
Vol 194 (3) ◽  
pp. 311-331 ◽  
Author(s):  
V V Varfolomeev
Keyword(s):  
Inscribed Polygons
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