104.22 Proof without Words: Minimum perimeter of an inscribed quadrangle to a square

2020 ◽  
Vol 104 (560) ◽  
pp. 338-339
Author(s):  
Ángel Plaza
Keyword(s):  
Minimum Perimeter

Minimum Perimeter Coverage Set Based on Points of Tangency and Strong Barrier for an Extended WSN Lifetime

2017 ◽  
Vol 97 (2) ◽  
pp. 2339-2358 ◽  
Author(s):  
Wahiba Larbi-Mezeghrane ◽  
Louiza Bouallouche-Medjkoune ◽  
Ali Larbi
Keyword(s):  
Wsn Lifetime ◽  
Minimum Perimeter ◽  
Strong Barrier ◽  
Perimeter Coverage

scholarly journals Geometric Entropies of Mixing (EOM)

2006 ◽  
Vol 13 (01) ◽  
pp. 91-101 ◽  
Author(s):  
B. H. Lavenda
Keyword(s):  
Convex Sets ◽  
Convex Bodies ◽  
Axiomatic Characterization ◽  
Hermite Functions ◽  
Maximal Entropy ◽  
Maximum Area ◽  
Entropy Reduction ◽  
Minimum Perimeter ◽  
Phase Functions ◽  
New Inequalities

Trigonometric and trigonometric-algebraic entropies are introduced and are given an axiomatic characterization. Regularity increases the entropy and the maximal entropy is shown to result when a regular n-gon is inscribed in a circle. A regular n-gon circumscribing a circle gives the largest entropy reduction, or the smallest change in entropy from the state of maximum entropy, which occurs in the asymptotic infinite n-limit. The EOM are shown to correspond to minimum perimeter and maximum area in the theory of convex bodies, and can be used in the prediction of new inequalities for convex sets. These expressions are shown to be related to the phase functions obtained from the WKB approximation for Bessel and Hermite functions.

scholarly journals Minimum Perimeter-Sum Partitions in the Plane

2019 ◽  
Vol 63 (2) ◽  
pp. 483-505
Author(s):  
Mikkel Abrahamsen ◽  
Mark de Berg ◽  
Kevin Buchin ◽  
Mehran Mehr ◽  
Ali D. Mehrabi
Keyword(s):  
Minimum Perimeter

scholarly journals Minimum perimeter rectangles that enclose congruent non-overlapping circles

2009 ◽  
Vol 309 (8) ◽  
pp. 1947-1962 ◽  
Author(s):  
Boris D. Lubachevsky ◽  
Ronald L. Graham
Keyword(s):  
Minimum Perimeter

MINIMUM POLYGON TRANSVERSALS OF LINE SEGMENTS

1995 ◽  
Vol 05 (03) ◽  
pp. 243-256 ◽  
Author(s):  
DAVID RAPPAPORT
Keyword(s):  
Convex Hull ◽  
General Problem ◽  
Line Segment ◽  
Simple Polygon ◽  
Fixed Number ◽  
Line Segments ◽  
Geometric Objects ◽  
Finite Set ◽  
Minimum Perimeter ◽  
Set Of Points

Let S be used to denote a finite set of planar geometric objects. Define a polygon transversal of S as a closed simple polygon that simultaneously intersects every object in S, and a minimum polygon transversal of S as a polygon transversal of S with minimum perimeter. If S is a set of points then the minimum polygon transversal of S is the convex hull of S. However, when the objects in S have some dimension then the minimum polygon transversal and the convex hull may no longer coincide. We consider the case where S is a set of line segments. If the line segments are constrained to lie in a fixed number of orientations we show that a minimum polygon transversal can be found in O(n log n) time. More explicitely, if m denotes the number of line segment orientations, then the complexity of the algorithm is given by O(3mn+log n). The general problem for line segments is not known to be polynomial nor is it known to be NP-hard.

scholarly journals Adding Layers to Bumped-Body Polyforms with Minimum Perimeter Preserves Minimum Perimeter

10.37236/1032 ◽  
2006 ◽  
Vol 13 (1) ◽  
Author(s):  
Winston C. Yang
Keyword(s):  
Two Dimensions ◽  
Grid Cells ◽  
Minimum Area ◽  
Hexagonal Grid ◽  
Finite Set ◽  
Minimum Perimeter ◽  
Additional Assumptions

In two dimensions, a polyform is a finite set of edge-connected cells on a square, triangular, or hexagonal grid. A layer is the set of grid cells that are vertex-adjacent to the polyform and not part of the polyform. A bumped-body polyform has two parts: a body and a bump. Adding a layer to a bumped-body polyform with minimum perimeter constructs a bumped-body polyform with min perimeter; the triangle case requires additional assumptions. A similar result holds for 3D polyominos with minimum area.

Nets of Small Solids with Minimum Perimeter Lengths

2015 ◽  
pp. 213-233
Author(s):  
Jin Akiyama ◽  
Kiyoko Matsunaga
Keyword(s):  
Minimum Perimeter
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