All Questions
62 questions
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On largest convex m-gons contained in a given convex n-gon where m < n
This post is the inside-out variant of On smallest convex m-gons that contain a given n-gon where m<n
Given a convex n-gon region P, and an m less than n, how to find the max area convex m-gon Q ...
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To maximize the volume of the polyhedron resulting from perimeter-halvings of a convex polygonal region
We add one more bit to Forming paper bags that can 'trap' 3D regions of max surface area (note: some possibly open related questions are also in the comments following the answer to above ...
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To optimally wrap convex laminae with paper
Ref: On folding a polygonal sheet, Multi-layered wrapping of polyhedra
Basic intent: to wrap a given convex planar lamina with a convex sheet of non-stretchable paper (such that every point on both ...
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Smallest trapeziums containing a given convex n-gon
Question: Given a planar convex $n$-gon $C$, to find the smallest area / smallest perimeter trapezium (trapezoid) - a convex quadrilateral with at least one pair of mutually parallel edges - that ...
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Construction of an integral point set given the set of distances, its minimal description to get a measure of its complexity and its unique identifier
Given a set of distances between every pair of points of an integral point set $P$ of $n$ points; say $D = \{{d_i}\}$.
Q1. What is the least time complexity
possible/known for recreating the
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A claim on the largest area circular segment that can be drawn inside a planar convex region
This post adds a little to To find the longest circular arc that can lie inside a given convex polygon
A circular segment is formed by a chord of a circle and the line segment connecting its endpoints....
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A center of convex planar regions based on chords
This is based on Chapter 6 of 'Convex figures' by Yaglom and Boltyanskii. This post also continues On two centers of convex regions.
A point $P$ in the interior of a planar convex region $C$ divides ...
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Multi-layered wrapping of polyhedra
This post continues from How big a box can you wrap with a given polygon? and Convex polyhedra that can be folded from convex polygons. One can also mention 'k-fold coverings of the plane' as examined ...
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Deployment and dispersion in triangular regions
Definitions (from C. Stanley Ogilvy's 'Tomorrow's Math'):
Deployment: To place a specified number $n$ of points (stations) in a region such that the maximum distance of any point in the region from ...
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Covering the annulus of symmetric convex body
Consider a symmetric convex body $A$ in $\mathbb{R}^d$. Now, we draw another object, $A'$, concentric and translated with respect to $A$ and having radius slightly greater than twice to the radius of ...
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Comparing partitions of a given planar convex region into pieces with equal diameter and pieces of equal width
We continue from Cutting convex regions into equal diameter and equal least width pieces. There we had asked for algorithms to partition a planar convex polygon into (1) $n$ convex pieces of equal ...
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On smallest convex m-gons that contain a given n-gon where m<n
Given a convex n-gon region P, and an m less than n, will the least area convex m-gon Q that contains P be such that an edge of Q coincides with an edge of P (in other words Q cannot be such that P ...
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