Questions tagged [packing-problem]
Questions on the packing of various (two- or three-dimensional) geometric objects.
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Mondrian Art Problem Upper Bound for defect
Divide a square of side $n$ into any number of non-congruent rectangles. If all the sides are integers, what is the smallest possible difference in area between the largest and smallest rectangles?
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"Perfect" solutions to the kissing number problem besides in dimensions 1,2,8, and 24.
The kissing number problem asks how many n dimensional unit spheres can fit around a central one with no overlapping; a natural question is in what dimensions can this be done so that there is no ...
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Oblongs into minimal squares
Consider $a(n)$, the minimal number of squares into which the oblong of size $(n+1)\times(n)$ can be divided. What is the behavior of $a(n)$? The first 379 terms of the oblong square packing sequence ...
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Packing problem - how to fit things nicely with just the aspect ratio of the objects
Suppose you have a rectangle that is w units wide and h units tall (bounding rectangle). You also have an even ...
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For what values of $n$ can coins of radius $\frac12,\frac13,\frac14,...,\frac1n$ be held rigidly in a circular tray of radius $1$?
For what values of $n$ can circular coins of radius $\frac12,\frac13,\frac14,...,\frac1n$ (at least one of each, and no other kind of coin) be held rigidly in a circular tray of radius $1$?
By "...
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Marjorie Senechal (2011): "The question of packing tetrahedra is still unsolved" Is it still unsolved?
At about 15:49 in her 2011 talk Prof. Marjorie Senechal - "Quasicrystals Gifts to Mathematics":
But Hilbert understood that groups aren't everything and maybe not even the main thing. And ...
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Sequential square packings
There are various studies for packing sequential squares of size $1$ to $n$. We can try to find the smallest square they will pack into, as in tightly packed squares. We can find the smallest square ...
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The number of circles that will fit inside the area of larger circle?
Let's say circle $\omega_1$ has a diameter $X$. Let $X>Y$; $Y\in \mathbf{R}^{+}$. How many circles with diameter $Y$ will fit inside $\omega_1$?
Is there a formula for this?
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Gardening problem - mass planting in a circular area
First of all I am not a mathematician, forgive me if this is a stupid question.
A circular area is given. How to place n plants within the area so that the minimal distance between any of two plants ...
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Perfect Mondrian Triangle Dissections
In the Mondrian Art Problem, a square is divided into non-congruent integer-sided rectangles so that the largest area and smallest area are as close as possible.
A lattice square can be divided ...
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Stacking circles
When I tried to stack 21 circles of radii $(30, 31, 32... 50)$ on top of each other in a tube (ID of $100$ wide), I thought they would reach the same height regardless of the order, however I was ...
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Hexagonal circle packings in the plane
I have been reading the paper Spiral hexagonal circle packings in the plane (Alan F. Beardon, Tomasz Dubejko and Kenneth Stephenson, Geometriae Dedicata Volume 49, Issue 1, pp 39-70), which proves ...
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Sphere Covering Problem
Is it possible that one can cover a sphere with 19 equal spherical caps of 30 degrees(i.e. angular radius is 30 degrees)? A table of Neil Sloane suggests it is impossible, but I want to know if anyone ...
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how many smaller circles(radius is equal) I can fit within a larger circle
then the question is,the larger radius D,the small radius d,get the largest number of small circle put in the larger?
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Can ellipsoids pack better than spheres?
It is known that same-sized spheres can be packed at a density of $\pi/3\surd2$. If we uniformly stretch or compress the packed configuration as a whole, in any direction, the packing density does not ...
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