# Tagged Questions

Questions on the packing of various (two- or three-dimensional) geometric objects.

12 views

### Disjoint Hamming spheres

I'm reading the From Error-Correcting Codes through Sphere Packings to Simple Groups since I'm really interesting to face this topic first as a undergad approach, then to land to the SLAG book, more ...
27 views

### Determining Locations of Circles to Optimally Cover a Polygon

I want to completely cover a region on a map(Continental US)/polygon with circles of a certain radius. Is there a way to determine the best locations and how many circles would be needed to completely ...
31 views

### Fitting Rectangles

I have a quantity of small rectangles I need to fit in a larger rectangle frame. I need an equation to figure out what is the maximum size I can make the small rectangles before they are all too big ...
51 views

### Any algorithm in literature to solve my problem? Should call it “Segment ordering”?

A slot with length $L$. I have $n$ segments, they have a positive integer length $x_1, x_2, \cdots, x_n$, respectively, and $\sum\limits_{i=1}^n x_i = L$. My goal is to fill the slot with these ...
15 views

### 2D Bin Packing with Ordering Along One Dimension

This is my second attempt at solving this particular problem (original is here: Topological sort into a limited number of bins, each with limited capacity). For clarity, I have reproduced the relevant ...
17 views

11 views

50 views

### Integral Apollonian circle packing with unique curvatures

I was wondering if it is possible to construct an Apollonian gasket where every circle has a unique integer curvature. Take for instance the following gasket, defined by curvatures (−10, 18, 23, 27): ...
102 views

49 views

### Circular biscuits in a circular pan.

This question comes from a discussion with my wife about the more efficient way for cooking biscuits. Here the problem: We have a circular pan with a diameter of $30 cm$ and we have two round stamps ...
143 views

### Method for optimally packing a group of squares from (1 x 1) to (n x n) into a larger square?

As far as my investigation has gone, I can see that people have worked on the optimal way to pack incrementally larger squares into rectangles (page 2, .pdf), as well as the optimal ways to pack equal ...
54 views

### k'th best solution or Top k solutions to the 1-0 knapsack problem via dynamic programming

How do I find the k'th best solution to the 1-0 knapsack problem via the modification of the standard dynamic programming algorithm? LP solution will also be interesting. Thanks, Vladimir
188 views

### The smallest 8 cubes to cover a regular tetrahedron

A regular tetrahedron $T$ of edge-length $\sqrt{2}$ fits inside a unit cube:                     (Image from MathWorld.) This means that $8$ ...
Given $x$ the number of circles of radius $r$, what is a good approximate size of the radius of a bigger circle which they fit in? To explain in actual problem terms. I want to move units in a ...
### Maximum no. of laddoos of diameter $6$cm in a box of given dimension
What is the maximum number of laddoos having diameter of $6\text{ cm}$ that can be packed in a box whose inner dimensions are $24\times 18\times 17\text{ cm$^3$}$. I found that at the lower label ...