# Cutting up squares

1. Dec 19, 2011

### 6.28318531

I don't really know if this is in the right place, or what the problem is called, if its in the wrong place I'm sorry. Anyway my question is apart from intuition is there any method to solve a problem like say we have an object like a square, and we are given for instance rectangles, that in one dimension are larger than the square, but their total area is less, how do we cut up the square to fit the the most number of rectangles, in the least number of cuts? Can it be extended to higher dimensions?

2. Dec 24, 2011

### abiyo

i)the number of rectangles
ii) is any cut allowed? Can I cut a triangle out of the square and fill it in the rectangle? Is there
a restriction on the shape or size of the cut area?
The more rectangles you need to fill, the more cuts you need to do but at the same time
number of cuts have to be minimized so what you want is a middle ground in between
Anyways from top of my head sphere packing or things
along that line sound similar to me but in all honesty I might have to think
more and see where the problem leads

3. Dec 24, 2011

### checkitagain

**) For a given square, are all of the rectangles congruent to each other?

4. Dec 27, 2011

### 6.28318531

Sorry been busy for the last few days.
Maybe just let it be that you can only make up rectangles from rectangles, so you are restricted in the cuts you can make.I think the number of rectangles would be specified. Yeah its sort of like the sphere problem, but different.

and @checkitagain not necessarily.

5. Dec 27, 2011

### checkitagain

Because the total area of the rectangles is less than the square,
shouldn't we be able to "fill up" $all \$ of the rectangles using a
finite number of cuts of the square?

6. Dec 28, 2011

### 6.28318531

Yeah you should always be able to do that, I suppose I was asking what is the least number of cuts required, and what is the most efficient use of the square's area. I was also curious if there is a way to work it out rather than using intuition.