Maximize the number of tiles on the wall.?

Question

If you are tiling a rectangular wall with rectangular tiles,how to maximize the number of tiles on the wall.Or if cutting a large sheet to make a certain size of book,how to maximize the pages of book.

Answer 1

think square.

let's say I had 20 m of fencing and I want to MAXIMIZE my area, what should the dimensions be?

how bout...

1 x 1 x 9 x 9 the area here would be 9

how bout...

2 x 2 x 8 x 8 area = 16

3 x 3 x 7 x 7 area = 21

you can see the area getting bigger as the dimensions conform to a square...

5 x 5 x 5 x 5 area = 25

this is the maximum area I can have with 20 m of fencing. This holds true for 3-d as well, cubes, spheres...

you want to make as 'square-like' as you can!

(this was not a proof, just examples to help demonstrate)