# Geometry: Dividing up a pic

1. Aug 15, 2015

### DaveC426913

I've got this project that I'm having trouble pinning down.

I'm cutting a pic up into squares to make a sort of jigsaw puzzle. I want the pieces to be a pleasing shape and the number of pieces to be within a small range.
- proportions of pic: 3:2 (so, say 6000 wide by 4000 high) this is slightly variable by a small amount, say < 5%, if that makes the numbers work
- total number of pieces: between 80 and 96
- proportions of pieces: between 1:1 and 2:3 (so, say 600 wide and 800 tall)
Not that the pic is horizontal but the pieces are vertical.

If I used the example dimensions, I get 6000/600 by 4000/800 = 50 pieces, which is too few.

Not sure how to do this except by brute force.

2. Aug 15, 2015

### Staff: Mentor

You could select a piece count of 96 because its divisible by 6 ie 2x3 and then find its prime factors.

From there solve 2x* 3y=96 where x is rows and y is columns or vice versa.

3. Aug 16, 2015

### DaveC426913

Not sure I follow.
If y=8 then x would have to be 12.
So, each piece would be 24x36?

4. Aug 16, 2015

### DaveC426913

I guess, now that I've clearly defined my required parameters,
- number = 80 to 96,
- proportions between 1:1 and 1.5:1 (vertical),
there's only a very few valid combinations.
6x14..84..667x429..1.55:1
7x12
..84..571x500..1.14:1
7x13..91..571x462..1.24:1
8x12
..96..500x500.....1:1

Last edited: Aug 16, 2015
5. Aug 16, 2015

### Staff: Mentor

The idea was to take your 4000 x 6000 image and to say its ratio is 2 by 3 and you want to tile it with say 96 tiles

so it has a tile area of 96 with one side being 2x units and the other side being 3y units hence the 2x * 3y = 96

which then leads to x * y = 16 and from there the squarest choice is x = y = 4

this then give 2x = 8 tile units by 3y = 12 tile units

which means you slice your image up into 8 rows by 12 columns and you'll have 96 pieces to play with.

6. Aug 16, 2015

### DaveC426913

Thanks. Although I think that's approaching it from the other end, now that I try it.

The number of pieces is flexible, between 80 and 96.
If I wanted a pleasing shape for the pieces, the 7x13 gives me a 1.4:1 . That's 91 pieces.
I'd have to do 13x*7y=91, which simply gives me the unit 1.

Hm. I've done something wrong there. I've misused the formula.

Though I'm pleased with the answer. 91 pieces in a 5:4 proportion.

7. Aug 16, 2015

### Staff: Mentor

Doesn't the number of pieces have to have at least two factors? I could see 90 but not 91.

8. Aug 16, 2015

### DaveC426913

Yes. 7 and 13.

So, I throw away the border, with no useful information for assembly.
Still, a lotta squares with just black in em...
And ther "nothin-but-curtain" squares above the rather diminutive bride.

It seems Curry's Art Store sells sheets of 3/16" foam core in 48"x96" sheets for \$16 (frankly sounds too good to be true).

I could make this thing 8'x5'4" with each piece being 7.4"x9.1" (so that's ... 63dpi).

The next tricky part is going to be sizing and printing each image piece out so that it registers with the next one.

Last edited: Aug 16, 2015
9. Aug 16, 2015

### MrAnchovy

10. Aug 16, 2015

### DaveC426913

11. Aug 17, 2015

### MrAnchovy

Oh 8 feet wide, I see what you mean!

12. Aug 17, 2015

### DaveC426913

There's a Spinal Tap joke in here somewhere.