Geometry (Possibly Algebra) Question

Dr Rotwang! · March 22, 2007, 09:59:33 AM

Sort of off-topic, since it's actually for a mapping project.

What's a good way to find the dimensions of an area besides getting its square root?

Like, say you have an area that measures 20 km². Square root of 20 is 4.47 (and a bunch more decimals), so an area 4.47km x 4.47km will give you a perfect square of that size. If you wanted a different shape, you can just take some other factors like the obvious ones (4x5, 2x10)to get rectangles...but one's too square and one's too skinny for, say, the city I'm mapping*.

So how do I get other factors that result in 20? Or any other number, for that matter?

I don't need an exacting map, but I'd like to know the math procedures. Call it...education.

*It's actually about 5.5 sq. mi., but 20 is a rounder number for example time.

James J Skach · March 22, 2007, 10:09:14 AM

If I'm not mistaken - and it's been 20 years since Marquette tried to teach me these things - you might actually be looking for calculus - particularly if you want irregular shapes. Polygons/straight edges, not so much. But once you get into curves you have to start dealing with the "Sum of the blah blah as the limit approaches blah blah." It's hard to remember cause it all seems a distant dream now.

Of course, take it all with a huge grain of sodium chloride.

I'd love to see the responses as well as it seems there enough geeks around here to know this stuff - "simplified."

Dr Rotwang! · March 22, 2007, 10:12:30 AM

Quote from: James J SkachIf I'm not mistaken - and it's been 20 years since Marquette tried to teach me these things - you might actually be looking for calculus - particularly if you want irregular shapes. Polygons/straight edges, not so much. But once you get into curves you have to start dealing with the "Sum of the blah blah as the limit approaches blah blah."

YIKES! Well, no, not THAT exacting -- just a regular rectangle will do. I'll fudge the rest.

It's just a Lankhmar rip-off!

James J Skach · March 22, 2007, 10:41:29 AM

If it's always going to be a rectangle? Do you always want to deal in integers?

Dr Rotwang! · March 22, 2007, 10:46:32 AM

Quote from: James J SkachIf it's always going to be a rectangle? Do you always want to deal in integers?

Yeah...I'm looking for rough approximations. Really it's just to decide what my map scale is going to be, and more-or-less how much space the city takes up.

Tom B · March 22, 2007, 11:23:30 AM

Factor it. If you have an area of 60, say, that gives you:

2, 3, 4, 5, 6, 10, 12, 15, 20, 30

Match them up for different sizes:
2x30, 3x20, 4x15, 5x12, 6x10

If you need something more specific, pick something close and modify it. If above, 6x10 is too narrow, then do 60/8=7.5 for dimensions of 8x7.5.

Tom

Dr Rotwang! · March 22, 2007, 11:51:03 AM

...

...

...good lord, I am stupid.

Thanks!

PS: Factoring odd numbers = hard for Rotwang!, though.

arminius · March 22, 2007, 12:29:34 PM

Chances are there's a web site that'll do factoring for you...as long as the numbers aren't astronomically huge.

Incidentally, multiples of 60 factor nicely, basically because the 2-3-4-5-6 factors can be combined in lots of ways. I.e., if you compare 100, the only ways it can be broken into two factors are:

1x100
2x50
4x25
5x20
10x10

But 60 can be factored as
1x60
2x30
3x20
4x15
5x12
6x10

i.e., more ways even though it's a smaller number. 120 gives you even more ways, for just being a little bigger than 100.

Dr Rotwang! · March 22, 2007, 01:07:18 PM

I settled on 6 x 9 = 54, because my city is about 5.4 sq. mi.

Only .6 x .9 = .54, and now I'm hella confused.

flyingmice · March 22, 2007, 01:24:54 PM

Quote from: Dr Rotwang!I settled on 6 x 9 = 54, because my city is about 5.4 sq. mi.

Only .6 x .9 = .54, and now I'm hella confused.

Try 2 X 3 = 6 mi. I'd scale it up by 3 to get 6 X 9 - i.e. 3 inches = 1 mile.

-clash

Tom B · March 22, 2007, 02:06:38 PM

Quote from: Dr Rotwang!I settled on 6 x 9 = 54, because my city is about 5.4 sq. mi.

Only .6 x .9 = .54, and now I'm hella confused.

Watch your decimal places. for 5.4 square miles, you would need either:

.9 x 6 = 5.4 or .6 x 9 = 5.4

For something more square, you might try 2 x 2.7 = 5.4

Dr Rotwang! · March 22, 2007, 02:51:05 PM

I was thinking 6 tenths of a mile times 9 tenths of a mile.

This is my math brain:

TonyLB · March 22, 2007, 04:04:01 PM

If you're planning to work back down to (at most) one decimal point then you want to be factoring 550, rather than anything near 55. That way, when you divide the length by 10 and the width by 10 your 550 area turns into 5.5.

So, for instance, 550 = 25 x 22. That means 5.5 = 2.5 x 2.2

Dr Rotwang! · March 22, 2007, 04:16:36 PM

Aha. I see. Thanks!

Again, please refer to the graphic provided above.