Why are these different??????

[margotb822]

Buying a dog run. It has a linear footage of 40 feet. It can be set up as 10'x10' for 100 sq ft or 15'x5' for 75 sq ft.

How can something with the same linear footage have different square footage??? This is not making sense to me...

[Rabrrrrrr]

1. Ummmm........

well..........

because linear footage and square footage are not directly proportional.

It's the beauty of math - the greatest area for a specific perimeter is a circle. The farther one gets from being a circle, the smaller the square footage.

So your 10'x10' square, which is closer to a circle than your 15'x5' rectangle, has a higher square footage, and that has a higher square footage than a rectangle of 19'x1', which only has 19 square feet.

If you want to maximize, set your 40 linear feet up as a circle, which will have an area of 127 square feet.

[margotb822]

2. This has something to do with calculus, doesn't it?

I knew I should have paid more attention! It just seems to me that it would be the same size, since I'd be working with the same amount of material...

[Rabrrrrrr]

5. Yes. Think of it at its extreme -

I gave the 19'x1' example, but imagine stretching it out even further - to a 40' long rectangle with zero width. That is, that you just take the 40 feet of fencing and stretch it out in a line.

Zero square footage on that one.

So then, it only makes sense that that maximum square footage would be the other extreme - one in which the length and the width are equal; or, even taken to a higher extreme, in which there is no width or length, just radius.

This is the reason that raindrops are spherical (or close to; gravity, alas, misshapes them slightly), because a sphere (like a circle) gives the most compact form for a given mass/volume.

[margotb822]

7. Thanks!

That actually helped a lot :)

[DS1]

4. happy Pi day, ya Chartreuse-sippin false Lord God

[flvegan]

6. BAHAHAHAHAAAAAAAAHA!!!!

Fucking Lounge post of the eon!

[qnr]

3. um, I think I could probably spell 'mathematics' but that's about it, sorry n/t

[otherlander]

8. It's like squeezing a tube of toothpaste.