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Lots of 1's in this year
- Thread starter Flysure1
- Start date
AtlantaSteve
Active Member
"Flysure1" said:
You can't do that in any world I'm aware of. Now multiplication of two negatives, that's a different matter
I stand corrected, I should have said multiply two negatives-----if I owe you 20 dollars (a negative out of my wallet) and say I want to multiply it by 2--in algebra would you owe me money??"AtlantaSteve" said:You can't do that in any world I'm aware of. Now multiplication of two negatives, that's a different matter
AtlantaSteve
Active Member
If you multiplied it by -2, but that's illogical in the accounting of money. If you said "I want to double what I owe you) (in other words, x2) then you'd be handing me 40 instead of 20.
Not trying to be an annoying math prick, but I happen to be an annoying math prick.
Not trying to be an annoying math prick, but I happen to be an annoying math prick.
Gigantopithecus
Well-Known Member
Steve, your nerd is showing again......
blue65coupe
Well-Known Member
Here's one for ya Mr. Annoying Math Prick. Let's say you have 16 ft of fence and you're going to fence in an area for your dogs. Why is it that if you make a 4x4 square you have effectively given them 16 sq ft of area to move but if you give them a 6x2 rectangle you've only given them 12 sq ft of area? Why does having the exact same amount of linear perimeter result in different areas encompassed by that perimeter if the shape is altered? And if you want to give them the most area to move around in, assuming a set amount of linear feet of fence, what shape do you make their space? (I know, that one is pretty easy)
Gigantopithecus
Well-Known Member
"blue65coupe" said:
Ummm....potato?
AtlantaSteve
Active Member
"blue65coupe" said:
area and perimeter are related, but the perimeter just defines the minimum and maximum areas, but the result is a range.
I'm not going to get into the formulas (the geometric formulas are fairly easy to understand, but difficult to do all the math with...the calculus makes the math easier, but is MUCH more difficult to understand) instead I am going to try to get you to visualize the minimum.
Let's say you hate your dogs and want to give them NO room to run around..and when I say NO room, I mean that you want to give them a total enclosed area of zero square feet. How could you do that? Well you could do that by giving them not a 4x4 or a 6x2 or even a 7x1...Give them an 8x0. How could you do that?? by making two sides of the rectangle have NO FENCE. the distance between the two "sides" of the fences is exactly zero. in effect it's two fences laid up exactly side by side...now your dogs are gonna hate it...but mathematically you've proven a point. That'll teach them dogs!
Now, day by day you decide to give them a little bit more room. on day one you move the fences apart 1 inch. I don't know what the area would be...it'd be trivial to figure out but that's immaterial. You see you have granted them a little bit more area than they had (they had zero, now they have more than zero) by moving those fences a little bit a part. It stands to reason that the further you move those two sides apart from each other the more and more room they'll get, because each step takes you away from when you gave them zero.
Of course there is a limit to how far you can take those two walls apart, and that point is the exact point where you start drawing the OTHER two walls in toward each other...reversing the action you just took by moving the two walls apart.
Therefore, the rectangle that grants the most internal area is the point where all four sides are exactly equal, or, a square.
A square is the rectangular shape that will give you the most area for a fixed perimeter.
IF you don't want to do a rectangle you can get even more area by making a non-rectangular shape. For reasons I can't explain without dusting off my VERY rusty calculus, the shape that gives you the most area for a fixed perimeter is a circle.
How much more?
Well, you had a 16 foot fence, So we know our circumference is 16...and we know that C=2R*Pi
C=16, so:
16=2R*π (divide both sides by 2)
8=R*π (divide both sides by pi)
8/π=R
R=8/3.142
R=2.546
A = πR[sup]2[/sup]
A=π(2.546[sup]2[/sup]) (2.546 squaared = 6.485)
A=π*6.485
A=3.142*6.485
A=20.372
So you get 4.372 extra square feet by going with a circle instead of a square.
blue65coupe
Well-Known Member
Ding ding ding
You see, I knew you A) knew the answer or B) were gonna look it up. I also knew you were gonna explain it...see moving walls, getting into 0 sq ft and so on. I more or less needed a good chuckle tonight.
You see, I knew you A) knew the answer or B) were gonna look it up. I also knew you were gonna explain it...see moving walls, getting into 0 sq ft and so on. I more or less needed a good chuckle tonight.