Lets say there is a perimeter of a square 10 by 10
You add a 1 by 1 square inside of this perimeter. Now, you take 1/4 of the 1 by 1 square and add that within the perimeter. Then take 1/4 of that and add it within the perimeter. EVENTUALLY will the perimeter be filled up?
Mathematical Question
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Mathematical Question
by SpunkySkunk347 » Tue May 23, 2006 11:11 pm
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by Nick » Tue May 23, 2006 11:32 pm
No. Since what you're adding to the perimeter gets smaller and smaller, you will never fill it up, and the square you started with is smaller than the originaly square.
Now that I've reread my post, I think it might be possible to fill up the square... see what others think...
Now that I've reread my post, I think it might be possible to fill up the square... see what others think...
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by moonlord » Wed May 24, 2006 6:10 pm
S = Sum[i=0; i<inf; i++] {1/4^i} < Sum[i=0; i<inf; i++] {1/2^i} = 1 < 100 = 10^2. Therefore, the square never gets filled up.
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by houserichichi » Thu May 25, 2006 2:26 am
Since we're trying to find the area filled, not just the perimeter, the sum is
(1/4)^2n
where n runs from 0 to infinity. It's 2n rather than n because the area of each successive square is (1/4)^n * (1/4)^n.
The sum then turns out to be 16/15 which is still less than 100, but I just couldn't stomach letting that detail go missed.
(1/4)^2n
where n runs from 0 to infinity. It's 2n rather than n because the area of each successive square is (1/4)^n * (1/4)^n.
The sum then turns out to be 16/15 which is still less than 100, but I just couldn't stomach letting that detail go missed.
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Re: Mathematical Question
by moonlord » Thu May 25, 2006 12:43 pm
SpunkySkunk347 wrote:you take 1/4 of the 1 by 1 square and add that within the perimeter. Then take 1/4 of that...
A new square doesn't have the side 1/4 of the side of the previous square, but 1/4 of its area.
"God does not play dice." -- Albert Einstein, early 1900's.
"Not only does God play dice, but... he sometimes throws them where we cannot see them." -- Stephen Hawking, late 1900's.
"Not only does God play dice, but... he sometimes throws them where we cannot see them." -- Stephen Hawking, late 1900's.
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by houserichichi » Fri May 26, 2006 12:58 am
Oops, definitely made a poor mistake there!
I stand corrected!
I stand corrected!
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by Nick » Fri May 26, 2006 1:49 am
Hugh wrote:houserichichi wrote:Oops, definitely made a poor mistake there!
I stand corrected!
House corrected about something in math?
I never thought I'd live to see the day...
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by houserichichi » Fri May 26, 2006 2:09 am
Oh it happens! ... but I'll take this time to blame my mistake on...a herd of rhinos that stampeded by my place and clearly disrupted my thought process.
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by moonlord » Sat May 27, 2006 1:14 pm
You guys are comic :?. house's error is purely from not being attentive for a moment...
"God does not play dice." -- Albert Einstein, early 1900's.
"Not only does God play dice, but... he sometimes throws them where we cannot see them." -- Stephen Hawking, late 1900's.
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