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Posted by Tut-an-Geek (Member # 1234) on June 07, 2004, 12:19:
 
OK. We have this word problem that's really bugging me. I scanned in the text book:
 -
 -

I can tell that the common ratio is .5, but how do I figure out what the two sequences are and how high it will be?

Thanks [Smile]
 
Posted by Tut-an-Geek (Member # 1234) on June 07, 2004, 13:16:
 
Hmmm... A little PHP helped [Wink] http://stonewallcs.com/~jon/geoma.php?years=10&precision=10 :-D
 
Posted by quantumfluff (Member # 450) on June 07, 2004, 13:46:
 
The series are
2 + 1/2 + 1/8 + 1/ 32
and
sqrt(1/2) + sqrt(1/8) + sqrt(1/32) ...
My terminology may be rusty, but it looks like the common ratio to each is 1/4

The height will appoarch the sum of the limits of the two series. (8/3 and sqrt(2) - I think)
The width is 2(height - 2)
Length of each brand aproaches 0
Sum of lengths of branches is a constant 2
 
Posted by The Famous Druid (Member # 1769) on June 07, 2004, 14:59:
 
Sorry QF, you got that last one wrong.

Each term in the series adds 2 to the total length of the branches (i.e. 2 metres of branch grow each year), so the total legth is 2n, and the total length approaches infinity as n approaches infinity.
 
Posted by GMx (Member # 1523) on June 07, 2004, 15:08:
 
You could always use my answer to all word problems: "Who cares?" [Wink]
 
Posted by quantumfluff (Member # 450) on June 07, 2004, 19:07:
 
quote:
Originally posted by The Famous Druid:
Sorry QF, you got that last one wrong.
Each term in the series adds 2 to the total length of the branches

Duh! I didn't read the question right. At each year the length of the sum of the *new* branches is 2. I decided they meant that rather than the total.

Did my series sums turn out right? It's been a while (like 25 years) since I've done this stuff.
 
Posted by Tut-an-Geek (Member # 1234) on June 07, 2004, 19:08:
 
quote:
Originally posted by The Famous Druid:
Sorry QF, you got that last one wrong.

Each term in the series adds 2 to the total length of the branches (i.e. 2 metres of branch grow each year), so the total legth is 2n, and the total length approaches infinity as n approaches infinity.

But width and height have limits. (height's being width's + 2). For no particular reason I just calculated what the width would be in the 2000th year with 1000 point precision. [Wink]

1.60947570824873003253445914947313205237978125025129871545111982532715498564140469 25669249182184277151566758974872748646832832240372338248084294143313999572209421 48443951670395170533300334101854707047646739706647737313516356397908009819011612 42725946573970155282032287247621430055984173575199683427199312483559769755453921 97604137435055682633698305001918399744865570501468916879046742362497356056658981 06924599980466003210020362685193544302831882045661957945747720385642074397779142 00867707904599149149019233950990749966514361455561361904573734312164805142905699 16103771379785102480150990298010572534413756866407319585986197540312435956480567 33526426272083051487158789106046461913397924523366242233196543176756241573249801 35919827309022715998597353943267799970635153271158411441070683240540717963606509 24556191646167779732394572311118832150952303150153600009867423779764487841552091 01737799496047762349 meters :-D
 
Posted by quantumfluff (Member # 450) on June 07, 2004, 19:14:
 
But the question asked the total length of all the branches. The width and hieght do approach a limit, but the *path* length does not. I think that's what makes this a fractal curve.
 
Posted by The Famous Druid (Member # 1769) on June 07, 2004, 19:14:
 
Which is suspiciously close to ln(5)
 
Posted by Callipygous (Member # 2071) on June 08, 2004, 04:40:
 
quote:
Originally posted by GMx:
You could always use my answer to all word problems: "Who cares?" [Wink]

There is a parallel universe inhabited by these maths geeks where I am given to understand that these trees grow in profusion. So this problem is very important to the maths geek forestry team there and the man who supplies ladders to them.

The rest of us need not be over alarmed by this knotty problem.
 
Posted by The Famous Druid (Member # 1769) on June 08, 2004, 14:38:
 
*sigh*
It obviously doesn't pay to be too subtle in ones puns. Lets try again....

Tut-an-Geeks answer above is suspiciously close to the natural log of 5

Get it?
Tree ... log ... ?
Looks like /me won't be giving up the day-job any time soon.
 
Posted by Cap'n Vic (Member # 1477) on June 08, 2004, 15:17:
 
You could always branch out into another area!

Tree...log...branch
 
Posted by GMx (Member # 1523) on June 08, 2004, 15:23:
 
He obviously needs to get to the root of the problem. [Big Grin]
 
Posted by Cap'n Vic (Member # 1477) on June 08, 2004, 16:20:
 
It could be genetic. The apple doesn't fall far from the tree.....
 
Posted by The Famous Druid (Member # 1769) on June 08, 2004, 16:43:
 
Awww, leaf me alone will you !
 
Posted by dragonman97 (Member # 780) on June 08, 2004, 16:43:
 
Which apple - the one that caused original sin?
 
Posted by Ivan (Member # 2622) on June 08, 2004, 19:44:
 
Watch it DMan, you're barking up the wrong tree by raising that topic =P
 
Posted by dragonman97 (Member # 780) on June 08, 2004, 20:16:
 
Ivan: Hmm? I'm confused, 'cos I was just making a frivolous post.

*sigh* I dream of using vi as my text box editor :-/.
 
Posted by The Famous Druid (Member # 1769) on June 08, 2004, 20:23:
 
quote:
Originally posted by dragonman97:
Ivan: Hmm? I'm confused, 'cos I was just making a frivolous post.

*sigh* I dream of using vi as my text box editor :-/.

I'm going to go out on a limb here and guess that his attack on you was just an excuse to make a pun.
 


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