Solve Fibonacci Sequence Triangle Problem: Find Shortest Length

[aisha]

It says you have 12 sticks of different whole number lengths in a bag. What must their lengths be if, when u pull out any 3 of them, you cannot make a triangle? What is the shortest legnth of the longest stick?

This is known as a fibonacci sequence. What am I supposed to do in this question was I just supposed to read it and know this is fibonacci? I don't understand.

 

[Hurkyl]

It often helps to start with a simpler problem.


Suppose you have three sticks with distinct integer lengths that cannot form a triangle. What can you tell me about them? What's the smallest example you can find? (Where the "size" of an example is the longest length)

What about four sticks, where no three form a triangle?

 

[Curious3141]

It says you have 12 sticks of different whole number lengths in a bag. What must their lengths be if, when u pull out any 3 of them, you cannot make a triangle? What is the shortest legnth of the longest stick?

This is known as a fibonacci sequence. What am I supposed to do in this question was I just supposed to read it and know this is fibonacci? I don't understand.

I love this problem, because, to be honest, I've never thought of the Fibonacci that way.

Here's a hint : Let's say you're considering a set of three distinct positive integers that are always arranged in increasing order, and these are actually lengths of line segments. Put the shorter two lengths together, and try varying the angle between them to "fit" the third line segment into form a triangle. Try taking longer and longer lengths of the third (longest) segment, while keeping the shorter segments constant in length. There will come a point when no matter how you vary the angle between the shorter line segments, you won't be able to fit the third segment into form a closed triangle. Can you figure out at what point this comes ?

To see the relationship to Fibonacci, think of the rule that determines the next number in that sequence.

 

[dextercioby]

Yes,i'll have to agree.Intelligent way of perceiving Fibonacci's series...

Daniel.

 

[aisha]

I still have no idea lol

 

[dextercioby]

I still have no idea lol

If i told you (as a hint) that the first 2 were 1 & 1,could you build the next 10??

Daniel.

 

[polyb]

That is a neat way to think of the fibonacci sequence.

aisha, do you know what the fibonacci sequence is?

 

[Curious3141]

If i told you (as a hint) that the first 2 were 1 & 1,could you build the next 10??

Daniel.

Of course, properly, you'd have to start with 1,2... because the stipulation was that the lengths all had to be distinct.

 

[dextercioby]

Yes,of course,you're right.That detail evaded me.Anyways,though it applies only to the first 2,it decides the next 10 (by shifting every term with one unit)...

Daniel.

 

[aisha]

That is a neat way to think of the fibonacci sequence.

aisha, do you know what the fibonacci sequence is?

nope lol sorry I don't know what it is maybe that's y I am not getting this

 

[Curious3141]

nope lol sorry I don't know what it is maybe that's y I am not getting this

OK, the Fibonacci is a famous series that starts out like this :

1,1,2,3,5,8,13,...

Can you see the pattern here, and how it pertains to this question ?

 

[The Bob]

OK, the Fibonacci is a famous series

Clearly not that famous.

Anyway, you must be able to give us the smallest length that one stick can be. It has to be an integar and you have to be able to see it (BIG HINT: It can't, therefore, be 0 as that will have no length and so no width and so you can't see it and can't use it).

The Bob (2004 ©)

 

[polyb]

nope lol sorry I don't know what it is maybe that's y I am not getting this

That's what I thought! Dont worry about the others here, they are doing their best to not do your homework for you. So just ignore the cryptic allusions they make.

First off, the Fibonacci numbers are really easy. It goes like this: Starting at 1, add the previous number to get your next number, which in this case will be 1. So now you have 2. Repeat this again, so now you have 2 and you add 1 which yeilds 3. And again, 3+2=5, and again 5+3=8, so on 8+5=13, so on 13+8=21, and so on...

Hence the sequence is: 1,1,2,3,5,8,13,21,34,...

It is pretty easy but has some interesting implications. When you get the chance you may want to look into it's relation to the golden ratio. Here is a link to the mathworld write-up, though it may be a bit much for you at the moment:
http://mathworld.wolfram.com/FibonacciNumber.html

Hope that helps you see what the problem is asking! Good luck!

 

[The Bob]

That's what I thought! Dont worry about the others here, they are doing their best to not do your homework for you. So just ignore the cryptic allusions they make.

Curious3141 was one person that told aisha the sequence. Aisha has had problems with sequences before, IIRC, and we helped there. This sequence is a lot easier to understand and so, well I thought, that it didn't need explaining.

I apologise for the misunderstanding.

The Bob (2004 ©)