Question

For this christmas i m gonna make a christmas tree. I want to know the length of the wire needed to wrap around it. Christmas tree can be considered as a cone of heigt H and radius R. The gap between wire should be h in vertical direction.

Answer 1

https://drive.google.com/file/d/0B1unM4Vrjy8OZWNuU2pDTlFLVTg/view?usp=drivesdk

Answer 2

⬆⬆sketch🌲🌲

Answer 3

I think this has to do with transformations of a sine/cosine function. Unfortunately, I'm supposed to learn that next semester .-.

Answer 4

My brother says that we can get a approximation like \[\frac {H}{h}\times 2 \pi R\]

Answer 5

mmm,, that would be a good approximation if the tree was a cylinder. I'm gonna keep looking into polar equations.

Answer 6

But I dont know how it works

Answer 7

Yeah, me neither xD, but I think I got somewhere. Check this out:

https://www.desmos.com/calculator

I'm sure you're familiar with this graphing site. In the equation box on the left, type in:

r = -1.1^theta

Answer 8

Would it correct if we get the half of my brother's approximation?

Answer 9

It would be okay, but not necessarily exact. We have to use integrals for this.

Tag a calculus person, they should know this.

Answer 10

http://m.wolframalpha.com/input/?i=arc+length+of+%28x%2Cy%2Cz%29%3D%28%281-t%2F48%2Fpi%29*6*cost%2C%281-t%2F48%2Fpi%29*6*sint%2Ct%2F4%2Fpi%29+from+0+to+48pi&x=0&y=0

Answer 11

I did this for H=12 R=3 and h=.5

Answer 12

Approximation givea almost the same answer

Answer 13

WOah....okay that's beyond the scope of what I know. This question actually makes me wonder really.

Like if i were to think about it logically:


I'm trying to think of what a third rotation wuold be like but aaah, my brain.