As a hint, think about how quickly the thickness of the stack is growing. There is a function which perfectly models this growth.
Fun Math Puzzle Question
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the moon is 284,400 kms away on average, right? (Cant quite remember.) So.... 0.1, 0.2, 0.4, 0.8, 1.6, 3.2, 6.4, 12.8, 25.6, 51.2, 102.4, 204.8, 409.6, 819.2, 1,638.4, 3,276.8....thats 16 do far... 6,553.6, 13,107.2, 26,214.4, 32,428.8, 64,837.6, 129,675.2, 259,350.4, 318,700.8.
So the answer to 1 is 24.
im sure there was an easier way of coing that, but who doesnt enjoy some simple multiplication?
I dont understand Q2.
Why do I feel like these are trick questions? For example, if the paper is infinitely long, one might in one sense say that they would only have to fold the paper once.
I looked up the distance and found 384,403 kilometers from:
http://askville.amazon.com/distance-earth-moon/AnswerViewer.do?requestId=2346608
I am not sure if this number is accurate or not, I dont remember where I got the Half a million km number from.
" For example, if the paper is infinitely long, one might in one sense say that they would only have to fold the paper once."
- The question is not meant to be a trick question, you are meant to think about the thickness of the stack, the assumption that the paper is infinitely long is only here let you assume that you can fold it over as many times as you like.
"the moon is 284,400 kms away on average, right? (Cant quite remember.) So.... 0.1, 0.2, 0.4, 0.8, 1.6, 3.2, 6.4, 12.8, 25.6, 51.2, 102.4, 204.8, 409.6, 819.2, 1,638.4, 3,276.8....thats 16 do far... 6,553.6, 13,107.2, 26,214.4, 32,428.8, 64,837.6, 129,675.2, 259,350.4, 318,700.8."
- thats in Millimeters, and yes, there is an easier way of doing this.... Think back to Algebra 2 or Pre-Calculus. There is a special function which models this sort of behavior.
Question 2 just means how many times would you have to fold the stack over to where its height would actually be far enough out to include the entire moon.(So if the paper could somehow pass through the moon, the stack would extend past the moon):
___ <----------------- Top of Stack
| |
|0| <---------------- Moon
| |
| |
.
.
.
| | <---------------- Stack of folded paper
|__|
------------------------------------------- <------ Surface of the Earth
(Oh, he he, you need to know what the radius of the moon is to answer part 2...)
The radius of the moon is: 1737.4 km (according to Google)
well, then i think it would be 25 folds for both questions.
D_Plew wrote:
well, then i think it would be 25 folds for both questions.
Not quite, the stack's thickness is growing exponentially. So to compute the nessasary folds, you need to undo this exponential growth- so you use a logarithm:
If n=number of folds, then use the equation:
(0.1*10^-3) * 2^n = 304,403*10^3, now solve for n.
Be careful about your units, guys.
val08 wrote:
Be careful about your units, guys.
Yeah, good call.
0.1 mm = 0.1*10^-3 m
304,403km = 304,403*10^3 m
yeah.. big mstake with my units... is * multiplication symbol?
a) The thickness of the paper on the nth fold can be described by
2^n/5
(n = 1 is the first fold, so the paper would have a thickness of 2^1/5 = 0.2 mm on the first fold.) We can just set this equal to the distance to the moon (in mm) and solve for n:
2^n/5 = 384,399*10^6 mm
(384,399 km is the value of semi-major axis of the moon's orbit given by Wikipedia)
Multiply both sides by 5 to get
2^n = 1.922*10^12
Now take the logarithm base 2 of both sides to get
n = log_2(1.922*10^12) = 40.806
Since we cannot fold the paper a fraction of a fold we round up to 41.
b) To envelope the moon, we solve the same equation with the moon's diameter added to the distance:
2^n/5 = 384399*10^6 + 1738.14*10^6
n = log_2(5(384399+1738.14)*10^6) = 40.8123 -> 41 folds.
So our final fold attempting to reach the moon envelopes the moon.
elzoido238 wrote:
The thickness of the paper on the nth fold can be described by
2^n/5
(n = 1 is the first fold, so the paper would have a thickness of 2^1/5 = 0.2 mm on the first fold.) We can just set this equal to the distance to the moon (in mm) and solve for n:
2^n/5 = 384,403*10^6 mm
Multiply both sides by 5 to get
2^n = 1.922*10^12
Now take the logarithm base 2 of both sides to get
n = log_2(1.922*10^12) = 40.806
Since we cannot fold the paper a fraction of a fold we round up to 41.
Looks good to me, I see you are a Physics Grad student, where at?
Colorado School of Mines
elzoido238 wrote:
Colorado School of Mines
Wow, good school. I think my Grandpa went there for Civil Engineering. I am actually from the Loveland/Ft. Collins area.
ColdCoffee wrote:
elzoido238 wrote:
Colorado School of Mines
Wow, good school. I think my Grandpa went there for Civil Engineering. I am actually from the Loveland/Ft. Collins area.
Cool; I see you are a mathematics grad student; Where at?
elzoido238 wrote:
ColdCoffee wrote:
elzoido238 wrote:
Colorado School of Mines
Wow, good school. I think my Grandpa went there for Civil Engineering. I am actually from the Loveland/Ft. Collins area.
Cool; I see you are a mathematics grad student; Where at?
Cal Poly, San Luis Obispo. I am a Master's student. I am hoping to transfer to UCSB (Although I plan to apply to CSU Boulder too).
I'll post more fun math questions later, here is a question I posed to my Pre-Calculus students last quarter for fun.
The average thinkness of a sheet of paper is about 0.1 mm (millimeters)
The average distance from the surface of the Earth to the Moon is about 500,000 km.
Suppose you have an infinitly long piece of paper with the thickness stated above, and that you can fold the paper over as many times as you like. The paper, if not folded, has thickness 0.1 mm. If you fold it in half, the thickness of the folded paper is twice this (0.2 mm). If you fold, the folded paper on itself, the doubly folded paper has thickness 0.4mm. Continuing on, we have 0.8, then 1.6 mm and so forth.
1) Assuming all of this is true, how many times would you have to fold this paper on itself such that if you were to lay the folded paper stack down on the ground, then it's thickness is guaranteed to reach the surface of the moon?
2) How many times would you have fold the paper stack to envelope the moon?