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Blog RSS Feed by ContentBoxOrtus Solutions, Corp (www.ortussolutions.com)http://www.rssboard.org/rss-specificationFeedGeneratorSat, 02 Mar 2024 09:54:05 GMTSat, 02 Mar 2024 09:54:05 GMTWill A Piece Of Paper, Folded 42 Times, Reach The Moon?So I was at a friend's house Sunday night playing a game when this odd fact came up in conversation:
If you were to fold a piece of paper in half 42 times, it would reach the moon.
Several of those around the table scoffed at this, exclaiming that a single sheet of paper was simply too thin to have its thickness reach any substantial amount after only a few dozen folds. I pointed out it was entirely possible seeing as how doubling the thickness with each fold would lead to an exponential increase in thickness that would increase slowly at first before quickly getting larger. My friends were clearly imagining a linear increase in thickness.
I also knew that it is pretty much impossible to fold a single sheet of paper more than about 8 times -- though Myth Busters once folded a giant sheet the size of a football field 10 times. The resulting thickness (after hitting it with a bulldozer) was almost a foot tall, though there was quite a bit of air mixed in with the 1,024 sheets. The formula for finding out how many of something you'll have after doubling it N number of times is as follows where O is the original number (or size in our case).
o * 2^(n)
A standard sheet of paper is about 0.1 mm so 42 folds would give us this:
0.1 * 2^(42) =439,804,651,110 mm
That's 440 billion millimeters, or 439,804 kilometers. The moonon averageis 384,400 kilometers from Earth according to Google. I'd say this checks out.
To help visualize the data, I created a quick spreadsheet and graph that tracks the thickness of the paper for each fold.
# Folds
Thickness (mm)
0
0.10
1
0.20
2
0.40
3
0.80
4
1.60
5
3.20
6
6.40
7
12.80
8
25.60
9
51.20
10
102.40
11
204.80
12
409.60
13
819.20
14
1,638.40
15
3,276.80
16
6,553.60
17
13,107.20
18
26,214.40
19
52,428.80
20
104,857.60
21
209,715.20
22
419,430.40
23
838,860.80
24
1,677,721.6
25
3,355,443.2
26
6,710,886.4
27
13,421,773
28
26,843,546
29
53,687,091
30
107,374,182
31
214,748,365
32
429,496,730
33
858,993,459
34
1,717,986,918
35
3,435,973,837
36
6,871,947,674
37
13,743,895,347
38
27,487,790,694
39
54,975,581,389
40
109,951,162,778
41
219,902,325,555
42
439,804,651,110
And to graph that out in kilometers looks like this:
https://www.codersrevolution.com/blog/will-a-piece-of-paper-folded-42-times-reach-the-moon
Fri, 28 Mar 2014 00:35:00 GMTbrad@ortussolutions.com (Brad Wood)GeneralMathmaticshttps://www.codersrevolution.com/blog/will-a-piece-of-paper-folded-42-times-reach-the-moonGenerating Primes Revisited: My Modifications To The Sieve of EratosthenesIn a recent pissing match between ColdFusion and PHP, Jared Rypka-Hauer was demonstrating the performance of a function that generated prime numbers. The discussion really wasn't about the BEST prime generator as much as it was about how much ColdFusion can kick PHP's puny butt all over town. Never the less, I piped up in the comments to ask Jared to compare a prime number generator that I wrote a while back based on the Sieve of Eratosthene. After Jared asked some good questions about how my code worked I figured it was time I stopped high-jacking the comments of the PHP pooper train. I decided to spin off a new post to highlight some significant performance gains I was able to produce.
https://www.codersrevolution.com/blog/Generating-Primes-Revisited-My-Modifications-To-The-Sieve-of-Eratosthenes
Tue, 01 Feb 2011 11:28:00 GMTbrad@ortussolutions.com (Brad Wood)ColdFusionJavaMathmaticsPerformancehttps://www.codersrevolution.com/blog/Generating-Primes-Revisited-My-Modifications-To-The-Sieve-of-EratosthenesColdFusion UDF: Calculate A Number's DivisorsHere's another UDF I was tinkering with last week. I wanted to be able to count all of the numbers that divided evenly into a given integer. I couldn't find a ColdFusion implementation, so after getting some advice from Stack Overflow I created my own.
https://www.codersrevolution.com/blog/ColdFusion-UDF-Calculate-A-Numbers-Divisors
Sat, 15 Aug 2009 06:24:00 GMTbrad@ortussolutions.com (Brad Wood)ColdFusionMathmaticsPerformancehttps://www.codersrevolution.com/blog/ColdFusion-UDF-Calculate-A-Numbers-DivisorsCalculate Prime Numbers: Sieve of EratosthenesAhh... the quintessential math problem-- finding prime numbers. Last week while tinkering with a math challenge I needed to find all of the primes up to a given number. There was a version on cflib.org, but I thought I could do it in less code, so I dug in myself.
https://www.codersrevolution.com/blog/Calculate-Prime-Numbers-Sieve-of-Eratosthenes
Fri, 14 Aug 2009 06:34:00 GMTbrad@ortussolutions.com (Brad Wood)ColdFusionMathmaticsPerformancehttps://www.codersrevolution.com/blog/Calculate-Prime-Numbers-Sieve-of-Eratosthenes