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Sim glitch re: Halford numbers - the paradox of the WORM and the RUBBER BAND
| Gay deer antler | 08/10/15 |
| Hideous abusive factory reset button property | 08/10/15 |
| high-end cruise ship | 08/10/15 |
| Exciting Self-centered Gaming Laptop | 08/10/15 |
| low-t newt school | 08/10/15 |
| low-t newt school | 08/10/15 |
| Gay deer antler | 08/10/15 |
| aphrodisiac ultramarine shrine circlehead | 11/18/18 |
| Zombie-like curious indirect expression lodge | 11/18/18 |
| Gay deer antler | 07/09/25 |
| Galvanic Doctorate Resort | 07/09/25 |
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Date: August 10th, 2015 3:17 AM Author: Gay deer antler Suppose that a useless PISSworm crawls along a 1-metre rubber band at the same time as the rubber band is uniformly stretched. If the worm travels 1 centimetre per minute and the band stretches 1 metre per minute, will the worm ever reach the end of the rubber band?
The answer, counterintuitively, is "yes", for after n minutes, the ratio of the distance travelled by the worm to the total length of the rubber band is
\frac{1}{100}\sum_{k=1}^n\frac{1}{k}
(In fact the actual ratio is a little less than this sum as the band expands continuously). The reason is that the band expands behind the worm also; eventually, the worm gets past the midway mark and the band behind expands increasingly more rapidly than the band in front.
Because the series gets arbitrarily large as n becomes larger, eventually this ratio must exceed 1, which implies that the worm reaches the end of the rubber band. However, the value of n at which this occurs must be extremely large: approximately e100, a number exceeding 10^44. The exact value of n is 15092688622113788323693563264538101449859497. Although the harmonic series does diverge, it does so very slowly. |
Date: August 10th, 2015 3:44 AM Author: Hideous abusive factory reset button property 9245872459877474502487245987457264574572487265 (http://www.autoadmit.com/thread.php?thread_id=2959236&forum_id=2],#28519247) |
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Date: August 10th, 2015 6:59 AM Author: high-end cruise ship LOL, unmitigated 928374897239847982374923 (http://www.autoadmit.com/thread.php?thread_id=2959236&forum_id=2],#28519429) |
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Date: August 10th, 2015 8:44 AM Author: Exciting Self-centered Gaming Laptop (http://www.autoadmit.com/thread.php?thread_id=2959236&forum_id=2],#28519549) |
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Date: August 10th, 2015 9:04 AM Author: low-t newt school hard 2 understand this presentation with the rubber band and the latex. nobody reads latex faggot and after googling this i see that its not a circular BAND but a ROPE with fixed ends. i found this http://www.theproblemsite.com/problems/high-school-math/2002/long-walk but i still dont get it. why isnt it the case that the distance between the worm and the end of the rope is getting longer and longer over time, so the worm can never reach the end? |
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Date: August 10th, 2015 1:53 PM Author: low-t newt school (http://www.autoadmit.com/thread.php?thread_id=2959236&forum_id=2],#28520692) |
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Date: August 10th, 2015 5:07 PM Author: Gay deer antler (http://www.autoadmit.com/thread.php?thread_id=2959236&forum_id=2],#28522133) |
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Date: November 18th, 2018 10:20 PM Author: aphrodisiac ultramarine shrine circlehead hmmm... (http://www.autoadmit.com/thread.php?thread_id=2959236&forum_id=2],#37260869) |
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Date: November 18th, 2018 10:21 PM Author: Zombie-like curious indirect expression lodge (http://www.autoadmit.com/thread.php?thread_id=2959236&forum_id=2],#37260881) |
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Date: July 9th, 2025 4:22 PM Author: Gay deer antler (http://www.autoadmit.com/thread.php?thread_id=2959236&forum_id=2],#49087353) |
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Date: July 9th, 2025 4:23 PM Author: Galvanic Doctorate Resort fantastic bump (http://www.autoadmit.com/thread.php?thread_id=2959236&forum_id=2],#49087355) |