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Sim glitch re: Halford numbers - the paradox of the WORM and the RUBBER BAND
| Umber pontificating double fault mental disorder | 08/10/15 |
| khaki scourge upon the earth school | 08/10/15 |
| Excitant peach library | 08/10/15 |
| galvanic indian lodge deer antler | 08/10/15 |
| walnut jewess senate | 08/10/15 |
| walnut jewess senate | 08/10/15 |
| Umber pontificating double fault mental disorder | 08/10/15 |
| zombie-like maize really tough guy water buffalo | 11/18/18 |
| stubborn locus | 11/18/18 |
| Umber pontificating double fault mental disorder | 07/09/25 |
| swollen school cafeteria | 07/09/25 |
Poast new message in this thread
Date: August 10th, 2015 3:17 AM Author: Umber pontificating double fault mental disorder 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: khaki scourge upon the earth school 9245872459877474502487245987457264574572487265 (http://www.autoadmit.com/thread.php?thread_id=2959236&forum_id=2...id#28519247) |
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Date: August 10th, 2015 6:59 AM Author: Excitant peach library LOL, unmitigated 928374897239847982374923 (http://www.autoadmit.com/thread.php?thread_id=2959236&forum_id=2...id#28519429) |
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Date: August 10th, 2015 8:44 AM Author: galvanic indian lodge deer antler (http://www.autoadmit.com/thread.php?thread_id=2959236&forum_id=2...id#28519549) |
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Date: August 10th, 2015 9:04 AM Author: walnut jewess senate 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: walnut jewess senate (http://www.autoadmit.com/thread.php?thread_id=2959236&forum_id=2...id#28520692) |
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Date: August 10th, 2015 5:07 PM Author: Umber pontificating double fault mental disorder (http://www.autoadmit.com/thread.php?thread_id=2959236&forum_id=2...id#28522133) |
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Date: November 18th, 2018 10:20 PM Author: zombie-like maize really tough guy water buffalo hmmm... (http://www.autoadmit.com/thread.php?thread_id=2959236&forum_id=2...id#37260869) |
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Date: November 18th, 2018 10:21 PM Author: stubborn locus (http://www.autoadmit.com/thread.php?thread_id=2959236&forum_id=2...id#37260881) |
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Date: July 9th, 2025 4:22 PM Author: Umber pontificating double fault mental disorder (http://www.autoadmit.com/thread.php?thread_id=2959236&forum_id=2...id#49087353) |
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Date: July 9th, 2025 4:23 PM Author: swollen school cafeteria fantastic bump (http://www.autoadmit.com/thread.php?thread_id=2959236&forum_id=2...id#49087355) |