The most prestigious law school admissions discussion board in the world.
|
 |
 
|
Sim glitch re: Halford numbers - the paradox of the WORM and the RUBBER BAND
| Topaz multi-colored national private investor | 08/10/15 |
| lake fragrant ratface organic girlfriend | 08/10/15 |
| umber marvelous heaven | 08/10/15 |
| Copper den | 08/10/15 |
| electric bright becky love of her life | 08/10/15 |
| electric bright becky love of her life | 08/10/15 |
| Topaz multi-colored national private investor | 08/10/15 |
| citrine appetizing garrison jewess | 11/18/18 |
| cowardly 180 tattoo prole | 11/18/18 |
| Topaz multi-colored national private investor | 07/09/25 |
| Twisted Roommate Headpube | 07/09/25 |
Poast new message in this thread
Date: August 10th, 2015 3:17 AM Author: Topaz multi-colored national private investor 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: lake fragrant ratface organic girlfriend 9245872459877474502487245987457264574572487265 (http://www.autoadmit.com/thread.php?thread_id=2959236&forum_id=2)#28519247) |
|
Date: August 10th, 2015 6:59 AM Author: umber marvelous heaven LOL, unmitigated 928374897239847982374923 (http://www.autoadmit.com/thread.php?thread_id=2959236&forum_id=2)#28519429) |
|
Date: August 10th, 2015 8:44 AM Author: Copper den (http://www.autoadmit.com/thread.php?thread_id=2959236&forum_id=2)#28519549) |
|
Date: August 10th, 2015 9:04 AM Author: electric bright becky love of her life 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? |
 |
Date: August 10th, 2015 1:53 PM Author: electric bright becky love of her life (http://www.autoadmit.com/thread.php?thread_id=2959236&forum_id=2)#28520692) |
|
Date: August 10th, 2015 5:07 PM Author: Topaz multi-colored national private investor (http://www.autoadmit.com/thread.php?thread_id=2959236&forum_id=2)#28522133) |
|
Date: November 18th, 2018 10:20 PM Author: citrine appetizing garrison jewess hmmm... (http://www.autoadmit.com/thread.php?thread_id=2959236&forum_id=2)#37260869) |
|
Date: November 18th, 2018 10:21 PM Author: cowardly 180 tattoo prole (http://www.autoadmit.com/thread.php?thread_id=2959236&forum_id=2)#37260881) |
|
Date: July 9th, 2025 4:22 PM Author: Topaz multi-colored national private investor (http://www.autoadmit.com/thread.php?thread_id=2959236&forum_id=2)#49087353) |
|
Date: July 9th, 2025 4:23 PM Author: Twisted Roommate Headpube fantastic bump (http://www.autoadmit.com/thread.php?thread_id=2959236&forum_id=2)#49087355) |