Here's the "Troll Pi" or "Pi equals 4" image.
Here's the breakdown, as simple as I can make it.
All of the following facts are true:
These facts are also true:
And so is this final fact:
The limit of a sequence isn't necessarily a member of that sequence.
Because of this, the limit of a sequence doesn't necessarily share any properties with the members of that sequence.
Here, you've seen a sequence of curves of length 4, whose limit does not have length 4.
You've also seen a sequence of jagged, right-angled curves whose limit is not jagged or right-angled at all, but smooth.
Here's another example of this:
1, 1/2, 1/3, 1/4, 1/5, ...
All of the numbers in this sequence are positive, but the limit, 0, is not.
This is not a problem. It's not a contradiction. It's just the way it is.
Breathe in. Breathe out. Carry on with whatever you were doing.
Discussion (69)
2010-12-09 01:43:11 by atomicthumbs:
2010-12-09 01:55:59 by Randall:
2010-12-09 02:13:50 by Joseph:
2010-12-09 02:39:24 by Ross:
2010-12-09 09:22:15 by qntm:
2010-12-09 09:36:54 by qntm:
2010-12-09 09:39:11 by qntm:
2010-12-09 11:56:48 by Sean:
2010-12-09 13:15:46 by Chris:
2010-12-10 17:30:49 by pascal:
2010-12-11 00:33:44 by Hans:
2010-12-11 04:17:40 by David:
2010-12-12 17:35:14 by TeX:
2010-12-14 09:33:55 by Ross:
2010-12-19 11:23:34 by FinDude:
2010-12-24 23:31:07 by danny:
2010-12-25 09:16:24 by qntm:
2011-01-03 03:54:24 by Mirdan:
2011-01-03 12:32:54 by qntm:
2011-01-13 15:12:58 by Aether:
2011-01-21 22:26:23 by anon:
2011-01-23 18:40:36 by quintopia:
2012-02-09 03:31:42 by Prafull:
2012-03-25 19:41:36 by anon:
2012-03-25 19:55:43 by qntm:
2012-05-14 15:52:01 by LawrenceColes:
2012-05-17 21:34:29 by SmexyFish:
2012-05-23 00:13:35 by Luke:
2012-05-30 00:13:31 by Anonymous:
2012-05-30 17:21:22 by Ramki:
2012-07-03 12:25:18 by daleofcourse:
2012-07-04 22:03:51 by Daniel:
2012-07-05 15:30:58 by JanWillem:
2012-07-22 20:53:05 by qntm:
2012-10-31 04:33:46 by Jakim:
2012-11-01 13:48:26 by Tim:
2012-11-01 14:03:59 by qntm:
2012-11-02 16:35:52 by Tim:
2012-11-05 13:37:45 by qntm:
2012-11-20 06:33:25 by Carl:
2013-01-15 06:22:28 by Steven:
2013-03-05 03:42:43 by pelrun:
2013-03-14 15:07:08 by PiThagaurus:
2013-07-05 19:44:09 by ANon:
2013-07-05 22:28:37 by benevolentwanderer:
2013-07-05 22:34:40 by qntm:
2013-12-30 09:37:19 by JohnGabriel:
2014-07-05 07:22:48 by Coda:
2014-07-05 11:05:15 by qntm:
2014-08-26 04:42:43 by Rodney:
2014-08-26 04:58:56 by Rodney:
2014-08-27 22:14:11 by Rodney:
2015-04-13 19:23:22 by Coda:
2015-12-08 15:41:46 by Alexander Iurovetski:
2015-12-08 19:24:41 by qntm:
2015-12-09 00:34:49 by Alexander Iurovetski:
2015-12-09 01:30:04 by qntm:
2015-12-09 12:44:37 by Alexander Iurovetski:
2015-12-09 13:26:24 by qntm:
2015-12-09 20:49:09 by Alexander Iurovetski:
2015-12-09 21:23:06 by qntm:
2016-06-14 19:26:51 by edward789121:
2016-09-26 15:08:19 by katesisco:
2016-09-26 15:34:10 by qntm:
2018-03-03 19:18:43 by John Gabriel:
2019-04-14 23:42:27 by thingymajigabob:
2019-04-15 00:32:43 by qntm:
2020-05-11 03:16:02 by Jonnyboyo:
2021-03-28 00:41:14 by caydenja: