# The Gap Theorie **URL:** \ **Category:** Factual Questions\ **Created:** [March 21, 2011, 1:21pm UTC](https://boards.straightdope.com/t/the-gap-theorie/575464 "2011-03-21T13:21:08Z")\ **Posts on this page:** 5\ **Page:** 1
**Author:** ![Simple\_Mind](https://avatars.discourse-cdn.com/v4/letter/s/7cd45c/32.png) [@Simple\_Mind](https://boards.straightdope.com/u/Simple_Mind)\ **Post date:** [March 21, 2011, 1:21pm UTC](https://boards.straightdope.com/t/the-gap-theorie/575464/1 "2011-03-21T13:21:08Z")
Hi, I had a conversation with a friend and he brought up this story where one has for example, a square of 1 m2, each side is 1 meter long, resulting in a 4 meter long border. Now, one takes a rigid string that does not stretch at all nor does it shrink, one lays it around the outside of the square and adds 10 cm or 0.1 m to its length, resulting in a 4.10 meter long string. He now claims that there will be a gap between the 4 meter border of the square and the string of 1.25 cm all around at any point, this also is, according to him, true no matter how long the sides of a square, rectangle or the circumference of a circle are, he says that even if one lays a string around the Equator and then adds 10 cm, this would result in a gap of 1.25 cm all around the Globe between the surface and the string. Can that be true? :dubious: ---
**Author:** ![Darth\_Panda](https://avatars.discourse-cdn.com/v4/letter/d/ee7513/32.png) [@Darth\_Panda](https://boards.straightdope.com/u/Darth_Panda)\ **Post date:** [March 21, 2011, 1:37pm UTC](https://boards.straightdope.com/t/the-gap-theorie/575464/2 "2011-03-21T13:37:41Z")
c = pi\*2r for any 2 circles, the “gap” between the 2 will be equal to the difference between their radii. r = c / 2\*pi, so delta r = (c - c) / 2 \* pi Let’s call pi 3.14 for sake of example delta r = (c - c) / 6.28 10 / 6.28 = 1.59 So, the idea is there - that the starting size of the body is irrelevant, since the relationship is linear, but the math is off a little because his example applies to rectangles and not circles, which have a different relationship between perimeter and radius than rectangles have betwen perimieter and the length of a side. eta: I am not a mathemagician. ---
**Author:** ![Exapno\_Mapcase](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/exapno_mapcase/32/1051_2.png) [@Exapno\_Mapcase](https://boards.straightdope.com/u/Exapno_Mapcase)\ **Post date:** [March 21, 2011, 2:19pm UTC](https://boards.straightdope.com/t/the-gap-theorie/575464/3 "2011-03-21T14:19:09Z")
The story is usually told by adding a yard to a string laid around the earth’s equator. Then the string is six inches above the ground everywhere, because 3 feet divided by 2 pi is about 6 inches. It’s the factor of 2 pi or 6.28 that’s the heart of this surprising result. ---
**Author:** ![Darth\_Panda](https://avatars.discourse-cdn.com/v4/letter/d/ee7513/32.png) [@Darth\_Panda](https://boards.straightdope.com/u/Darth_Panda)\ **Post date:** [March 21, 2011, 2:59pm UTC](https://boards.straightdope.com/t/the-gap-theorie/575464/4 "2011-03-21T14:59:17Z")
Now if you imagine a sphere with that kind of gap, you’ll get much different results and working through the math will let you understand the perimeter thing better. ---
**Author:** ![Thudlow\_Boink](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/thudlow_boink/32/320_2.png) [@Thudlow\_Boink](https://boards.straightdope.com/u/Thudlow_Boink)\ **Post date:** [March 21, 2011, 5:24pm UTC](https://boards.straightdope.com/t/the-gap-theorie/575464/5 "2011-03-21T17:24:15Z")
The “string around the earth’s equator” is a classic problem. [Here’s one online explanation.](http://www.dennymath.com/?p=449)