# Folding something into halves or quarters is easy. Any tips or tricks for folding into thirds? **URL:** \ **Category:** Factual Questions\ **Created:** [October 27, 2022, 2:07pm UTC](https://boards.straightdope.com/t/folding-something-into-halves-or-quarters-is-easy-any-tips-or-tricks-for-folding-into-thirds/973876 "2022-10-27T14:07:09Z")\ **Posts on this page:** 20\ **Page:** 1
**Author:** ![filmore](https://avatars.discourse-cdn.com/v4/letter/f/7993a0/32.png) [@filmore](https://boards.straightdope.com/u/filmore)\ **Post date:** [October 27, 2022, 2:07pm UTC](https://boards.straightdope.com/t/folding-something-into-halves-or-quarters-is-easy-any-tips-or-tricks-for-folding-into-thirds/973876/1 "2022-10-27T14:07:09Z")
Something like a piece of paper or rope can easily be folded into halves or quarters. All you have to do is line up the ends. But folding something into thirds is a lot more challenging. You have to estimate and feel your way to getting it folded in equal thirds, and often it’s hard to get it right. Are there any ways to reliably fold something so it comes out in equal thirds like you can with folding it into half? ---
**Author:** ![LSLGuy](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/lslguy/32/5813_2.png) [@LSLGuy](https://boards.straightdope.com/u/LSLGuy)\ **Post date:** [October 27, 2022, 2:18pm UTC](https://boards.straightdope.com/t/folding-something-into-halves-or-quarters-is-easy-any-tips-or-tricks-for-folding-into-thirds/973876/2 "2022-10-27T14:18:06Z")
Assuming something thin like paper … Once you’ve made the first fold correctly, you’ll see that visually one half of the page is one sheet thick and the other half is two sheets thick. In other words, the edge of the folded over part divides the visible surface exactly in half. For me at least, seeing that halfway point is easy. Once I started to think of the problem not as “fold in thirds”, but as “divide the remaining unfolded part in half.” That may work for you and it may not. Spatial awareness and estimation are not equal gifts among everyone. ---
**Author:** ![Elmer\_J.Fudd](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/elmer_j.fudd/32/1211_2.png) [@Elmer\_J.Fudd](https://boards.straightdope.com/u/Elmer_J.Fudd)\ **Post date:** [October 27, 2022, 2:19pm UTC](https://boards.straightdope.com/t/folding-something-into-halves-or-quarters-is-easy-any-tips-or-tricks-for-folding-into-thirds/973876/3 "2022-10-27T14:19:06Z")
Without rulers or creasing it with reference folds, the only way is intuition (eyeballing it). ---
**Author:** ![Crane](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/crane/32/3495_2.png) [@Crane](https://boards.straightdope.com/u/Crane)\ **Post date:** [October 27, 2022, 2:28pm UTC](https://boards.straightdope.com/t/folding-something-into-halves-or-quarters-is-easy-any-tips-or-tricks-for-folding-into-thirds/973876/4 "2022-10-27T14:28:57Z")
Seems to me this was called trisecting an angle in Geometry class. It can only be estimated. ---
**Author:** ![running\_coach](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/running_coach/32/15836_2.png) [@running\_coach](https://boards.straightdope.com/u/running_coach)\ **Post date:** [October 27, 2022, 2:32pm UTC](https://boards.straightdope.com/t/folding-something-into-halves-or-quarters-is-easy-any-tips-or-tricks-for-folding-into-thirds/973876/5 "2022-10-27T14:32:09Z")
Fold in thirds as best you can. Trim off any overhang. 😉 ---
**Author:** ![solost](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/solost/32/11776_2.png) [@solost](https://boards.straightdope.com/u/solost)\ **Post date:** [October 27, 2022, 3:16pm UTC](https://boards.straightdope.com/t/folding-something-into-halves-or-quarters-is-easy-any-tips-or-tricks-for-folding-into-thirds/973876/6 "2022-10-27T15:16:59Z")
Back in the ancient days of folding a letter-sized piece of paper into thirds to fit into a business envelope, it didn’t seem too difficult- loosely fold one end of the paper at about the 1/3 fold point, then loosely fold the other end over that. That shows you pretty accurately what exact thirds should be. You can make any necessary adjustment, then press down to make two crisp fold creases. That gets you to within a couple millimeters of exact thirds. ---
**Author:** ![pjd](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/pjd/32/3009_2.png) [@pjd](https://boards.straightdope.com/u/pjd)\ **Post date:** [October 27, 2022, 3:20pm UTC](https://boards.straightdope.com/t/folding-something-into-halves-or-quarters-is-easy-any-tips-or-tricks-for-folding-into-thirds/973876/7 "2022-10-27T15:20:38Z")
That’s how i do it. ---
**Author:** ![mixdenny](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/mixdenny/32/2962_2.png) [@mixdenny](https://boards.straightdope.com/u/mixdenny)\ **Post date:** [October 27, 2022, 3:58pm UTC](https://boards.straightdope.com/t/folding-something-into-halves-or-quarters-is-easy-any-tips-or-tricks-for-folding-into-thirds/973876/8 "2022-10-27T15:58:24Z")
Thank goodness we’re not metric, they don’t even have thirds. ---
**Author:** ![DavidNRockies](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/davidnrockies/32/6279_2.png) [@DavidNRockies](https://boards.straightdope.com/u/DavidNRockies)\ **Post date:** [October 27, 2022, 4:01pm UTC](https://boards.straightdope.com/t/folding-something-into-halves-or-quarters-is-easy-any-tips-or-tricks-for-folding-into-thirds/973876/9 "2022-10-27T16:01:31Z")
If you don’t want to screw around, but just want to _nail_ it on the first try, here’s a cool woodworking trick that I’ve used many times: > **[How to Divide a Board Evenly—The Easy Way](https://www.familyhandyman.com/article/how-to-divide-a-board-evenly-the-easy-way/)** > > To divide a board into thirds, choose any number that’s divisible by three, like nine, 12, 18, etc. Lay a square or tape measure diagonally across the board ---
**Author:** ![naita](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/naita/32/5862_2.png) [@naita](https://boards.straightdope.com/u/naita)\ **Post date:** [October 27, 2022, 4:06pm UTC](https://boards.straightdope.com/t/folding-something-into-halves-or-quarters-is-easy-any-tips-or-tricks-for-folding-into-thirds/973876/10 "2022-10-27T16:06:32Z")
Trisecting an angle is perfectly doable if you don’t arbitrarily limit your tools: > **[Angle trisection | With a marked ruler](https://en.wikipedia.org/wiki/Angle_trisection#With_a_marked_ruler)** > > Another means to trisect an arbitrary angle by a "small" step outside the Greek framework is via a ruler with two marks a set distance apart. The next construction is originally due to Archimedes, called a Neusis construction, i.e., that uses tools other than an un-marked straightedge. The diagrams we use show this construction for an acute angle, but it indeed works for any angle up to 180 degrees. > This requires three facts from geometry (at right): ---
**Author:** ![Crane](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/crane/32/3495_2.png) [@Crane](https://boards.straightdope.com/u/Crane)\ **Post date:** [October 27, 2022, 4:12pm UTC](https://boards.straightdope.com/t/folding-something-into-halves-or-quarters-is-easy-any-tips-or-tricks-for-folding-into-thirds/973876/11 "2022-10-27T16:12:18Z")
An approximation is possible with a ruler but the angle is not trisected. ---
**Author:** ![naita](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/naita/32/5862_2.png) [@naita](https://boards.straightdope.com/u/naita)\ **Post date:** [October 27, 2022, 4:24pm UTC](https://boards.straightdope.com/t/folding-something-into-halves-or-quarters-is-easy-any-tips-or-tricks-for-folding-into-thirds/973876/12 "2022-10-27T16:24:37Z")
The linked construction divides an arbitrary angle into three equal parts with the same kind of precision (i.e. only limited by how perfectly the tools and your use of them can mimic mapping distances between zero dimensional points) as bisection with a compass and straight edge. If you want to define the word “trisection” as only relating to the classical problem of trisecting the angle, go ahead, but I’m going to stick with the definition that doesn’t leave thousands of schoolkids thinking a perfectly doable task is somehow “impossible”. Which makes me think of a way to find the points that let your fold something in thirds. If you already have something with at least three equal divisions and the minimum distance across three full divisions is no more than the diagonal of the thing to fold into thirds you can find the points to fold by putting either the opposite corners on the dividing lines of the reference or, better, the corners of one edge. If you use the edge the divisions you cross will cross the edge exactly at the folding points. If you use the corners they will cross the diagonal at the folding points. The closer the distances are to the thirds you are trying to make the easier it is to be precise. ---
**Author:** ![gnoitall](https://avatars.discourse-cdn.com/v4/letter/g/bb73d2/32.png) [@gnoitall](https://boards.straightdope.com/u/gnoitall)\ **Post date:** [October 27, 2022, 4:27pm UTC](https://boards.straightdope.com/t/folding-something-into-halves-or-quarters-is-easy-any-tips-or-tricks-for-folding-into-thirds/973876/13 "2022-10-27T16:27:04Z")
The “marked straightedge” “cheat” to classic compass-and-straightedge construction is, indeed, based on approximation – the accuracy of the markings on the straightedge. So using a ruler to trisect a sheet of paper isn’t true geometric trisection, but I doubt anyone but geometrists would care. Also, you could always buy a machine to do it for you. > **[Folding machine | Paper folders](https://en.wikipedia.org/wiki/Folding_machine#Paper_folders)** > > Folding machines exclusively used for folding paper are commonly referred to as paper folders. These machines are typically used for creating letter folds (C Folds) and accordion folds (Z Folds). Other commonly used folds include a half fold, fold-out, double parallel fold, gate (brochure) fold, and right angle fold. > The fold type in a buckle folder is set by adjusting folding plates. Most paper folders allow for a wide range of fold types. Right angle folds require the paper to rotate 90 degree... ---
**Author:** ![Andy\_L](https://avatars.discourse-cdn.com/v4/letter/a/c67d28/32.png) [@Andy\_L](https://boards.straightdope.com/u/Andy_L)\ **Post date:** [October 27, 2022, 4:33pm UTC](https://boards.straightdope.com/t/folding-something-into-halves-or-quarters-is-easy-any-tips-or-tricks-for-folding-into-thirds/973876/14 "2022-10-27T16:33:25Z")
Trisecting a line segment is a different task than trisecting an angle. ---
**Author:** ![Crane](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/crane/32/3495_2.png) [@Crane](https://boards.straightdope.com/u/Crane)\ **Post date:** [October 27, 2022, 4:34pm UTC](https://boards.straightdope.com/t/folding-something-into-halves-or-quarters-is-easy-any-tips-or-tricks-for-folding-into-thirds/973876/15 "2022-10-27T16:34:05Z")
> [@naita](#): > > If you want to define the word “trisection” as only relating to the classical problem of trisecting the angle, go ahead, but I’m going to stick with the definition that doesn’t leave thousands of schoolkids thinking a perfectly doable task is somehow “impossible”. The problem is presented to schoolkids specifically for the purpose of illustrating that bisection exists only in the theoretical process and the diagrams they draw are approximations. Trisection has so far eluded us. ---
**Author:** ![Andy\_L](https://avatars.discourse-cdn.com/v4/letter/a/c67d28/32.png) [@Andy\_L](https://boards.straightdope.com/u/Andy_L)\ **Post date:** [October 27, 2022, 4:43pm UTC](https://boards.straightdope.com/t/folding-something-into-halves-or-quarters-is-easy-any-tips-or-tricks-for-folding-into-thirds/973876/16 "2022-10-27T16:43:38Z")
In fact many false proofs of angle trisection are from people who have trisected line segments and assumed that angle trisection can be easily done from there. ---
**Author:** ![filmore](https://avatars.discourse-cdn.com/v4/letter/f/7993a0/32.png) [@filmore](https://boards.straightdope.com/u/filmore)\ **Post date:** [October 27, 2022, 5:02pm UTC](https://boards.straightdope.com/t/folding-something-into-halves-or-quarters-is-easy-any-tips-or-tricks-for-folding-into-thirds/973876/17 "2022-10-27T17:02:42Z")
I guess I was wondering more about simple methods that could be used in regular life to fold paper and split things like ropes into thirds. It doesn’t have to be super precise. Like with folding a sheet of paper, I can sort of get it into thirds by eye and feel, but I’m usually off by about 1/4" by the time I make the creases. And with things like rope, it’s lots of iterations of making one segment longer, one segment shorter, one segment longer, etc. It doesn’t really matter a whole lot if it’s super exact or not. It’s more for the nice feeling of satisfaction from getting it into generally even thirds. ---
**Author:** ![Crane](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/crane/32/3495_2.png) [@Crane](https://boards.straightdope.com/u/Crane)\ **Post date:** [October 27, 2022, 5:10pm UTC](https://boards.straightdope.com/t/folding-something-into-halves-or-quarters-is-easy-any-tips-or-tricks-for-folding-into-thirds/973876/18 "2022-10-27T17:10:48Z")
With practice you could develop the skill of dividing an angle into three equal parts. Something like practicing hand drawing a perfect circle. Just do as an interesting diversion. ---
**Author:** ![naita](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/naita/32/5862_2.png) [@naita](https://boards.straightdope.com/u/naita)\ **Post date:** [October 27, 2022, 6:01pm UTC](https://boards.straightdope.com/t/folding-something-into-halves-or-quarters-is-easy-any-tips-or-tricks-for-folding-into-thirds/973876/19 "2022-10-27T18:01:10Z")
> [@Crane](#): > > The problem is presented to schoolkids specifically for the purpose of illustrating that bisection exists only in the theoretical process and the diagrams they draw are approximations. Trisection has so far eluded us. Trisection by compass and straight edge only hasn’t “eluded us”. It’s been proven to be impossible. It would be just as useful for kids to be taught that we can do arbitrarily precise trisections if including transferring a known length from one part of a diagram to another. ---
**Author:** ![Keith1](https://avatars.discourse-cdn.com/v4/letter/k/6de8d8/32.png) [@Keith1](https://boards.straightdope.com/u/Keith1)\ **Post date:** [October 27, 2022, 6:16pm UTC](https://boards.straightdope.com/t/folding-something-into-halves-or-quarters-is-easy-any-tips-or-tricks-for-folding-into-thirds/973876/20 "2022-10-27T18:16:53Z")
3 5/8" - 3 11/16" - 3 11/16" This is for an 11" sheet (letter size). You can make a light pencil mark at 3 5/8 for the first fold. No one will notice. Next fold is easy. If you want to get really professional, make the first fold slightly smaller (1/32), which will allow the front panel to overhang the center panel just a little bit. If you have various sizes to fold it’s probably easier to use centimeters or millimeters to do the math. I would often use picas, but not everyone has a pica pole. [Next page](https://boards.straightdope.com/t/folding-something-into-halves-or-quarters-is-easy-any-tips-or-tricks-for-folding-into-thirds/973876.md?page=2)