The Origami Forum

After about 40 years of folding I started an anlysis of all the books I had accumulated to get ready to make my Web site. I came to the obvious conclusion that nealy all origami creations that do not use measuring devices begin with one of two possible folds.

1. Fold the paper in half diagonally
2. Fold the paper in half side to side

More simply, the first fold of orgami is to fold the paper in half.

Thus the same "firstfold" is an experience that is common to all who choose to fold

DOC

I would like to report that "DOC" stands for the DUPAGE ORIGAMI CLUB (I live in Dupage County near Chicago) or that I look like Doc Holiday when I wear my cowboy hat but there is a much more obvious and less creative but truthful answer. My students started calling me "Doc" after I finished with a doctorate after 16 years going (mostly part time) to the same university.

Ah, but a model doesn't necessarily have to have measured references. Though I am not very familiar with his work (blasphemy, I know), I do know that Yoshizawa used a lot of approximated folds-and surely he started off with some.

Please note that I said "nearly" all. At least 2 of Jeremy Shafer's models do NOT start with a center fold -
the "Origami Square" (a non-fold) and the "Monolithic Rubblestone Boulder" (what appears to be a crumple)

However, "nearly all" of his other creations do start with a center fold.

I have over 60 orgami books. I started writting a catalogue in Excel for my own reference and stopped after about 4,000 models. Much less than 1% of the models do NOT start with a center fold.

I tried for a while to design an exacltly repeatable starting folds on a square that were not dependent on folding a center fold (without using external measuring devices). By rolling and squashing I could get multiple lines folded all at once but any method that was "exactly repeatable" always had a center line.

I guess, due to my own failure, I will have to stick with "Firstfold".

Oh, Oh - I just did it !

Bring three corners together and squash.
Fold the last corner to meet the last three, squash and you get a blintz without folding a center line.

Now, who can fold a starting line (or lines)that is neither parralell or perpendicular to center line and can be exactly replicated without a measuring device?

Does using the width of your finger or imperfections in the paper count as using a measuring device? And does using a programmed robot count?

No bots, blotches (imperfections), fingers widths or even finger prints can be used. All are considered a device to measure with other than the paper itself.

Here is a possibility -
Curl two side points together matching the sides towards the center but do NOT fold a line (this forms a cone). Curl another point of the square tucking in the cone to the tip and squash the fold.

What do you think?

Excluding right about there folds, thirds as a first fold are possible to make exactly without measuring device by rolling the paper into a tube and pressing flat.

Ah! Do you mean match 2 corners together and squash so the creases hit a corner of the paper? This would work to make a kite base as the first fold.

No - not quite My technique. It involves curing the third corner all the way to the tip inside of the cone. You make only one folded line. You do NOT flatten the cone. It is a delicate maneuver WITHOUT a traditional first-fold but can be done with (almost) perfect accuracy.

The resulting single line is neither papallel nor perpendicular to any traditional first-fold

To do the same fold WITH a traditional first fold - fold the paper in half sided to side and unfold. Then place the corner where the first-fold meets the edge and flatten.

The kite-fold maneuver would result in three line with one that is parallel to a traditional diagonal first-fold.

Dividing in thirds by rounding the paper also results in parallel lines to a traditional first-fold.

I am still not sure what you mean about the cone, but do you mean make a book fold without creasing and bring a corner to the center point of the top edge? If so, that is not entirely precise.

With the kite fold maneuver that I mentioned, there would not be a diagonal first-fold. The corners would be together and the folds would hit the corner, giving you all the references you need.

I will put together a video showing what I mean. Please be patient, I need about a week. I will try to demonstrate all the firstfolds discussed so far. Until then, keep the suggestions comming.

Traditional starting folds:

1. Fold the paper on half on the diagonal
2. Fold the paper in half side to side

Folds that are parallel or perpendicular to the traditional starting fold but are made without using one of the traditional starters

1. Folding a blintz by bringing three points together and squashing. (3 folds at the same time)
2. Folding in in thirds by roling the paper into position (2 folds at the same time)


Folds that are not parallel or perpendicular to the taditional starting folds:

1. Rolling a cone by brining adjacent corners together then bringing up another point inside the cone up to the tip of the cone and squashing a single fold. 1 fold only
2. Rolling two oposite corners together like a kite and perhaps using the bottom point as a reference to form 1 or 2 or 3 simultanious folds.

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What other ideas do any of you have?

I will be putting together a video to demonstate my understanding of these folds. Other diagrams, pictures or videos welcome.

Corners can also be folded into thirds using the same method as described above. In this case the two first folds aren't perpendicular to a typical first fold.

By the way: I've splitted the topic into an own one and included the text firstfold wrote in the new created topic into his last post.

Here is the video I had promised –
Initially the video consisted of 14 information sections (green background) with 14 challenges (red background). I thought I could make this into a comprehensive treatment and tutorial of the subject but when I reviewed the first very long ten minutes of this video I realized that I spent way too much time stating the obvious and that made the video very boring. Therefore, I cut out the first ten minutes and kept what I think is essential for our discussion. It makes the video a bit choppy.

Johnycakes, you may not recognize the kite-fold procedure you suggested but I believe that the second to last fold is actually based on your idea. Anna, rolling into a tube was not shown but was, I believe, addressed as a possibility and how that idea could be extended to 5ths., 7ths. Et. al.. I recognize that rolling as a tube is more effective than rolling as a wave for thirds but has even more drawbacks when the idea is extended beyond thirds (each segment inside a tube rolled in fifths is progressively smaller). The very last procedure is what I was trying to describe with words – I hope the video helps.

<embed src="http://www.youtube.com/v/WrWA7pVTlp0&hl=en&fs=1" type="application/x-shockwave-flash" allowfullscreen="true" width="425" height="344"></embed>

The second-to-last fold was very interesting. Believe it or not, when I saw you holding the 2 corners together, I got the idea to slide them until the crease hit the corner-exactly what you did! Good job figuring that out-you probably already know, but the other corner can be flattened as a reference line too.