Paper and Folds

Origami and Paper Folding 🏆

Course 1 · Chapter 1 · Paper and Folds: Your First Square, Your First Crease, Your First Boat

Origami is the art of making shapes by folding paper, and nothing else. No scissors, no glue and no tape, at least in the traditional style. That one constraint is what makes it fun: a flat sheet becomes a boat, a bird or a box using only your fingers and a good crease. This chapter gets you started with the sort of paper you need, how to turn a sheet of A4 into a perfect square, the two folds that everything else is built from, and a boat you can finish in a few minutes.

What Origami Is, and Where It Came From

The word comes from Japanese: ori means "folding" and kami means "paper" (the sound changes to "gami" when the two words join). Folding paper for decoration and ceremony is old in Japan, and paper folding of various kinds also grew up independently in China and in Europe, so it is a shared craft rather than one country's property. The exact dates of the earliest models are debated (check), and you do not need them to start folding.

The one rule Traditional origami uses one uncut sheet and no glue. Modern folders sometimes break that rule (cutting, joining several sheets), and later chapters, such as Modular Origami in Origami and Paper Folding 7, join units together. For now, one sheet and your hands.

Choosing Paper

You can fold with almost any paper, but some papers make life far easier. Thin paper holds a sharp crease and takes many layers. Thick paper is stiff and fights you at every fold. Here is a quick guide.

Paper	Feel	Good for	Watch out for
Printer paper (A4 or Letter)	Cheap, a little thick	Practice, boats, boxes, first attempts	Not square, and gets bulky after many layers
Packet origami paper (kami)	Thin, coloured on one side, white on the other	Almost every model in this course	Tears if you rub the crease too hard
Sticky-note pads	Small and square, a weak tacky strip	Tiny models, desk practice	The sticky edge grabs other layers
Gift wrap	Thin, patterned	Free practice paper, large models	Often has a white or plain back and can crack along creases
Card or cartridge paper	Stiff	Boxes that need to keep their shape	Hard to crease neatly, so avoid for complex models

For this course a pack of ordinary 15 cm square origami paper (about 6 in) is the most useful buy, but printer paper costs nothing and is fine for a first boat. Whatever you choose, keep a stack of spare sheets nearby. Everyone ruins the first few.

Which Side Is Which

Many sheets have a coloured side and a white side. Diagrams usually show the coloured side as shaded and the white side as plain, so you can see at a glance which way up the paper is. Start every model with the side the instructions tell you, and if they say nothing, start coloured side up (check the book or site you are following, since habits differ).

Making a Square from A4

Most origami models start with a square. Printer paper is a rectangle, but you can make a square from it in under a minute, and the maths is neat: the diagonal of a square 210 mm wide is almost exactly 297 mm, the long side of A4. That is not a coincidence. A4 is built so that its sides are in the ratio 1 to the square root of 2, which means folding the short edge diagonally onto the long edge lands the corner exactly on the long edge. Here is a tiny script that checks the numbers.

import math

w, h = 210, 297
print('A4 side', w, 'x', h)
print('Square side', w)
print('Leftover strip', h - w, 'mm x', w, 'mm')
print('Diagonal of the square', round(w * math.sqrt(2), 1), 'mm')
print('Ratio h/w', round(h / w, 4))

Output when run:

A4 side 210 x 297
Square side 210
Leftover strip 87 mm x 210 mm
Diagonal of the square 297.0 mm
Ratio h/w 1.4143

The leftover strip (87 mm by 210 mm) is waste for now, but keep it: it makes a good practice strip for the crease exercises later on.

The Steps

Lay the A4 sheet in front of you with a short edge at the bottom (portrait).
Take the bottom-left corner and fold it up and across so the bottom edge lies exactly along the right-hand long edge. You now have a triangle sitting on top of a rectangle.
Press the crease flat from the fold outwards, running your thumbnail along it.
The rectangle at the top is the leftover strip. Crease its lower edge firmly (that edge is the top of the triangle) and then fold the strip back and forth over that crease until the paper tears cleanly along it, or open the sheet out and cut along the crease with scissors. Unfold the triangle.
The sheet you hold is a square, and the diagonal crease across it is already in place for later models.

# A4, portrait. Fold the bottom-left corner up to the right edge.

 +------------------+            +------------------+
 |                  |            |                  |  <- leftover strip
 |                  |            +------------------+
 |                  |            |                 /|
 |                  |    ==>     |               /  |
 |                  |            |             /    |
 |                  |            |           /      |
 +------------------+            +----------+-------+
                                  bottom edge now lies
                                  along the right edge

Check it really is square Fold your finished square in half along both diagonals. If the corners meet exactly each time, it is square. If one pair sticks out, one side is slightly longer than the other and every model made from it will lean. A square that is off by even 2 mm is worth trimming.

The Two Folds Everything Is Built From

Almost every origami model, however clever, is made from two basic folds and the order you do them in.

Fold	What the crease looks like from your side	How you make it	Diagram line
Valley fold	A valley: the crease sinks away from you and the paper folds up toward you	Fold the paper toward you, like closing a book	Dashed line: - - - - -
Mountain fold	A ridge: the crease points up at you and the paper folds away behind	Fold the paper away from you, behind the sheet	Dash-dot line: - . - . - .

# Side view of the paper, you looking from above

 Valley fold               Mountain fold

   \        /                   /\
    \      /                   /  \
     \____/                   /    \
   the crease is low        the crease is high

Here is the helpful trick: a valley fold from the front is a mountain fold from the back. Turn the paper over and the same crease reverses its name. That is why diagrams show the paper turned over so often, and why you should keep the paper on a clean table while you work.

Making a Good Crease

A fold is only as good as its crease. A crisp crease makes later steps easier and the finished model neater.

Line up first, press second. Match the two edges or corners exactly before you press anything. A fold made to the wrong place cannot be corrected without leaving a ghost crease.
Hold the first point, then press from the middle out. Pin the corner with one finger and flatten the paper out toward the other end with the thumb of the other hand.
Sharpen with a fingernail. Run a nail firmly along the fold. For hard-to-crease paper, a bone folder, the side of a ruler or the back of a spoon helps.
Unfold gently. A "pre-crease" is a crease you make and then open again to mark a guide. Open it slowly so the paper does not stretch or tear.
Don't rework a bad crease. If it is in the wrong place, start another sheet. Practice paper is cheap, and unfolding and refolding weakens paper fast.

The table is part of the tool Fold on a hard, flat surface such as a table or a book rather than on a soft sofa arm. Soft surfaces make the paper wobble and your crease blurry.

Your First Model: The Paper Boat

This is the classic fold-it-from-a-sheet boat that most people half remember from childhood. It starts with a plain rectangle, so ordinary printer paper works well. Use A4 for a large boat, or fold a square-ish scrap for a little one. (Several versions exist, and what follows is the common one: if your memory of it differs, that is normal, since it has been passed down by hand for a long time.)

Folds You Will Use

The boat uses valley folds only, plus some opening and flattening at the end.

Half fold. Lay the paper landscape (long edge at the bottom). Fold the top edge down to the bottom edge, crease firmly, then open it out. You now have a horizontal crease across the middle. Fold the paper in half again along that crease, with the fold at the top.
Fold in the top corners. Fold the top-left and top-right corners down to meet the centre of the fold so they make a triangle (like a house roof) with a strip of paper along the bottom.
Fold up the cuffs. Fold the bottom strip of the front layer up over the triangle's lower edge, then turn the model over and do the same on the back.
Open and flatten. Put your thumbs into the bottom opening and pull the sides apart until the model flattens into a diamond shape.
Fold up the lower corners. Fold the bottom corner of the front layer up to the top point, then the back one. You now have a smaller triangle.
Open and flatten again. Open the bottom and flatten into a diamond again.
Pull the boat open. Hold the top two points and gently pull them apart. The model opens into a boat shape. Squeeze the base so the bottom is flat.

# Stage by stage, front view

 1. Half-folded        2. Corners in         3. Cuffs up
 +---------------+        /\                    /\
 | fold at top   |      /    \                /    \
 |               |     /      \              /______\
 +---------------+    +--------+             |        |
                      |        |             +--------+

 4. Opened flat        5. Corners up         6. Opened flat
      /\                  /\                     /\
     /  \                /  \                   /  \
    /    \              /____\                  \  /
    \    /              \    /                   \/
     \  /                \  /
      \/                  \/

 7. Pulled apart: the boat
    \          /
     \________/
      \______/

Common trouble spots If the diamond will not flatten, check that the layers are aligned and that the cuffs are folded in the right direction. If the boat leans to one side, the first half fold was probably off by a few millimetres. Start again on a fresh sheet: the second boat always goes faster than the first.

Challenges

Each challenge has a worked solution you can open after you have tried it.

Challenge 1

Make a square from a sheet of A4 using the corner fold, then prove it is square by folding it along both diagonals. Write down the side length you measured and how far each diagonal crease differs from the other, if at all.

→ Solution

Challenge 2

On a spare square, fold a valley fold, then a mountain fold, then turn the paper over and describe what has happened to each crease. Then change the numbers in the script so it prints the square and leftover strip for A3 (297 mm by 420 mm) and for Letter paper (216 mm by 279 mm). Does the folding trick still give the same diagonal?

→ Solution

Challenge 3

Fold the paper boat from a sheet of ordinary printer paper, then fold a second one from a small square (for example one quarter of an A4 sheet). Float both in a bowl or sink. Which one floats better, and why do you think that is? Write two sentences.

→ Solution

Quick Reference

Origami: ori (folding) + kami (paper)
A4 to square: fold a short edge onto a long edge, remove the strip, side = 210 mm
Valley fold: toward you, dashed line
Mountain fold: away from you, dash-dot line
Good crease: align first, press from the middle, sharpen with a nail
First model: paper boat, from a plain rectangle

Next, in Origami and Paper Folding 2, we learn to read the symbols used in fold diagrams, so you can follow any model in any book without a teacher.