What is the Paper Boat?
... 
The paper boat is a folded boat able to swim  for a
while.
Obviously it is well known all over the world. 
Folding a Paper
Boat top
1

Take a sheet of paper of the size A4 (8 1/2" x 11").
Paper used for ink jet printers will do.
Fold the upper half down on the red line.

2

Find the centre line by folding the left side on the
right side and by unfolding.

3

Fold downward both upper triangles on the red line.

4

It must look like this.

5

At the bottom fold the top strip upward on the red line.

6

Fold the two small triangles on the left and on the right
backwards to make them disappear.

7

It must look like this.

8

Turn the paper over and fold the other lower strip
upwards. You have formed the well known hat.

9

Turn the hat 90 degrees and open it. The thumbs must
be inside. Lay the upper and the lower parts on each other. 
10

It must look like this.

11

Fold the lower front triangle upwards on the red line.

12

It must look like this. .
. 
13

Turn the paper over and fold up the other lower triangle.
You get a hat without a brim.

14

Open the hat again and put the upper part on the lower
one.

15

Pull the upper corners of the triangles in direction
of the arrows...

16
Pull the upper corners of the triangles in direction
of the arrows...

... as much as possible. Form the boat.
The paper boat is finished.
If using 8.5" x 11" ink jet paper the sail will be
visible above the sides of the boat.

17

Stretch the boat both to the right and left, and then
separate it slightly from underneath so it can float. 
The Boat With
Three Sails
top
Perhaps it is unknown, that you can give the boat three
"sails" in the middle.

Don't make step 15. Fold the lower front triangle upwards
on the red line. Turn the paper over and repeat this folding.


It must look like this.


Turn the hat 90 degrees and open it. Lay the upper and
the lower parts on each other.


Pull the upper corners of the triangles in direction
of the arrows. Form the boat.

If the paper is not too thick, you even can repeat these
steps and look for more sails ;).
The Boat with
a Big Sail top
Follow steps 1 to 10.

Fold the lower front triangle upwards on the red line
and unfold. So you find the centre of the square.


Fold the lower front triangle upwards on the red line.
The tip should touch the centre of the square.


It must look like this.
Turn the paper over and fold the lower front triangle
upwards, too.

Make the steps 14, 15 und 16.
If the lower triangles are a little bit larger, the sail
will be smaller.
Some Mathematics top
Shape

From the mathematical point of view the start for the
boat is a shape of two isosceles, rightangled triangles connected at the
sides at the right angle. You get the boat, if you reflect the lower parts
of the two triangles on the middle (red) line. 
Unfolded
... 
The boat has three parts, the front side, the reverse
side and the sail. The unfolded sheet (on the far left) shows these parts.
The boat has only a vertical symmetry axis. 
The Best Paper
Size
...... 
If you use A4 paper and if you colour the outer walls
of the boat red and the inside walls pink and unfold the sheet, you'll
get the results on the left. The strips belonging to the inside walls are
a bit too narrow. It would be ideal, if the pink strips were the same height
as the red ones. This would work with the size 6:4=1.5. The sheet A4 has
the size 1:1.4 (=1: [square root of 2]).
The net also shows all boats are equivalent.
Only the width of the paper and not the height influences
the size of the boat. 
Joke top
...... 
If you tear off the ends of the boat and the top of the
sail and unfold the rest, you get the shapes of a shirt  with sleeves
or without. 
Gruesomely beautiful is the story to that: A boat is sinking.
Weeks later you only find the captain's shirt ...
Samayne Phillips from South Australia
sent me the Australian version, that she heard as a kid:
"Once upon a time there was a pirate boat that set off
in search of treasure, one day (as it neared an island) a storm blew up
and the boat crashed into some rocks (tear off the front of the boat),
so the Capitan decided to turn around and try to sail to shore that way
(turn boat around). Then they crashed into some more rocks (tear
off the other end). “No worries mate” (it was an Australian pirate)
“we’ll just turn her over and sail in upside down” (turn boat over).
Then there was a huge wave and more rocks and the top of the sail broke
off (tear off top of boat). Well after that there was no help for
it, the ship sank. The exhausted crew swam for the shore, but the
Capitan went down with the ship (‘coz that’s what captains do) and all
they found of him was his shirt."
Paper Boats
on the Internet top
Englisch
The Spruce Crafts
Making
an Easy Origami Boat
Recordholders (Peter Koppen)
The
Paper Ship Folding World Record
Deutsch
etsy
Paperboat
Johanna (Elian Pahlow)
Papierschiff
falten
Robert Bronsart (Universitaet Rostock  Fakultaet fuer
Maschinenbau und Schiffstechnik)
Internationaler Papierschiff
Wettbewerb
Stockfotos
Papierschiff
(Bildersammlung)
References top
Joachim Schönherr: Wir falten und falzen, Leipzig
1990
Gail from Oregon Coast, thank you for supporting
me in making this website.
Feedback: Email address on my main page
This
page is also available in German
URL of
my Homepage:
http://www.mathematischebasteleien.de/
©
2001 Jürgen Köller
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