HOW TO MAKE A MÖBIUS STRIP….
Why did
the
chicken
cross
the
Möbius
strip?
First, cut out a long, thin strip of paper (about
3cm wide).
2.
Holding it the tall way, label the top left corner "A"
the top right corner "B" the bottom left corner "C"
and the bottom right corner "D“.
3.
Give the strip a twist and tape the two ends together so that "A"
touches "D" and "B" touches "C“.
4.
Draw a line around the strip (in the middle). What happens?
5.
Use the scissors to cut along the line you drew. How many
bands do you have now?
Take another strip of paper and twist it twice.
Tape it closed. Cut it in the middle, the same as
before. What happens?
SO… WHAT IS A MÖBIUS STRIP?
Most surfaces have two sides – like a sheet of paper
– you can paint each side with a different colour. A
Möbius strip doesn't have a front or a back. The top
and the bottom are the same. The twist in the strip
connects what was the top to the bottom, making one
big side and only one edge.
Möbius strip was named after the famous German astronomer and
mathematician August Ferdinand Möbius (1790-1868), who was a
pioneer in the field of topology. He came up with his 'strip' in
September 1858
6.
What do they do
with them?
Giant Möbius Strips
have been used as
conveyor belts (to make
them last longer, since
"each side" gets the
same amount of wear)
and as continuous-loop
recording tapes (to
double the playing
time). In the 1960's
Sandia Laboratories
used Möbius Strips in
the design of versatile
electronic resistors.
Free-style skiers have
christened one of their
acrobatic stunts the
Möbius Flip.
The famous artist, M.C. Escher, used
mathematical themes in some of his work,
including a Möbius parade of ants. His flight of
swans looks like it might be a Möbius Strip, but
it's not. Can you see why not?
Make your strip this wide (6cm)
1.
To get to
the same
side.
iThemba LABS (Laboratory for Accelerator Based Sciences) ~ P O Box 722, Somerset West 7129 ~ (021) 843 1000 / ¬ (021) 843 3525 /
http://www.tlabs.ac.za
What you need: paper, scissors and tape
M.C. Esch
All you need, cardboard, scissors,
several pieces of paper of different sizes
Using a piece of cardboard about ¼ of the size of an A4
piece of paper, make three cuts in the index card that go
almost to the top of the card.
Try to pull on both of the ends of the index card
at the same time, ripping it so that the middle part falls
to the ground. Impossible, huh?
Invisible Ink
Stuff you need: paper, toothpick, lemon juice and a
heat source (like a lamp or a toaster).
Dip the toothpick in lemon juice and write a secret
message on a piece of paper. Let the paper dry for a
couple of hours.
Then hold it over a lamp or toaster to warm it up. The
message will magically appear.
Take a piece of A4
paper and cut it in half.
Using one of the pieces
see if you can you cut a
hole in it big enough for
you to climb through
without breaking it.
How this works:
pull
pull
Experiment with other liquids such as orange juice, apple
juice and milk. Do they work as well as lemon juice? Also try
different kinds of paper. Which types of paper work best?
Does more absorbent paper such as newspaper work as
well as less absorbent paper such as notebook paper?
Why is this?
There are two reasons why it's
impossible to do this: First, it's
almost impossible to make two cuts
that are exactly even. So, when you
pull both sides, one side will almost
always break first.
Second, it's almost impossible to
pull equally on both sides. So, the
side you pull on with more force, or
pull on first, will rip first.
Stuff you need: Ruler, newspapers
What you do: Slide a ruler underneith several flat sheets of newspaper,
until only 5cm of the ruler sticks out. Strike the ruler suddenly with a thick
roll of (additional) newspaper. The ruler and flat sheets of newspaper will
stay in place.
How it works:
Air pressure on top of the newspaper keeps the ruler in place.
If the ruler is slowly pressed down, the newspaper will lift. But
if the ruler is struck hard, air cannot move out of the way fast
enough and holds the ruler in place.
Try this with a different sized piece
of paper and see what happens.Try changing
Q. What do you call a chicken who
crossed the road, rolls around in
the dirt, and crosses the road
again?
A. A dirty double-crosser!
After the lemon juice dries, a residue of organic solids
is left behind on the paper. When heated, the solids
darken and reveal the writing.
the length of ruler that sticks out from
beneath the newspaper. What is the maximum
distance that the ruler can stick out before the
newspaper can no longer hold down the ruler. Put
more newspapers on the first several sheets of
newspaper. Which holds the ruler to the tabletop
better: (a) stacking the paper straight up and down
on top of each other or (2) overlapping the papers on
top of each other?
Did you know
that you can't fold a
piece of paper in half
more than eight
times, no matter how
big the paper is?
Go on… try it.
Can’t huh! Ok – try cutting it this way instead.
First fold the paper in half length ways.
Make a cut along the fold – be careful not to cut all
the way to the ends, leave a space on either side.
Make cuts as indicated on the diagram below.
Be careful NOT to cut all the way through the
paper.
Try different sizes of paper. Try making the cuts
closer together and see what happens.
cut
Q.
Which side of a
chicken has the
most feathers?
A.
The outside!