STEM GRADE 7 LESSON
View video on how to make Mobius strips.http://www.youtube.com/watch?v=DnJNOQWmC_c
Topology is the study of shapes.
Specifically, it is the study of the properties that don't change when the
shapes are twisted or stretched. Size and proportion have no meaning in
topology. A small oval is the same as an enormous circle. A sphere the size of
the sun is the same as a dumbell you hold in your hand.
To topologists, what matters is the
number of holes and twists. Thus a teacup is identical to a donut, but there is
no way that a teacup could ever be a figure-8. One of the most intriguing
topological constructions is the Mobius Band.
TOPOLOGISTS are mathematicians who study what happens to various shapes when pushed and pulled.
TOPOLOGISTS are mathematicians who study what happens to various shapes when pushed and pulled.
Mobius
was a German astronomer born in 1790. Although he is usually given credit for
the discovery of the band named after him, he was actually the second person to
publish its description. The mathematician Johann Benedict Listing described
the band in 1861, four years before Mobius.
Three
experiments using a Mobius Strip
Supplies for the basic Mobius band
a
strip of paper
a
pencil
cellophane
tape
scissors
The
basic Mobius band
Bring
the two ends of the strip together, turn one end over, and tape the ends
securely. Be sure to tape all the way across the edge, or the band will fall
apart when you cut it. You will have a loop with a half-twist in it.
Make
the loops into Mobius bands.
INVESTIGATION #1
1.
How many faces, or sides, does a
piece of paper have? (TWO)
- How many faces does the Mobius band have?
Most
people would say two.
Proof that the Mobius Strip only has one side.
1.
Draw a line down the middle of the band. If
the band has two sides, you will end up with a line on one side, but not on the
other.
2.
Using a marker, draw a large dot on
your demonstration loop. Draw a line down the middle, moving the loop
conveyer-belt fashion, until you reach the dot. The line is on both sides of
the loop. This means the Mobius band has only one side.
INVESTIGATION #2
a.
What will happen if you cut the
Mobius band lengthwise down the middle? Usually people will predict two
separate loops.
b.
Cut your loop in half. Begin by
putting a small hole in the center. Then carefully cut down the middle until
your reach your starting point. Pull the band apart into one big loop.
INVESTIGATION
# 3
Cutting
the Mobius band in thirds.
- What do you think will happen when you cut your Mobius band
in thirds lengthwise?
- Cut your strip in thirds. As you do so, you have a wide
section and a narrow section. You are cutting all the way around two
times, and on the second time around, you are cutting the wide section in
half.
Separate
the loops. You will end up with two interlinked loops.
STEM
Using math and science to solve a
problem.