Would you like to make this site your homepage? It's fast and easy...
Yes, Please make this my home page!
The Biggest Hole; A Lab Activity
This is activity has the "WOW" factor of a discrepant event, that is
the result is "impossible". In my experience most students will
desire to repeat the activity for themselves.
Topology is the study of surfaces and edges. Our piece of paper
has two surfaces and one edge. We generally refer to the surfaces
as the front and back of the paper. And we divide the edge into
the sides, top and bottom of the paper. In topology we don't
worry about the shape of a surface or edge. When we cut a hole in
the paper, we add a second edge. One edge around the outside of
the surface, and one around the inside of the surface (the outside of
the hole). Student will intuitively know that the inside edge can
not be longer than the outside edge, and will estimate the largest
diameter of their hole accordingly. What student almost never
recognize is that we can make the outside edge of the paper longer.
Ordinary lined paper, preferably without holes, 8.5 X 11 inches is what
But any paper (including newspaper) will work.
Scissors for each group.
Here we have an ordinary piece of
writing paper. It has two surfaces, and
one edge. If we cut
a hole in the paper, it will have two edges.
Remember, a diameter is the length of a straight line drawn
area, in this case the area of the hole.
Without actually cutting the
paper, I want each
estimate the longest diameter they will be able to get for a hole cut
paper. Who can cut the largest hole in
the paper without separating the paper so that it has to be taped back
or anything like that. I’ll give you 3
minutes for your team to think about it, then I will ask for your
(Request estimates from volunteers.)
Now that we have your best
thoughts on the
subject, I am
telling you that I am going to cut a hole in this sheet of paper with a
diameter of more than 5 feet. Watch!
John, please stand and hold this
part of the paper. Jane, please stand over
here and hold this
corner carefully, it tears easily. Ok,
hold it higher. There, a hole you could
ride your bicycle through!
Now you each have a chance to try
it for yourself.
- Take a standard
of 8.5 X 11 inch
lined paper, preferably without holes.
- Fold it in half
lengthwise, and crease
- From the side
beginning with the second line from the bottom, cut both thicknesses of
paper along the line to about 0.5 inch from the fold.
- Continue to cut
similarly on alternate
lines. Be sure leave a strip at the top at
least as wide as the others.
- From the fold side,
cut along each
uncut line to about 0.5 inch of the edge.
- Being sure that you do
not cut either
of the end strips, cut along the fold.
- Gently unfold and
stretch the paper
out. The diameter of hole will be many
times larger than the diameter of the whole paper.
what you learned
in school, you
an amazing answer.