This time I taped the edges of a long band of paper into a twisted strip.
I drew a blue line on one side and a red line on the other side. After I
twisted and taped, the lines connected into one long line!
Möbius Strip
This twisted strip is usually called a
Möbius Strip.
Its named after a person. I want to avoid using names of mathematical objects
based on the names of people in this series.
I'll include them if I think its necessary for looking up related material
I often find these sort of names confusing when learning math
I don't always like how this sort of naming honors some people but not
others
Interactive Taping Diagram
Here's a diagram showing how to tape the paper strip to itself. Tape the two
horizontal edges so that the arrow heads are aligned with eachother to get a
twist!
The diagram is interactive, so please try exploring this twisted space by
moving the circle around and through the blue arrows.
Twisted in Two Directions
Now I want to show you a space where both the horizontal and
vertical edges are taped in a twisted way.
Unlike the torus, the arrows on opposite edges are pointed in different
directions.
When I started playing around with this, I was surprised by how different the
space feels; I actually thought I taped it incorrectly.
The Same Space, But Round
This space is also a Real Projective Plane. It is connected in the same way as
the rectangle.
Unfortunately, you cannot really make a paper model of the Real Projective
Plane. It doesn't embed in 3D space. If you cut slits in the paper so that the
paper can pass through itself you can though. Check out the link above to see
what a 3D model of that looks like.
In the previous "Exploring Spaces", I
made a torus out of paper.