Dimensional Views [ 01.08 ] Special : Moebius Strip and Tesseract

Published: 14.02.2006
Updated: 02.07.2015

Let's build our own moebius strip:


Take a strip of paper: L ength ~ 30 cm, width ~ 4 cm


Give it a half twist


Tape the ends together

Now we are ready to find out what a nonorientable surface is:

  • When you take the strip of paper between thumb and first finger - you are sure you touch the 2 sides of the strip.

Now let's proof the moebius strip has only 1 side:

  • Take a pen and draw a line along the middle of the strip marking the surface:

You end on the same side as you started.

That means:

  1. Back and front are the same = there is only 1 side.
  2. There is only 1 border (although you can touch and see 2).
Start marking one border with a coloured pen.... you end up where you started on the same border - after 2 rounds.



Moebius Strip Inside the Tesseract

Now we put one of the 8 cubes of the tesseract on our moebius strip:
...and move it along the surface....after the 1st round.... on the same position:
bottom
is on top!


The 8 cubes of a tesseract are moving simultanously on moebius strips in 4D hyperspace, which is hard to imagine. The single cube on a moebius strip proves that it is possible: top = bottom and viceversa while moving on a nonorientable surface.

more about: August Ferdinand Möbius
  • Remember, we draw a line along the middle of the strip marking the surface:
Now take a scissors and cut along the drawn middle line........ anf you get...
    • Not 2 stripes by cutting (as exspected)
    • but doubled the length of the moebius strip!
      Sources

      © Christian & Carla Geerdes, Editors HereNow4U online magazine

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      1. Carla Geerdes
      2. HereNow4U
      3. Tesseract
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