Video/Topology and Geometry 1

Tokieda, Tadashi (12 May 2014). Topology and Geometry. 1/15. African Institute of Mathematical Sciences. 

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Content

Lecture 1: Mobius Strip

1. Mobius strip
2. In Topology and Geometry There are three points to remember.
   1. There is so much more to mathematics than numbers and formulas. (For example, there is pictorial thinking)
   2. Always draw pictures whenever you work on mathematics.
   3. There is so much more to pictures than photos of objects.

Video

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Starting from Lecture 1 of this course, we have realized that the Mobius strip is a very powerful mathematical idea. --Benkoo (talk) 03:35, 18 July 2021 (UTC)

The Mobius strip is a strip twisted one or more times. One twist is equal to $180^{o}$. Before the strip becomes a Mobius strip, it can be divided into two sides. We will name them red and blue. Then, you twist the strip to turn it into a Mobius strip. If the Mobius strip has an odd twist the blue side will be connected to the red side. If you have an even twist, the blue side will be connected to the blue, and the red will be connected to red. If you start to cut the middle of the blue part and the red part of the Mobius strip you will get two different outcomes:

1. The Mobius strip has an odd twist so you will get a bigger Mobius strip

2. The Mobius strip has an even twist then you will get two Mobius strips. (that are the same length and same number of twists as the Mobius strip before it was cut)

In Topology and Geometry There are three points to remember.

1. There is so much more to mathematics than numbers and formulas. (For example, there is pictorial thinking)

2. Always draw pictures whenever you work on mathematics.

3. There is so much more to pictures than photos of objects.

In Topology and Geometry, you should learn to see and draw things that can't be seen physically. For example take the Mobius strip. When you are doing the experiment of cutting the Mobius strip you will still know what will happen but if you draw it out it will be easier to understand what is happening.