Topology
The following video[1] is presented by Dr. Tadashi Tokieda {{#ev:youtube|https://www.youtube.com/watch?v=SXHHvoaSctc&l%7C%7C%7C%7C%7C}} Mobius strip is a strip twist by one or more times . One twist is equal to . Before the strip becomes a Mobius strip can be divided into to two side we will name it as red and blue, after you twist the strip and make turn it into Mobius strip. If the Mobius strip has a odd twist the blue part will connected to the red Part, If you have a even twist the blue part will connected to the blue red will connected to red. if you start to cut the middle for the blue part and the red part of the Mobius strip you will get to different kinds of out come: 1. The Mobius strip has an odd twist so you will get bigger Mobius strip 2. The Mobius strip has an even twist then you will get two Mobius strip. (that has the same length and same number of twist as the Mobius strip before you cut)
Strategies in Topological Problem Solving
Prof. Tokieda demonstrated that mathematical thinking, particularly in the world of topology, strategically pave solutions in the following ways:
- Always draw pictures for you problem
- Try to first convert a problem to simpler forms and solve it there
- Many problems can be converted between different forms
James Munkres wrote a well-known textbook[2] on Topology. Another interesting video by Tony Feng is here[3].
References
- ↑ Tokieda, Tadashi (12 May 2014). Topology and Geometry. 1/15. local page: African Institute of Mathematical Sciences.
- ↑ Munkres, James R. (January 7, 2000). Topology (2nd ed.). local page: Pearson College Div;. ISBN 978-0131816299.
- ↑ Feng, Tony (Nov 10, 2020). Some analogies between arithmetic and topology - Tony Feng. local page: Institute for Advanced Study.