Difference between revisions of "Topology"
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{{WikiEntry|key=Topology|qCode=42989}} is a field of mathematics that initially studies geometrical objects deformed under continuous transformations. Many of its analytical techniques can be applied to other kinds of mathematical analysis, including algebra and language interpretation, and compilation. It is also the starting point of [[Category Theory]] and can be thought of as the origin of [[meta mathematics]]. | |||
The following video<ref>{{:Video/Topology and Geometry 1}}</ref> is presented by Dr. [[Tadashi Tokieda]] | The following video<ref>{{:Video/Topology and Geometry 1}}</ref> is presented by Dr. [[Tadashi Tokieda]] | ||
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Mobius strip is a strip twist by one or more times . One twist is equal to <math>180^o</math>. | Mobius strip is a strip twist by one or more times . One twist is equal to <math>180^o</math>. | ||
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: | 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: | ||
| Line 6: | Line 11: | ||
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) | 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) | ||
= | =Tokieda's advise in Topological Problem Solving= | ||
Prof. Tokieda demonstrated that mathematical thinking, particularly in the world of topology, strategically pave solutions in the following ways: | 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]] | # [[Always draw pictures for you problem]] | ||
# [[Problems may exist in different forms]] | # [[Problems may exist in different forms]] | ||
# [[Try to first convert a problem to simpler forms and solve it there]] | ## [[Try to first convert a problem to simpler forms and solve it there]] | ||
## [[Some problems have dual forms and can be converted bi-directionally]] | |||
=Application Areas= | |||
One of the areas to apply Toplogy is in fact: politics<ref>{{:Book/Political Numeracy}}</ref>. | |||
James Munkres wrote a well-known textbook<ref>{{:Book/Topology}}</ref> on Topology. Another interesting video by Tony Feng is here<ref>{{:Video/Some analogies between arithmetic and topology - Tony Feng}}</ref>. | James Munkres wrote a well-known textbook<ref>{{:Book/Topology}}</ref> on Topology. Another interesting video by Tony Feng is here<ref>{{:Video/Some analogies between arithmetic and topology - Tony Feng}}</ref>. | ||
Latest revision as of 10:06, 13 January 2024
Topology(Q42989) is a field of mathematics that initially studies geometrical objects deformed under continuous transformations. Many of its analytical techniques can be applied to other kinds of mathematical analysis, including algebra and language interpretation, and compilation. It is also the starting point of Category Theory and can be thought of as the origin of meta mathematics. The following video[1] is presented by Dr. Tadashi Tokieda |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)
Tokieda's advise in Topological Problem Solving
Prof. Tokieda demonstrated that mathematical thinking, particularly in the world of topology, strategically pave solutions in the following ways:
Application Areas
One of the areas to apply Toplogy is in fact: politics[2].
James Munkres wrote a well-known textbook[3] on Topology. Another interesting video by Tony Feng is here[4].
References
- ↑ Tokieda, Tadashi (12 May 2014). Topology and Geometry. 1/15. local page: African Institute of Mathematical Sciences.
- ↑ Meyerson, Michael (2002). Political numeracy : mathematical perspectives on our chaotic constitution. local page: Norton Publisher. ISBN 0393323722.
- ↑ 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.