application of toplogy

 

39 minutes ago, junaid shahzada said:

application of toplogy

 

 

Giving the best hairstyle to a tennis ball.

 

(The Hairy ball theorem - Brouwer

https://en.wikipedia.org/wiki/Hairy_ball_theorem

)

 

Predating the actual development of "topology" but considered an application of basic topology:

Euler's "Seven Bridges of Konigsberg'.

https://en.wikipedia.org/wiki/Seven_Bridges_of_Königsberg

Topology is useful for telling the difference between, say, a doughnut and a coffee cup. Or not. (Depending how many holes the doughnut has. Or how many handles on the coffee cup.)

Edited December 28, 20178 yr by Strange

Early in the morning it can be difficult to tell the difference between your coffee cup and your doughnut- but it is very important to avoid pouring hot coffee over yourself!  So topology is important.

The Moebius Flask, which can have a liquid poured in, but cannot contain it as it pours out. The three-dimensional surface having volume but no inside or outside defined surface.

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During the year I taught high school math in very rural Missouri, I calmed down several boisterous classes by predicting the results of cutting two strips of paper apart, which I explained would totally befuddle them. They listened, observed, disbelieved, then owed they would spring this on friends and family! The Moebius Strip.

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A strip of thin material, rolled into a cylindrical form, must present height, diameter, and volume. The strip if twisted first, such that it's inner and outer edges are reversed, when rolled into a cylinder, become a moebius solid having no inside or outside, nor presenting a viable volume.   imp

 

EDIT: Even more befuddling is the process of taking a moebius strip prepared of paper of reasonable size, about a foot in length, which is then pierced anywhere at it's center between edges, then cut with scissors completely around it's length to produce two (?) pieces. Worse, the strip pierced 1/3 of it's width away from one edge, then cut lengthwise continuously until separated into two (?)  pieces becomes.....?? Two new volumes, one a cylinder, the other a new moebius strip having TWO twists, AND they are of differing diameters!  Try it!   imp

Edited November 17, 20187 yr by tinkerer