Please respond to each post below. Jonathan B. This class is introducing me to

Please respond to each post below.
Jonathan B.
This class is introducing me to so many new and complex mathematical concepts, its wild!
This week I chose to learn about mathematical knots. I used to work with knots all the time when I was a deckhand in the Coast Guard, and it never once occurred to me that there are ways of looking at these knots mathematically. This video does a really great job of explaining the first steps of understanding mathematical knots, and I was not surprised that there are an infinite number of mathematical knots, and that it is a very large and very complex theory. I was surprised to learn that if you have a knot with open ends, like say the laces on your shoes, then it’s not really a mathematical knot, it must have closed ends to form the most basic unknot.
I would be very curious to know the larger applications of this mathematical complications, it would seem as if knot theory could be used in things like sciences like biology or astrology. Is there a larger part of our known universe that scientists and mathematicians are using knot theory to try to unravel? (See what I did there?)
Evy H.
I decided to write about the Mobius band and Klein bottle for this week’s discussion. I’ve done quite of research on this topic for my final project and I think the Klein bottle and Mobius band is very fascinating! The Mobius band has both continuous physical and theoretical applications. Our brain sees in two- and three-dimensional space so understanding the Mobius band and Klein bottle makes it difficult for our brain to represent objects that are four-dimensional. In other words, the Mobius strip of the Klein bottle is a 2D manifold but can only exist in at least 4 dimensions. A theoretical idea that the Mobius band is used to help understand is time travel! That’s just a little background of the Mobius band I find cool but I digress. A way of thinking of topology in its math form is when topologists think circle, they imagine a rubber band that has constant movement but remains intact. It’s math with “squishy” shapes. To me, topology is very confusing because it has to do with a lot of theoretical math and multiple dimensions. A topologist can ignore certain details about shapes and focus attention on the fundamental properties.

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