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Welcome to MA 391: Composition and Communication at the University of Kentucky!

This semester we are going to be practicing the (sometimes frustrating and always ) important skill of communicating mathematics. At the start of the semester we are going to revisit some topics from calculus and for each of those topics you will pick an example you think really helps explain what is going on. You will design and print a 3d model of that example. Then you will write a blog post (here!) and a description card for your model and participate in the class show and tell.

After spending some time in calculus we will switch over to topics motivated by geometry and topology. You don't need to know anything about these area yet. We're going to look at them since they will be new to many of you, they lend themselves well to visualization projects and my research is in topology!

Popular posts from this blog

Do Over: Integration Over a Region in a Plane

Throughout the semester we have covered a variety of topics and how their mathematical orientation applies to real world scenarios. One topic we discussed, and I would like to revisit, is integration over a region in a plane which involves calculating a double integral. Integrating functions of two variables allows us to calculate the volume under the function in a 3D space. You can see a more in depth description and my previous example in my blog post, https://ukyma391.blogspot.com/2021/09/integration-for-over-regions-in-plane_27.html . I want to revisit this topic because in my previous attempt my volume calculations were incorrect, and my print lacked structural stability. I believed this print and calculation was the topic I could most improve on and wanted to give it another chance. What needed Improvement? The function used previously was f(x) = cos(xy) bounded on [-3,3] x [-1,3]. After solving for the estimated and actual volume, it was difficult to represent in a print...
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Do Over: Ruled Surfaces

Why to choose this project to repeat For the do over project, I would like to choose the ruled surfaces. I don't think my last project was creative, and the 3D printed effect was not very satisfactory. In the previous attempts, all the lines are connected between a straight line and a circle. This connection structure is relatively uncomplicated. The printed model has too many lines, resulting in too dense line arrangement. The gaps between lines are too small, and the final effect is that all the lines are connected into a curved surface, which is far from the effect I expected. What to be improved In this do over project, I would like to improve in two aspects. Firstly, a different ruled surface is chosen. In the previous model, one curve is a unit circle on the \(x-y\) plane, and the ruled surface is a right circular conoid. In this do over project, it is replaced by two border lines. Each borderline is in the shape of an isosceles right triangl...
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Knot 10-11

The knot I chose for this project was knot 10-11. That is the eleventh knot that has ten crossings. I picked it for no reason whatsoever. I 3D printed the knot as you can see here. A knot's crossing number is the smallest number of crossings possible in a 2D representation of the knot. This knot's crossing number is 10. A knot's unknotting number is the smallest number of crossings flipped that will give you the unknot. I found an upper bound on the unknotting number. If you switch the crossings circled below, then the knot will become the unknot and therefore has an unknotting number of at most 3. The colorability of a knot can help determine whether or not two knots are actually the same. When the number of crossings in a knot is high, it is actually pretty hard to know if two knots are secretly the same and are only represented differently through Reidemeister moves. Colorability can help confirm that two knots are indeed different. Colorabilit...
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