Posts

A Farewell For Now

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The end of the summer has arrived, which means that my research on minimal surfaces has come to a close. Honestly, I wish I had more time to continue my research because there is still so much to explore about minimal surfaces. I hope to continue studying minimal surfaces and other related concepts, such as manifolds, in my own time or perhaps I will have the chance to continue my studies in my future math classes. I am grateful to have had the opportunity to participate in the NSF-EXPLORE Summer Research program as it not only introduced me to the research process in mathematics, but it also enriched my critical thinking skills as well as helped me develop other skills that will be beneficial as my career progresses. The program gave me an opportunity to give my first poster presentation, which can be stressful but at the same time, I know it will be rewarding in the end. I have always wondered what it was like to do research in math; this program showed me what research consists...
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Today’s Research in Minimal Surfaces and Their Applications to Our World

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Image from Quanta Magazine Current Research Research in minimal surfaces has continued throughout the years, but recently, Karen Uhlenbeck, a U.S. mathematician, was named to be one of the most influential as her work led to remarkable advances in the last 40 years. In March 2019, Uhlenbeck became the first woman to be awarded the prestigious Abel Prize, which she received for her “pioneering achievements in geometric partial differential equations, gauge theory and integrable systems, and for the fundamental impact of her work on analysis, geometry and mathematical physics” ( Saplakoglu ). In her early work, Uhlenbeck and mathematician Jonathan Sacks studied minimal surfaces and soap films in higher dimensions. The more dimensions added, the more challenging it becomes to define the shape of the soap film; however, Uhlenbeck was able to determine the shapes that soap films can take in higher dimensional manifolds. A manifold, simply put, is a curved surface that can be diffic...
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An Exhibition of Minimal Surfaces

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In my previous blog post, I provided a brief history and explanation of the math of minimal surfaces. Now, in this post, I will give a plethora of examples of minimal surfaces as well as illustrate the relationship between minimal surfaces and soap films and demonstrate applications to 3D printing. Some of the examples will include images from Maple where I plotted the surface and colored it by its mean curvature, while other examples were taken from online because the minimal surfaces were too difficult to plot. Overall, this post is meant to be a visual presentation of minimal surfaces. The first nontrivial minimal surface was discovered by Leonhard Euler in 1744, which is now known as the catenoid (Dillen & Verstraelen, 2000, p.207) . The catenoid on the right is colored by its mean curvature. It is a single color because the mean curvature is zero at every point. In order to plot the catenoid in Maple, I used the uv -parameterization that  Weisstein provided on Wolf...
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