Redo: Minimal Surface

I chose to redo the minimal surface project due to the last one being a little bit too complicated to print, and implement. The Schwarz P-Surface was very cool and interesting but it was nearly impossible to print and it resulted in many hours spent trying to print it or assemble it in different ways. Now we are working with two simple shapes, a circle and a square. The improvements here are the simplicity and the ability to actually form a minimal surface between the shapes I am using to demonstrate the concept. It is very hard for me to use Openscad and it is also very hard to tell what will work on a printer and what won't, sometimes it seems like it simply depends on the day! Jokes aside I think this will demonstrate the concept better and will be easier to work with making it a better project in terms of presentation and utilization.

The utilization of simple shapes, easy to understand curves, and the like are key to having a good minimal surface project in my opinion. So, reducing the complexity and making it easier to see also aids in the understanding of whats being presented as well. I also think that it will be interesting to see the shape that forms between a smooth surfaced shape with rounded edges being the circle and the square which has more sharp edges. All in all I think the concept of the Schwarz P-Surface is very interesting but when it comes to being able to portray that in a 3-D print, it falls apart. Literally my surface fell apart many times and using glue was very strenuous. I also like this rendition because it seems like something you could actually see in a toy store or kids playing with, compared to the Schwarz P-surface which ended up looking like some sort of sci-fi orb that almost no one recognized.

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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...

Minimal Surfaces

Minimum surfaces can be described in many equivalent ways. Today, we are going to focus on minimum surfaces by defining it using curvature. A surface is a minimum surface if and only if the mean curvature at every point is zero. This means that every point on the surface is a saddle point with equal and opposite curvature allowing the smallest surface area possible to form. Curvature helps define a minimal surface by looking at the normal vector. For a surface in R 3 , there is a tangent plane at each point. At each point in the surface, there is a normal vector perpendicular to the tangent plane. Then, we can intersect any plane that contains the normal vector with the surface to get a curve. Therefore, the mean curvature of a surface is defined by the following equation. Where theta is an angle from a starting plane that contains the normal vector. For this week’s project, we will be demonstrating minimum surfaces with a frame and soap bubbles! How It Works Minimum surfac...

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...

MA 391 Composition and Communication

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