Skip to main content

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.

Comments

Popular posts from this blog

The Approximation of a Solid of Revolution

Most math teachers I've had have been able to break down Calculus into two very broad categories: derivatives and integrals. What is truly amazing, is how much you can do with these two tools. By using integration, it is possible to approximate the shape of a 2-D function that is rotated around an axis. This solid created from the rotation is known as a solid of revolution. To explain this concept, we will take a look at the region bounded by the two functions: \[ f(x) = 2^{.25x} - 1 \] and \[ g(x) = e^{.25x} - 1 \] bounded at the line y = 1. This region is meant to represent a cross section of a small bowl. While it may not perfectly represent this practical object, the approximation will be quite textured, and will provide insight into how the process works. The region bounded by the two functions can be rotated around the y-axis to create a fully solid object. This is easy enough to talk about, but what exactly does this new solid look like? Is...

Knot 9-31

Knot 9-31 A knot is mathematics is defined as a closed, non-self-intersecting curve that is placed in three dimensions and cannot be the "unknot". The main difference between a knot in the real world and a known in mathematics is that a knot in mathematics does not contain any extra strands. The example following will help visualize this. Today, I have specifically chosen knot 9-31 from the Knot Atlas. This knot is very unique and contains some very interesting properties that we are going to look into. The Crossing Number For my knot today, I chose knot 9-31 from the Knot Atlas. This knot contains 9 crossings! The Unknotting Number The unknotting number is exactly what is sounds like. This is the minimum number of times the knot must be passed through itself to untie it. Luckily, the Knot Atlas is super useful and provides the unknotting number for us, but I still...

Do Over: Integration for Over Regions in the Plane

Introduction Earlier in the semester, we visited the topic of integration for over region regions in the plane. This was our first experience with taking integration in the third dimension. To do this, we had to use double integrals to calculate the volume of a region between two surfaces. This topic seems relatively straightforward and anyone who has taken a higher calculus class knows of double integrals. Today, we are going to revisit this topic for a couple of reasons. Why Double Integrals Again? As mentioned before, I am revisiting this topic for a couple of reasons. One of the main reasons is due to how the 3D print turned out. Due to the function, I chose, the final rectangular prism was stand alone. When printing, this resulted in a sloppy prism that lacked structural integrity. The image below is a reference to my original design that includes the prism that had the issue. The main cause of ...