Minecraft 4th iteration Menger Sponge

Minecraft Menger sponge (Menger Universal Curve) :

The Menger sponge is a 3 dimensional cube that models the Sierpinski carpet. The Sierpinski carpet is a fractal generalization of the Cantor set.

The Sierpinski carpet is a 2 dimensional figure starting with a square and then subdividing into 9 sections. You then remove the center section.

  

The next step is to take the remaining 8 sections and repeat the process for each one.

After that you are left with an image where the middle section is missing from each of the 8 subsections of the original figure. You then take each of those subsections and repeat the process again. This will leave you with this figure:

You can then repeat the process again....

An amazing property of the Sierpinski carpet is that as the number of iterations of this process approaches infinity the area will approach 0

When this process is moved up into 3 dimensions you construct a Sierpinski sponge. The Menger cube is slight alteration of the Sierpinski sponge.

The Menger sponge has a similar amazing property that as the iterations approach infinity the Surface area approaches infinity and the Volume approaches 0..  

I created a 4 iteration Menger sponge in Minecraft, starting with a 3X3X3cube.

Then I removed the center block from each of the 6 faces.

I Then cloned this cube using the Minecraft /clone command to get to 20 cubes arranged to show the next iteration of the Menger sponge.

I then cloned that cube to make 20 more copies to construct the next iteration.

At this point I will note that for the Menger sponge the number of cubes (or in this case blocks) is given by the formula (Number of blocks) N = 20ⁿ where n is the number of iterations and the above cube is iteration 3. which is N = 20³ = 8000 blocks.

For the final project I decided to move over into my realms server and construct a 4 iteration Menger cube with N = 20⁴ = 160,000 blocks...!!!!

The controversy with common core:

The controversy with common core:

     Math has become a new phobia among youth and current parents. It has many wearing math illiteracy as a badge of honor. The problem began with adults experiencing negativity at a young age toward the subject. It was often taught in very rigid and mechanical tone. The rigidity is where the problem we face today finds its roots. Math was drilled into our heads with the idea that there is only one way to do things, and anything else leads to lower grades. Many teachers were strictly against alternative methods, and led to an ingrained aversion to the subject for their students.

     Other issues include the teaching methods themselves, as well as the lack of guidance for students who may take longer to grasp the subject. In the interest of time, and testing, the teachers are encouraged to cover large amounts of material in a short amount of time. These factors in combination are what has resulted in the attitude toward math that parents possess today. This attitude is also being passed on to their children, by encouraging an avoidance of mathematics. The parents own aversion and lack of proper education in mathematics makes it difficult to understand the material their children are bringing home. The new common core standards and teaching tools are incredibly different from what many of these parents are familiar with.

      

      Currently students are being introduced new concepts for learning math with the development of common core. Altering how things are done, can be beneficial to finding better teaching options. Sure many of these methods are breaking from tradition, but as with all things we are learning. Which forces us to integrate new information and approaches to teaching. Parents and educators all need to stay aware of this. As we learn and grow intellectually, knowledge must force us to change. However, this change conflicts with the fact that the parents of these children are unable to help them to better their skills in these areas. Here we see the roots of the problem. The parents were not taught by common core standards, and therefore cannot aid their children until first learning the methods themselves.

     If parents or teachers see common core standards as a problem maybe schools could host a week long open seminar on what is actually going to be taught and how it is implemented. The schools could have qualified instructors in the common core standards come and talk with parents and teachers. They could even teach some of the new math strategies to the parents so they can be better informed on how to help their children adapt to the new material.

     Given the chance to come to understand the common core math standards could help change the way some respond to them. I understand the problems many people have with common core math. Seeing a drop in test scores with new standards being put into place is a shock, but when you look into it you see it is not the problem with the tests, it is us. We are failing our children. The common core math standards are well informed and vetted by leaders in the stem fields. And these are the things our children need to learn to remain competitive with their peers around the globe.