Analysis of menger sponge and sierpinski triangle

Thesis Bachelor of Science in Mathematics University of Rizal System-Morong 2018

EXECUTIVE SUMMARY: The Menger Sponge (also known as the Menger universal curve) is a fractal curve. It is a three-dimensional generalization of the Cantor set and Sierpinski carpet, though it is slightly different from a Sierpinski sponge. It was first described by Karl Menger in 1926, in his studies of the concept of topological dimension. Sierpinski Triangle (also with the original Orthography Sierpinski), also called the Sierpinski gasket or the Sierpinski Sieve, is a fractal and attractive fixed set with the overall shape of an equilateral triangle, subdivided recursively into smaller equilateral triangles. Originally constructed as a curve, this is one of the basic examples of self-similar sets, it is a mathematically generated pattern that can be reproducible at any magnification or reduction. It is named after the Polish mathematician Waclaw Sierpinski, but appeared as a decorative pattern many centuries prior to the work of Sierpinski. The study entitled Analysis of Menger Sponge and Sierpinski Triangle was conducted at University of Rizal System located at Sumulong St., Morong Rizal. The researchers used the qualitative method because it is primarily explanatory research. It is used to gain an understanding of underlying reasons, opinions, and motivations. During the conduct of this study, the researchers were able to gather data for analysis. Based from the analysis, the researchers concluded that Menger Sponge and Sierpinski Triangle has a non-integer dimension that remains the same however stages or iteration has made. Menger Sponge can be made in some building block games like Minecraft which its' main purpose. Sierpinski Triangle can also be seen in the form of Pascal's Triangle, odd numbers are shaded in differently color from the even numbers. Those even numbers represents the removed triangular subsets.