Sierpinski Pyramids
Description:
Sierpinski pyramids, or gaskets, are equilateral triangular pyramids formed by joining 4 smaller pyramids together in such a way that the larger pyramid is similar in shape to the original smaller pyramids.
Purpose:
Sierpinski pyramids serve as an introduction to the study of fractals, and are useful in exploring the concepts of similarity and iteration which are significant in art, math and science.
Connections & Applications:
Although the pyramid at first only appears to be a paper sculpture, it has many mathematical properties. Sierpinski pyramids demonstrate a mathematical principle called iteration. Iteration is when a single process is repeated over and over. The number of small pyramids in each stage is always a power of four. Interesting mathematical relationships appear when you compare surface areas and volumes of successive stages.