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Project a – Classroom construction of Sierpinski Pyramids In this group project, a large Sierpinski pyramid is assembled by small pyramids that are made of cardboard paper, such as, a gift box from stores. Begin with a basic building-block pyramid with label "1," as shown.
Gluing together four basic pyramids, we get a larger Sierpinski pyramid with label "2," which is twice taller than the basic pyramid. Now, by assembling four Sierpinski pyramids with label "2," the Sierpinski pyramid with label "4" is formed, which is four times taller than the basic pyramid. If desired, the construction of taller Sierpinski pyramids can be carried out in a similar fashion. A pattern for 3-sided pyramids is provided here, and the solid line is for equilateral-triangle pyramid.
Return to main text Project b – Classroom construction of Menger sponges The objective of this group project is to build up the Menger sponges containing 20 and 400 basic cubes, respectively, as shown.
The basic building-block cubes of side, say, 1 inch are made out of cardboard paper (for instance, a gift box from stores). We then construct the Menger sponge with label "3" by putting together 20 basic cubes as shown
Similarly, we assemble 20 Menger sponges with label "3" to form the Menger sponge with label "9" by the same scheme as shown above. It requires in all 400 (= 20 x 20) basic cubes. Can you estimate the number of basic cubes required to construct the next generation Menger sponge with label "27"? Return to main text |
