How many squares do we need to build the 1st iteration of a Menger sponge? Children can easily count this, if they chose 6 different colors to make it, such that all squares looking at the same face have the same color. In the picture below, we see for instance that the yelow exterior face has 8 squares, and we have 4 more yelow squares in the interior. This gives12 squares per color, so times 6 gives 72 squares. For the second iteration we would need 1056 squares!! We will try to make it soon. If you are interested on a mathematical formula for this and the nth-iteration of the Menger sponge, please visit our blog Juegos Topológicos.
|Here, we have pushed the corners to make this nice version with octogonal faces. The flexibility of this material allows to make new figures and shapes.|
Mathematics is always fun with 3D Polyfelt, but children also like to play and make its own figures and constructions!
|David Crespo with a Soma cube.|
|Lidia García making a kind of "dodecahedron" with 60 squares.|