What happens when this well-studied cube-like fractal is sliced on a diagonal plane? Try to predict the solution the puzzle before minute 3:25 in this video
From Simons Science News (find original story here).
The Menger Sponge, a well-studied fractal, was first described in the 1920s. The fractal is cube-like, yet its cross section is quite surprising. What happens when it is sliced on a diagonal plane? Try to predict the solution to the puzzle proposed in this video.
References:
The Menger Sponge (Wikipedia page)
Photo by Sébastien Pérez-Duarte
Related:
More videos from the Mathematical Impressions series.
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2 Comments
Add CommentIt is possible to visualize it quicker than the subsequent explanation in the video. If you wonder why the star is composed of regular triangles, you may look at minute 5:52. What is the shortest path connecting two opposite vertices of the cube and lying inside the sponge?
Reply | Report Abuse | Link to thisThis is nicely done content from Simons Science News! I prefer minutes 5:00-5:40, but I think it would be much clearer if each of the 'square' (rectangular) tunnels, and each of the rhombi slices, were differently colored. This would highlight the separate rhombus components of the six-sided star...
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