We had one correct answer to the Geek Challenge last month, and it came from Allen Hutchison of Smalley Steel Ring. The correct answer is D, that all three transformations are possible. Thanks to Han Yang for providing the content for the Malleable Mystery challenge. She found the images we used on a Chinese math blog. Allen’s solution was to do some Terminator style morphing and re-joining.
However, the transformations can also be done using continuous transformation, and without re-joining surfaces.
Just as the coffee cup to doughnut transformation is demonstrated by an animation, a great way to demonstrate a continuous deformation is to show a series of intermediate that show the transformation is possible.
The final step is the hardest to see, but because the shape has been turned inside-out and contains two big connected loops, those can be shrunken, and the material moved to the segment in-between.
I think the intermediate drawings make this one easier to understand, however the result seems even more paradoxical.
This one is the most complicated of the bunch. However, after a few moves it becomes the starting point for Challenge 1, and the same solution takes it to shape B.
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