3D Kirigami v. Clean Sheet of Paper
Hiro started with multiple clean sheets of paper. He wanted to learn more about the surface areas of 3D kirigami models. Kirigami is the variant of origami that involves both cutting and folding the paper (as the example shown above).
For the first one, he left it unfolded and uncut. Then, for the rest of the papers, he created distinct models by neatly cutting and extending the paper bases without extra use of papers and removing any portion.
After observing the surface areas of the objects, he claimed that
No matter how the model is decorated, it must have less surface area than the clean sheet of paper.
Based on the given information of the problem, is his statement true or false?
Clarification: Surface area refers to the total area of the surface of the object.
Image Credit : Pinterest.
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Imagine reverting all extended bases back to their original positions and smoothing the paper as shown above. Then, this turns into a simple case - finding the surface area of the original paper, which is the area of the paper. Thus, since there are no "holes" removed, regardless of the number of extended bases and the number of cuts, the surface areas remain the same .