3D Kirigami v. Clean Sheet of Paper

Geometry Level 3

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.
True False It depends on the models

This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try refreshing the page, (b) enabling javascript if it is disabled on your browser and, finally, (c) loading the non-javascript version of this page . We're sorry about the hassle.

2 solutions

Michael Huang
Jan 21, 2017

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 \boxed{\text{same}} .

Richard Landry
Jan 24, 2017

Not a solution but Gabriel's Horn

0 pending reports

×

Problem Loading...

Note Loading...

Set Loading...