Here’s an article in English, written in simple language, inspired by the provided headline to encourage interest in science:
Shapes That Can Unfold! A Math Mystery for Everyone!
Have you ever loved playing with building blocks or origami? You know how you can fold flat paper into a cool 3D shape, like a box or a boat? Well, imagine if you could take a 3D shape, like a dice or a pyramid, and unfold it flat, like a special kind of puzzle!
This is a super cool idea that mathematicians have been thinking about for a very long time. In fact, even really smart people from thousands of years ago, like Plato, who was a famous philosopher, and Euler, a brilliant mathematician, were fascinated by this!
What’s a “Polyhedron”?
Let’s talk about shapes! We all know about squares and circles. But in the world of math, there are special 3D shapes called polyhedra. Think of them as shapes made of flat surfaces, like a dice (which is a cube) or a pyramid. These flat surfaces are called faces, and they meet at lines called edges, and at pointy corners called vertices.
The Amazing Idea of “Unfolding”
Now, imagine you have a shape made of cardboard. If you carefully cut along some of the edges, you could probably flatten it out into one connected piece of paper. This flattened-out shape is called a net or an unfolding of the polyhedron.
Think about a cardboard box. If you carefully cut along some of the corners and sides, you can lay it flat! That flat piece of cardboard is the net of the box. It’s like a special map that shows you how to fold it back into the 3D shape.
A Big Question: Can ALL Polyhedra Unfold?
Here’s where the mystery comes in! For many of the polyhedra we know and love, like cubes, pyramids, and even more complicated shapes, we can find these special unfolding nets. It’s like a secret code for building them!
But the big question that smart people like Plato and Euler wondered about is: Does every single polyhedron have one of these special unfolding nets?
Imagine a super, super complicated 3D shape. Could we always find a way to cut it just right so it lays flat into one piece without any parts overlapping or falling off?
Why Is This So Interesting?
This isn’t just about pretty shapes! Understanding how shapes can unfold helps us in many ways:
- Building and Design: Engineers use these ideas to design all sorts of things, from packaging for your favorite snacks to parts for airplanes! Knowing how to fold and unfold is important for making things efficiently.
- Art and Creativity: Artists use geometry and shape to create amazing sculptures and designs. Understanding nets can help them create even more interesting forms.
- Problem Solving: Math is all about solving puzzles! This is a big, exciting puzzle that mathematicians are still exploring. It teaches us to think carefully, test ideas, and never give up!
What’s Still a Mystery?
While we know many polyhedra have unfoldings, proving it for every single possible polyhedron is a really, really hard problem. It’s like trying to prove that you can untangle every single knot in the world!
Scientists and mathematicians are still working on this. They might use computers, draw lots of pictures, and try out different ideas to find the answer. Sometimes, even with all the smart brains working on it, some math puzzles can take a very, very long time to solve.
Your Turn to Be a Math Explorer!
You can be a math explorer too!
- Get some paper and scissors! Try making your own 3D shapes by folding paper. Can you unfold them again?
- Look at the world around you! What 3D shapes do you see? Can you imagine how they would unfold?
- Think about the big question: If you had a very strange 3D shape, could you figure out if it could be unfolded?
Science and math are full of amazing discoveries and intriguing mysteries, just waiting for curious minds like yours to explore them! Who knows, maybe one day you’ll be the one to help solve this ancient puzzle!
講談社 現代ビジネスに薬学科 西来路先生「プラトンもオイラーも定理を発見した！…それでも未解決の謎、果たして「すべての多面体」に「展開図」は存在するのか」の記事が掲載されました。
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The following question was used to generate the response from Google Gemini:
At 2025-08-19 05:35, 広島国際大学 published ‘講談社 現代ビジネスに薬学科 西来路先生「プラトンもオイラーも定理を発見した！…それでも未解決の謎、果たして「すべての多面体」に「展開図」は存在するのか」の記事が掲載されました。’. Please write a detailed article with related information, in simple language that children and students can understand, to encourage more children to be interested in science. Please provide only the article in English.