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A University of Tartu student has come up with a new proof of the Pythagorean theorem using origami. While folding paper is already used, even in basic school, to demonstrate the well-known geometric principle involving right triangles, Karl-Robert Mõttus managed to do it without ever touching a pair of scissors.
To date, the Pythagorean theorem (which states that for any right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides) has been proven nearly 400 times.
Karl-Robert Mõttus, who recently defended his bachelor’s thesis at the University of Tartu, initially set out to demonstrate how one of the existing proofs doesn’t always hold. But what began as an attempt to challenge a known proof ultimately led to an entirely new one.
“My approach involves paper folding, more specifically, one-fold origami,” Mõttus explained. “That basically means that for every crease line to appear on the paper, we fold the paper and then unfold it again.”
In his proof, he used the side lengths of two similar triangles to demonstrate that the sum of the areas of the two similar triangles is equal to the area of the third, larger triangle.
According to one of the thesis supervisors, mathematics education lecturer Tiina Kraav, this solution is the most elegant of its kind.
“Karl-Robert was able to carry out the proof without going beyond the edges of the paper,” Kraav noted. “Previous proofs tend to go beyond the paper, or require cutting it.”
Folding isn’t just a fun activity for kids, it’s also something scientists and researchers do in laboratories, where each type of fold is accompanied by precise calculations.
“You can achieve a great deal with folding! Not just in math and in proving theorems,” said Kraav. “Folding is widely used in engineering, mechanics, gene technology and various other scientific fields.”
Mõttus admitted that it’s a treat to now be counted among researchers that have proven the famous geometry theorem. Even so, he acknowledged that the origami-based approach is easy for anyone to understand.
“Using folding is interesting in that it’s something you can actually assign to regular school students,” he said. “You can try it out and (understand) how some of the things we learn in math class in school can actually be applied.”
Thesis can be found HERE!
Author: Airika Harrik. This article was originally published on the the Estonian Public Broadcasting online news portal.
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