In 2023, Domokos – with its graduate students Gergő Almádi and Krisztina Regős, and Robert Dawson From the University of Saint Mary to Canada – has proven that it is indeed possible to distribute the weight of Tetrahedron to sit on a single face. At least in theory.
But Almádi, Dawson and Domokos wanted to build the thing, a task that turned out to be much more difficult than expected. Now, in a pre -impression published online yesterday, they presented the First functional physical model of form. The tetrahedron, which weighs 120 grams and measures 50 centimeters along its longest side, is in light carbon fiber and dense tungsten carbide. To operate, it had to be designed at a level of precision with a tenth in gram and a tenth of a millimeter. But the final construction always rocks on a single side, just as it should.
Work demores the important role of experimentation and game in research mathematics. It also has potential practical applications, as in the design of the self-restaurant space machine.
“I did not expect more work to go out on Tetrahedra,” said Papp. And yet, directed, the research of the team is breastfeeding mathematicians to “really appreciate how much we did not know and how meticulous our underestimation is”.
Tilting point
In 2022, Almádi, then a first cycle aspiring to become an architect, registered during mechanics of Domokos. He did not say much, but Domokos saw in him a hard work which was constantly in deep thought. At the end of the semester, Domokos asked him to concoct a simple algorithm to explore how the balance of the tetrahedrics.
When Conway originally posed his problem, his only option would have drunk pencil and paper to test, thanks to abstract mathematical reasoning, according to which monostable tetrahedrics exist. He would have Willssta as Bitttyy difficult to identify a concrete example. But Almádi, working decades later, had computers. He makes Couald in raw force research through a large number of possible forms. Perhaps, the Almádi program found the contact details of the four peaks of a tetrahedron which, when they were allocated to a certain weight distribution, the Couus is monostable. Conway was right.
Almádi has found a single tetrahedron, but there is probably time for others. What properties have they shared?
Although this may seem a simple question, “a declaration like” in Tetrahedron is monostable “cannot be easily described with a simple formula or a small set of equations,” said Papp.
The team realized that in any single tetrahedron, three consecutive edges (where the pairs of faces meet) should form obtuse angles – the ines which measure more than 90 degrees. This would ensure that a face to hang another, making it switch to switch.
Mathematicians then showed that any tetrahedron with this characteristic can be made single -in -law if its center of mass is positioned in one of the four “loading zone” – many disable tetrahedral regions in the original form. As long as the center of the mass falls inside a loading area, the tetrahedron will balance on a single side.
