This New Pyramid-Like Shape Always Lands With the Same Side Up
In 2023, Domokos – as well as his graduate students Gergő Almádi and Krisztina Regős, and Robert Dawson of the University of Saint -Mary in Canada – proved that it is indeed possible to distribute the weight of a tetrahedron so that it is seated on one side. 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 the 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 in a tenth of a gram and a tenth of a millimeter. But the final construction always rocks on a single side, just as it should.
The work demonstrates the important role of experimentation and game in research mathematics. It also has potential practical applications, as in the design of autonomous spacecrafts.
“I did not expect more work to go out on Tetrahedra,” said Papp. And yet, he added, the team search allows mathematicians “to really appreciate how much we did not know and how meticulous our understanding 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 worker who was constantly in 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 been to use a pencil and paper to prove, thanks to an abstract mathematical reasoning, that monostable tetrahedres exist. It would have been almost prohibitive difficult to locate a concrete example. But Almádi, working decades later, had computers. He could do a raw force research through a large number of possible forms. Finally, the Almádi program found the coordinates of the four peaks of a tetrahedron which, when they were allocated to certain weight distributions, were able to be made single. Conway was right.
Almádi found a single tetrahedron, but there were probably others. What properties have they shared?
Although this may seem a simple question, “a declaration like” a tetrahedron is single “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, allowing it to switch.
The 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 zones” – many smaller tetrahedral regions in the original shape. As long as the center of the mass falls inside a loading area, the tetrahedron will balance on a single side.
