“Impossible” pyramid always falls on the same face – and confirms theory at 40

Tetrahedron, with its pointed corners and small sharp angles on its four faces, was always the monostable object impossible to invent. Until a miracle of engineering undid this impossibility.

It’s called “BillAnd is the first monostable tetrahedron ever created: a pyramidal form with four triangular faces that has a stable resting position.

This means that the bizarre pyramid, regardless of how we shoot it and how it falls, will always be exactly with the same side down.

In a recently submitted to arXiva team of mathematicians reveals Bille’s first physical model, which confirms a proposed theory for decades by the renowned British mathematician John Conway.

Made of light carbon fiber and dense tungsten carbide, Bille is the result of a series of Ridiculately sophisticated engineering decisions—What makes it a technological achievement as mathematicssays the.

It is not surprising, therefore, that your self-repositioning property already has some potential interesting applications for the space industry– What recently went through Two accidents with lunar probes.

In its initial conjecture, Conway supposed that a tetrahedron with distributed weight unevenly on his faces would always return to the same side, although a few years Later Conway himself rejected The idea.

Some mathematicians continued, however, trying to prove the theory – including Robert Dawsonone of the co-authors of the study now presented, which in the 1980s almost got proofR that Conway was right using a tetrahedron made with a lead sheet and bamboo sticks.

“I remember that at the time I almost worked due to the moment angulaR, just as if a car goes through an obstacle on the road and is already moving, it will be able to exceed it thanks to the angular moment, ”says Dawson, a mathematician at Saint Mary’s University in Canada, Gizmodo.

Ideally, The monostable tetrahedron should not need another impulse to go back to the “base” side.

For a while, it seemed that Conway’s theory would end in a box of mathematical ideas very fixed but unlikely – Until about three years ago, when the mathematician Gábor Domokosfrom the University of Technology and Economics of Budapest, and the architectural student Gergő AlmádiDawson contacted.

Domokos, expert in Complicated Balance Problems in Geometryhad already discovered the Gömböca rounded object that balances only two points like a “always-in” toy, and that.

Although it was an impressive discovery, the Gömböc, with its design essentially round and multi-facedepresents relatively easy conditions for self-equilibrium, explains Domokos to Gizmodo.

The less sides a figure has and the smaller the angles on each side, more difficult is to make this figure monostabledetails the mathematician.

Imagine a six -sided data. “If it is a fair data, it will fall on each face with equal probability“, Explica Domokos.

Even if someone makes a glow and modifies the data, putting some extra weight on some surfaces, probability will change slightlybut it should still be possible that the data stand on all its faces.

“In that regard, The tetrahedron, with its pointed songs and small acute angles on its four faces, becomes the hardest problemthe highest category of forms in terms of monostability ” – except if someone disenchanted any kind of engineering miracle.

That’s what really happened. After deriving a theoretical model to calculate the dimensions of Bille, Almadi sought to build a structure that had somehow had A side made of “really heavy materialthe lighter parts almost air, And an almost empty skeleton“, Explica Domokos.

The team decided to use carbon tubes for the skeleton and, for the base, carbide of dense tungsten“A metallic connect twice as heavy than steel.”

Even after all this, a problem remained: for some reason, Bille continued to fall on two different sidesnot just on the intended side.

“So we looked at him, and there was umale drop of glue that was glued to one end! ” Exclaimed Domokos. Despite the guarantees of the chief engineer that it made no difference, Domokos insisted on removing the small drop Cola – Cuja density and shape were also calculated with ridiculous accuracy.

And so it was: the Bille entered the story of mathematics.

The engineers played a huge role to make this possible, highlights Domokos. “They They did all part of the creation process – Geometry, engineering and technological design. Everyone needed to fit. If you withdraw any of these, does not work“.