{"id":312887,"date":"2025-10-18T07:59:12","date_gmt":"2025-10-18T07:59:12","guid":{"rendered":"https:\/\/www.europesays.com\/us\/312887\/"},"modified":"2025-10-18T07:59:12","modified_gmt":"2025-10-18T07:59:12","slug":"mathematicians-just-found-a-hidden-reset-button-that-can-undo-any-rotation","status":"publish","type":"post","link":"https:\/\/www.europesays.com\/us\/312887\/","title":{"rendered":"Mathematicians Just Found a Hidden ‘Reset Button’ That Can Undo Any Rotation"},"content":{"rendered":"

\"\" <\/a>Some of the many paths that can be taken through the mathematical space SO(3), corresponding to sequences of rotations in real space. Credit: Tsvi Tlusty.<\/p>\n

If you twist something \u2014 say, spin a top or rotate a robot\u2019s arm \u2014 and want it to return to its exact starting point, intuition says you\u2019d need to undo every twist one by one. But mathematicians Jean-Pierre Eckmann from the University of Geneva and Tsvi Tlusty from the Ulsan National Institute of Science and Technology (UNIST) have found a surprising shortcut. As they describe in a new study, nearly any sequence of rotations can be perfectly undone by scaling its size and repeating it twice.<\/p>\n

Like a mathematical Ctrl+Z, this trick sends nearly any rotating object back to where it began.<\/p>\n

\u201cIt is actually a property of almost any object that rotates, like a spin or a qubit or a gyroscope or a robotic arm,\u201d Tlusty told New Scientist<\/a>. \u201cIf [objects] go through a highly convoluted path in space, just by scaling all the rotation angles by the same factor and repeating this complicated trajectory twice, they just return to the origin.\u201d<\/p>\n

A Hidden Symmetry of Motion<\/p>\n

\"\" <\/a>A random walk on SO(3) shown as a trajectory in a ball of radius \u03c0, where a rotation R(n,\u03c9) is mapped to the point r=n\u03c9 and antipodal points are identified, n\u03c0 = \u2212n\u03c0 (the real projective space RP3). The walk traverses from the center (small red sphere) to the blue end. Crossing antipodal points is indicated by dotted lines. Credit: Physical Review Letters.<\/p>\n

Mathematicians represent rotations using a space called SO(3)<\/a> \u2014 a three-dimensional map where every point corresponds to a unique orientation. At the very center lies the identity rotation: the object\u2019s original state. Normally, retracing a complex path through this space wouldn\u2019t bring you back to that center. But Eckmann and Tlusty found that scaling all rotation angles by a single factor before repeating the motion twice acts like a geometric reset.<\/p>\n

So for example:<\/p>\n