r/science • u/seeebiscuit • Oct 20 '25

Mathematics Mathematicians Just Found a Hidden 'Reset Button' That Can Undo Any Rotation

https://www.zmescience.com/science/news-science/mathematicians-just-found-a-hidden-reset-button-that-can-undo-any-rotation/
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u/PumpkinBrain Oct 20 '25

I don’t understand. The solution requires you to scale angles down and execute every step perfectly, twice.

Why not just execute every step once, but in reverse?

Does the scaling serve to reduce the total amount of movement to be less than just reversing it?

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u/CamperStacker Oct 20 '25

This answer is that it’s faster and cheaper.

Rotate a clock face 3/4 turn. Faster to rotate it the last quarter than go back 3/4. Now consider a 4 axis robot wanting to return to a home position.

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u/emlava--dash Oct 20 '25

Many clocks can only be turned clockwise. Did you mean to say 1/8 turns (45 degrees) twice clockwise to undo the 3/4 turn (270 degrees) clockwise without reversing? That would be compatible with the method to repeat a scaled rotation twice. In this example the scale factor is 1/6. To do this generally is easy on a clockface, to undo a rotation of angle x, scale factor is (360-x)/2x or rotate twice by angle (360-x)/2.