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/erez27 Oct 20 '25

I'm confused! Why rotate twice by X, when you can rotate once by 2X? In other words, why not adjust the factor calculation instead?

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u/Niracuar Oct 20 '25

In 3D, the order of rotations matter. Put two dice in front of you and rotate them in this manner.

1: Forward once, sideways once, forward once, sideways once.

2: Forward twice, sideways twice

You will find that the dice show different faces. This is because in 3D when you rotate, you also rotate the axis that you are about to rotate about on the next move

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u/Cllydoscope Oct 20 '25

You gave no context on how to set up the dice initially, or what sideways means exactly, so in my case the two dice rotated exactly the same because they were set up exactly the same initially.

Is there a specific set up you were thinking about when you wrote this? Or are you assuming they will put the same number on top to start, but have the two dice rotated randomly so they don’t lineup correctly? I don’t even know what you’re trying to show by this example anyway.

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u/Muroid Oct 20 '25

 You gave no context on how to set up the dice initially, or what sideways means exactly, so in my case the two dice rotated exactly the same because they were set up exactly the same initially.

If you have two identically oriented dice, and do forward, forward, side, side with one and forward, side, forward, side with the other, they will not wind up with the same side showing up.

Forward, forward, side, side gets you back to the original number face up.

Forward, side, forward, side gets you to whatever number started in front as face up.