Plate trick

<p>In <a href="/facts/Mathematics/pxTouaz4">mathematics</a> and <a href="/facts/Physics/a7aH2y08">physics</a>, the plate trick, also known as <a href="/facts/Paul_Dirac/6bt5yRdk">Dirac</a>'s string trick (after Paul Dirac, who introduced and popularized it), the belt trick, or the Balinese cup trick (it appears in the Balinese <a href="/facts/Candle_dance/nYAbUSj0">candle dance</a>), is any of several demonstrations of the idea that rotating an object with strings attached to it by 360 degrees does not return the system to its original state, while a second rotation of 360 degrees, a total rotation of 720 degrees, does. Mathematically, it is a demonstration of the theorem that <a href="/facts/SU(2)/Qgy2orcu">SU(2)</a> (which <a href="/facts/Double_cover_(topology)/bDRGasl7">double-covers</a> <a href="/facts/SO(3)/yXbKPzhT">SO(3)</a>) is <a href="/facts/Simply_connected_space/xFlta63J">simply connected</a>. To say that SU(2) double-covers SO(3) essentially means that the unit <a href="/facts/Quaternion/T3tnu7mX">quaternions</a> represent the <a href="/facts/Group_(mathematics)/IQTYqINt">group</a> of rotations twice over. A detailed, intuitive, yet semi-formal articulation can be found in the article on <a href="/facts/Tangloids/q3lnXU6B">tangloids</a>.
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Plate trick open-in-new

Plate trick