360 Degrees is Not a Full Turn: A Ribbon, a Doll and the Mysterious, Wondrous Spinors and Quaternions
<p>I mean: croissants, chocolate crackles, cats, most people, Twergensisch Hubaskian Space Aardvarks of the 23rd Hasslonian Hyperplex, toilet brushes, T-Rexes, transcendentally meditating Sheep, kitchen sinks, acorns with love hearts drawn on them, chestnuts with carvings of Kate Bush on them (settle down, Selena), sex toys ….. anything i can think of, Selena, is left unchanged by a 360 degree turn!</p>
<p>No I haven't lost it! Listen up for something weird and worderful, good people! First, what precisely do we mean when we say that an object is untransformed by a 360 degree rotation? How about: its spatial relationships with everything around it are left unchanged by a 360 degree rotation? That seems to cut it, wouldn't you agree? Okay. Then Amber the Matryoshka Doll is here to tell you that she must rotate through 720 degrees — TWO FULL TURNS — to return to an unchanged state!</p>
<p>Wow! If that's so, then is 720 degrees the end of it? Or are there things in the world that must be rotated through three, four or another number of full turns to come back to their beginning state?</p>
<p>Here's another suprise from Amber — there are things that require a 360 degree rotation for restoration, some things…</p>
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