On rotations as continuously-reflected translations

Image of PDF file - single page

rotatn_is_reflected_translatns.pdf is a pdf of a little diagram I created this morning, where I muse with the ideas of transformations and how we can express Rotations (and circularity or curvature) using “not” – the ‘omni-dimensional’ Reflection (how would you describe a zero-yet-infinity-dimensional thing? “multi-“? or “trans-“?).

I don’t know why I called those vectors in the diagram ‘rays’  – they’re vectors which describe a translation transformation.

If this is right, why would we need ‘curved’ non-Euclidean spaces?


2 thoughts on “On rotations as continuously-reflected translations

  1. You don’t if you use Conformal Geometric Algebra.
    See online papers on the Geometric Algebra developed by David Hestenes.Also see papers by Cambridge group.
    See ROTORS, Bivectors, Versors, Spinors, Lie Groups,

    1. Hi Paul, and thank you for visiting and doubly for taking the time to comment – such a rare gesture from visitors! 🙂

      In a happy coincidence, I have just this weekend happened across Conformal Geometric Algebra (I can’t remember how, sorry) and bookmarked a site to read later. I see the name ‘bivector’ and instantly Grassmannian Algebra came to mind – is that to what you are alluding? Is CGA a development of Grassmann’s algebra? Thank you once again for these references – I am but a humble and non-uni-educated person, so my journey to Lie Groups (though I’ve come across the name many times) will happen quite far down the road… I love maths, but it doesn’t love me… so my progress is slow. At least you’ve placed some milestones ahead of me so I know what to look for! Thank you!

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