Hash Fellow robcat2075 Posted September 10, 2018 Hash Fellow Share Posted September 10, 2018 Quaternions, the numbers that make bone rotations in A:M so much easier and more predictable than in Brand X Meet The Four-Dimensional Numbers That Led to Modern Algebra ...To see what makes 3-D rotation so much harder, compare turning a steering wheel with spinning a globe. All the points on the wheel move together in the same way, so they’re being multiplied by the same (complex) number. But points on the globe move fastest around the equator and slower as you move north or south. Crucially, the poles don’t change at all. If 3-D rotations worked like 2-D rotations, Baez explained, every point would move. The solution, which a giddy Hamilton famously carved into Dublin’s Broome Bridge when it finally hit him on October 16, 1843, was to stick the globe into a larger space where rotations behave more like they do in two dimensions. With not two but three imaginary axes, i, j and k, plus the real number line a, Hamilton could define new numbers that are like arrows in 4-D space. He named them “quaternions.” The article also has an interesting video with visualizations. Quote Link to comment Share on other sites More sharing options...
dahoacuongvungtau Posted December 10, 2018 Share Posted December 10, 2018 where video? Quote Link to comment Share on other sites More sharing options...
Recommended Posts
Join the conversation
You can post now and register later. If you have an account, sign in now to post with your account.
Note: Your post will require moderator approval before it will be visible.