Summer of Math Exposition

Great video explaining geometric meaning of quaternions using images and equations. Might be better if one could show why it's better to use quaternions over 3-dimensional vector space.

Thanks for adding another quarternion video to the internet! There aren’t too many that visualize the rotations along with the proper math. I think I gorged on all of the ones I could find about a month ago

Lovely video! Much of this was already familiar to me from the 3B1B video, but it's always good to have more videos on difficult subjects like this. Well done!

Good pacing, which still leaves the need to go back at times, which is good because these are not topics you learn by just following the story once. I particularly liked the hand-drawn hands put in, as well as the handwriting. I did have trouble seeing the cube for a cube sometimes, and wonder if it would be possible to make this easier by making the further-away edges and corners a bit greyed out?

This was a great video! I know you've got much more on your channel, but for a submission like something like SoME, you may consider a brief intro where you discuss what kinds of math the viewer should be familiar with as they start watching. Your hook at the beginning with the sailboat is nice, but it is not clear what part of the screen is the quaternion that you are referring to. You and I know it's the number written at the top, but someone entirely unfamiliar may entirely gloss over the fact that there is a white-on-black number at the top (no box, no colors, no emphasis) and think that the colorful coordinate arrows in the center are what you are calling quaternions. Again thinking of the novice approaching this video, you may want to show a nifty example (with numbers!) of using this for rotation before diving right into what a quaternion is in general. Maybe present this as a "but how does this even work? how could we come up with this?" sort of hook. You called yourself out on this, but I wouldn't show the right multiplication by an inverse at the beginning. I loved how you showed the 3D rotation and 4th dimension rotating side-by-side; that was a very clever way to show why that flattening happens. You could then say that we want to keep the rotation happening in our 3 dimensions, but *invert* the rotation in that 4th dimension to introduce that quaternion inversion. Again, here I think a numerical example of how to compute that would have been beneficial, but time constraints do make things like that difficult. All in all, an excellent video! Very legible, even when switching to hand-writing, and the visual and conceptual transitions were smooth. My only reason for not rating it as "outstanding" is that you don't really establish who your mathematical audience is, which can be a turn-off to novices (who this is not catering toward) looking to get a handle on something like quaternions.

Nice intro. I was hooked right off the bat. I was begging for an animation, and then you put one in. Perfect! I appreciate the effort to try to visualize transformations in 4 dimensions.

extra points for impressive hand drawing

This taught me something useful, which should help with debugging 3D rotations.

Excellent

Couldn't get past the 5 minutes mark, sorry. I have no idea how the math is related to the things I see moving on the screen.

The pasing and explanation are on point. its easy to follow yet not too slow. The video has a very good grasp on what the viewer might have issues with, and points out that these issues will be addressed. For the animation of the rotation, i would, on top of giving the vectors different colours, also use different shapes/thicknesses. I would suggest making the base axes longer and thinner lines to prevent the sketch from looking too complex. It would also help if you were to point or emphasise what we are supposed to look at some other way. Overall its an amazing video of professional quality

Finally, I learned why the angle of rotation has to be divided by 2! Thank you! At first, I was a bit confused though, what the connection between r and q is.

I think the pacing made it feel a little slow and lecture-like at times, but this was very well made and animated. Only low marks are on novelty. Great work!

The multiplaction section was a little dry. That section could have been cut, especially the multiplication table. I would love more detail on f(p) = q.p.q^{-1} instead.

The animations are very beautiful. I like the color scheme, and I like how you mix hand-written formulas with automatic typesetting. Quaternions are very interesting, but also difficult to understand. Unfortunately, I have to say that this video went too quickly for me. Too many concepts were introduced at high speed. I think it might be better to split this video into a series of maybe 5 videos, so that the concepts can be introduced more slowly.

Doesn't explain all this can be used for - no follow up video channel on programming of this for games etc? Doesn't explain all the math eg what is _ over a letter?