We love you Jeff! Make some more videos/ lectures on various mathematics topic! You are the best online Math lecturer I have ever seen!

@ProfJeffreyChasnov

Жыл бұрын

Thank you!

Professor! This is perhaps the best exposition of quaternions I ever came across. May many more people revel in mathematics and learn from teachers like you.

I was hoping if you could explain what Hamilton meant by the square point and how the allure thereof led him to make his subsequent assumptions.

Amazing video I learned a lot! Really liked the historical parts and I didn't know how strongly connected Quaternions were to vector calculus before watching

This was so instructive and interesting! Thank you Jeff!!!

Thanks Prof. Chasnov! As a physics student who is also into computer graphics, I find this video to be very informative!

Amazing Professor, I also thought, when you talk about the cyclical and anticyclical multiplication, in the Levi Civita symbole that you taught us in your vector calculus course. Thanks for this material. See you soon with much more content too learn from you.

Thanks!

Great video. Thanks!

Thankyou sir for this insight on this topic .... Really learnt something new today 🙏

Respect history, put knowledge into proper perspective and context, a great deeds!

Thank you professor for this amazing video

I had a superficial knowledge of quaternions but didn't know about the vectors war... nice video! Now cross product and vector product make more sense, too! 😀

brilliant explanation. thank you.

Thank a lot for such beautiful video

Hey there! Thanks for the video!

Very interesting. Please, more math history.

I love your videos, I wanna a teacher like you. Could you tell your journey of maths?

Thank U sir for mix up maths with real life example by animation interesting vision

Professor, i think you should add statistics part on Mathematics for Engineers Specialization. Because statistics is super important part of engineering. Thank you Prof.

Very good!

Would be interesting to do a video on why the cross product doesn't work in more than 3 dimensions. Which leaves onto Geometric Algebra. Interesting that there were attacks on Grassman. I didn't know that.

Legend!

I love math history!

I am a physics major and I was completely unaware of this history. That you for teaching me!

@ProfJeffreyChasnov

11 ай бұрын

Most people are unaware. Quaternions have really been buried in physics and math.

Thanks, great

Perfect

Hey Jeff! Cool video! I found out about it through your email. Keep sending me emails if they're gonna include videos like these!

Okay this make sense now

Great video! I found the title a little misleading though. I associate vector calculus with the gradient operator, and div and curl and so on. I was looking forward to seeing how quaternions work when using those operations. But the explanation seems to stop before it reaches the "calculus" part of vector calculus

From what I can tell, the problem seems to be that physicists were trying to use quaternions as points, when they're most definitely not points. The computer graphics crowd actually had the right idea in using them for rotations, because they _are_ rotations. If you're not trying to rotate things, then quaternions would just get in the way. That said, a lot of modern physics, especially quantum mechanics _is_ just rotating things, which is why the physicists have since independently rediscovered quaternions and called them "spinors," which is a much more descriptive name for them, though the notation they use is even _more_ obfuscated than the already obfuscated quaternions.

oy vey

"Maths" .... Wow, the correct word! I take it you're not American.

@ProfJeffreyChasnov

2 жыл бұрын

Haha! I am but I am fond of the s

@godfreypigott

2 жыл бұрын

@@ProfJeffreyChasnov Good to know. But, sorry, I feel the need to check other Americanisms: (1) Do you pronounce the c in Arctic? (2) Does "buoy" have one syllable or two? (3) [my biggest bugbear] Do you say "I could care less" or "I couldn't care less"?

@Nickle314

2 жыл бұрын

@@godfreypigottWrite me. One of the Americanisms I hate. The other is burglarized. Take a verb, turn into into a noun, then add an extension to make it back into a verb. Why not just use the verb?

@godfreypigott

2 жыл бұрын

​@@Nickle314 I can only think of "coronate" at the moment. What other examples do you have? I also hate extro, "gas" for petrol, takeout, "period" instead of full stop, cookies, "in the hospital" instead of "in hospital", "herb" without pronouncing the 'h', pronouncing "semi-" as "sem-eye", drapes, faucet, normalcy, sidewalk, "meet" instead of "meeting", and having no clue what a fortnight is. And one for any fellow mathematicians - saying "quantity squared" instead of "all squared".

@Nickle314

2 жыл бұрын

@@godfreypigott Out of your list, normalcy I agree. I also hate the rocket launches with 'nominal' instead of normal. On the write me, I suspect that was English when people left England for the US. Then in the 19th century the academics got to work and decided there has to be a preposition. Gas, short for gasoline, I don't object too. herb with no h is odd too. Another perhaps is Cilantro.

Does this guy actually know what’s he’s talking about or is he just reading a script😂😂😂😂😂

@ProfJeffreyChasnov

2 жыл бұрын

I wrote the script. What's your point?

Thanks!