a quaternion version of Euler's formula

Comments · 283

• MR

  @MrDynamite110 · 3 years ago · pinned

  I think you should read the description.

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• SU

  @subpopulations · 3 years ago

  I really liked this video because of all the math this dude did. what a guy

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• TR

  @trueriver1950 · 3 years ago

  The reason we use H for the quarternions is only secondarily because the letter H stands for Hamilton.<br><br>Firstly: we can&apos;t use the now obvs is Q because that&apos;s already taken.<br><br>This is, of course, a rational reason.

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• SC

  @scottmiller2591 · 3 years ago

  Fun video. &nbsp;Lord Kelvin declared that quaternions, “though beautifully ingenious, have been an unmixed evil to those who have touched them in any way, including Clerk Maxwell” 👿

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• KA

  @kapoioBCS · 3 years ago

  I am waiting to see the octonions video with the nonassocietivity hell 😂

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• MA

  @manucitomx · 3 years ago

  What a gnarly way to start the week. <br>Thank you, professor.

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• TH

  @thefunpolice · 2 years ago

  God I love mathematics. It&apos;s so lovely to play with ideas in this way.

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• TE

  @Tehom1 · 3 years ago

  Fascinating, especially the last result which I hadn&apos;t seen before. &nbsp;<br>I find that an easy way to grasp quaternionic behavior under exponentiation is to see that any single quaternion (other than a purely real one) defines a complex sub-algebra of the quaternions and that sub-algebra behaves the same way as the complex numbers; its purely imaginary part, unitized, plays the same role as the complex number i. &nbsp;A lot of unintuitive stuff got much simpler when I understood that.

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• LO

  @lorisschirar6680 · 3 years ago

  Both of those formulae are special cases of the Clifford algebra formulation of 3D rotations :)

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• YA

  @YagyuBonze · 1 month ago

  i am so envious of this guy&apos;s chalkboard- legibility

• FE

  @felipegabriel9220 · 3 years ago

  wow, never though that i^j would be equal to i*j=k, thats is cool. Nice video as always Michael! :D

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• LA

  @la6mp · 3 years ago

  This is the first time quaternions made any sense to me, in spite of several attemps. As ususal presented in a clear no-nonsense way. Thanks a lot!❤

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