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Quaternions and spherical trigonometry

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Re: Quaternions and spherical trigonometry

#2

Post by aap_ »

Interestingly showing spherical trig identities was how Hamilton demonstrated his quaternions to the royal irish academy when he found them. See (D) through (K): https://www.maths.tcd.ie/pub/HistMath/People/Hamilton/Quater...

When i first read this i found it very hard to understand, because i was unfamiliar with spherical trigonometry, but there's quite some beauty to be found there.

Re: Quaternions and spherical trigonometry

#7

Post by seanhunter »

gamedever wrote: post #4

[flagged]

Do you think Terence Tao doesn't understand Geometric Algebra? Just trying to understand where your hot take is coming from.

My working hypothesis is he has at least an understanding of most fields of advanced maths and if he's looking into something it's because he thinks something interesting is there. That carries a lot of weight.

Edit to add: he has done research into Quaternionic Hilbert spaces in the past https://pubs.aip.org/aip/jmp/article-abstract/37/11/5848/465...

Re: Quaternions and spherical trigonometry

#9

Post by Joel_Mckay »

seanhunter wrote: post #7
gamedever wrote: post #4

[flagged]

Do you think Terence Tao doesn't understand Geometric Algebra? Just trying to understand where your hot take is coming from. My working hypothesis is he has at least an understanding of most fields of advanced maths and if he's looking into something it's because he thinks something interesting is there. That carries a lot of weight. Edit to add: he has done research into Quaternionic Hilbert spaces in the past https…

Quaternions have niche use-cases that greatly simplify some problems that otherwise create ambiguities using naive approaches.

Many first encountered them in sensor fusion for IMU sensors, or 3D graphics. =3

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