What does i^i = ?
1,617,554
Published 2017-09-12
Enjoy some more e^iπ with 3blue1brown's first video:
• e to the pi i, a nontraditional take ...
Plus the 2017 follow-up video with extra Group Theory:
• Euler's formula with introductory gro...
UPDATE: People have pointed out that I've been beaten to the video punch by blackpenredpen! They are also much more thorough about the multiple-value problem.
• i^i
If you don’t believe my value for i^i, I appeal to Wolfram Alpha.
www.wolframalpha.com/input/?i=i%5Ei
For those of you who just want to see the digits, here they are:
i^i = 0.20787957635076190854695561983497877003387784163176960807513588305541987728548213978860027786542603534052177330723502180819061973037466398699991126317864120573171777952006743376649542246381929737430538703760051890663033049700519005556200475866205294351834431843455027479745344769934714172383230815271481800760921074192047151878353489584821890186029582331295662952070823409567696363742039451439394183861901080820897771751705004348176454751714529894341134142...
CORRECTIONS:
None yet. Let me know if you spot anything!
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All Comments (21)
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"What is i^i?" Mathematician: Well, the math involved is actually quite beautiful, so first we employ this powerful technique... Physicist: It's about a fifth.
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-"Are you ready, kids?" -"0.20787..., captain." - "sqrt(-1) can't hear you." -"0.20787! Captain." -"ooooow"
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For the briefest moment, all the Tau fans held their breath that you had woken.
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"There are some nuances to keep an i on." 3:29
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I to the power of I? The result is pretty egotistic, I'd say
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i^i is a crying face what are you taking about.
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The thing about imaginary numbers is that they actually show up in real world physics, making them a real use. They’re in electrical engineering (well, that’s just a secondary method to avoid using complex differential equations, but I’ll count it), particle physics, relativity, and probably a lot more than I know about.
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"We should have a value of pi that is half the normal number!" Me: Ah, yes, quarter tau
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It's a Parker fifth
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you made a completely imaginary number real. In other words, you made dreams come true
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You know you haven't studied enough for the test when you read a question and on the little helper box it's written: "Approximate i^i to 0.21"
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i^i is a Parker Fifth. It's almost there, but it's cool anyway.
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"Parker identity"
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Is there going to be a party about i^i in 2078 ?
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Come on, StandupMaths. We made this video to go down a rabbit hole. You can’t just say “don’t worry about it.”
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2:23 Just want to highlight an amazing job pointimg at something that's not there
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"Eye to pie". My wife thought I was watching pies getting thrown in someone's eye.
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3:30 Some nuances to keep an i on, you say...
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Back in the olden days, the most controversial field of mathmatics, more controversial than zero, , more controversial than negative numbers , more controversial than irrational numbers , more controversial than immaginary numbers, was Stand-up Maths' perverse way of saying "on two" when the real way of saying it is "over two."
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"Although, you could argue I shouldn't just use two pi..." Me: Ayyy "Because it's just the angle 0." Me: AWWWWW YOU DID THAT IN PURPOSE
