e to the pi i for dummies
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Publicado 2015-12-24
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For this Christmas video the Mathologer sets out to explain Euler's identity e to the pi i = -1, the most beautiful identity in math to our clueless friend Homer Simpson. Very challenging to get this right since Homer knows close to no math!
Here are a couple of other nice videos on Euler's identity that you may want to check out:
• Math in the Simpsons: e to the i pi (one of our Math in the Simpsons videos)
• e to the pi i, a nontraditional take ... (by 3Blue1Brown)
And for those of you who enjoy some mathematical challenges here is your homework assignment on Euler's identity:
1. How much money does Homer have after Pi years if interest is compounded continuously?
2. How much money does Homer have after an imaginary Pi number of years?
3. As we've seen when you let m go to infinity the function (1+x/m)^m turns into the exponential function. In fact, it turns into the infinite series expansion of the exponential function that we used in our previous video. Can you explain why?
4. Can you explain the e to pi i paradox that we've captured in this video on Mathologer 2: • e to the pi i = -1 paradox .
If you own Mathematica you can play with this Mathematica notebook that I put together for this video
www.qedcat.com/misc/Mathologer_eipi.nb
Thank you very much to Danil Dmitriev the official Mathologer translator for Russian for his subtitles.
Merry Christmas!
Todos los comentarios (21)
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I feel like I'm cheating on numberphile but this guy is good
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i: Be rational! π: Get real! e: Stop fighting, you're gonna make me negative!
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"really awful to the power of awful"
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I remember seeing this video 3 years ago when I really was getting into maths and science. I could never make sense of how this could possibly work. What's nice about this video is that now I'm studying chemical physics and have the maths to fully understand this. Kind of nostalgic looking back on problems that I once was unable to grasp.
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If Euler's spirit were around, he would be so very, very pleased with this explanation!! Euler was known for simplified, and many, theoretical explanations for any given math "puzzle" (like e). He was not arrogant, his explanations were not configured to be hidden or difficult. He wanted everyone to enjoy/understand/be in awe of a given math puzzle - what this explanation does for this viewer. THANK YOU!!
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I seriously doubt Homer would be able to understand this.
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“This guide can be understood by anyone that knows how to do addition, subtraction, multiplication and division!” Uses exponents, graphs, imaginary numbers, funcions...
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Different school subjects' levels taught by youtubers: Anything else: middle school Math: University
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Thanks I now feel more stupid than Homer.
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You would have lost Homer @ 0:11 after you said "Pie"
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It took me more than a semester of teaching myself calculus, geometry, trigonometry and algebra but I finally understood a "for dummies" mathologer video :D
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I never never ever thought that I might see as strong visual proof for this amazing formula as this guy's👏🏻👏🏻👏🏻 this is so 100% enough
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e^πi = i²
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I like that quote "Really awful to the power of awful"
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Mathologer, you're one of the greatest explainers of math of all time. Loved this one!
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Fantastic. I didn't quite grasp complex multiplication and I definitely didn't understand e^πi but this gives me a solid starting point. Much appreciated even 7 years later.
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after so many years in my engineering life, first time to see what it means to multiply two complex number in graphical explanation. thanks.
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When m goes to infinity, it comes closer and closer to a Pokemon ball
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I am 14 and understood this. These videos are the types that remind me why I love math even tho my teacher is pretty bad since he spends the whole hour arguing with kids about eating in class and not teaching us. I love this video. Thank you for it :D
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Magnificent seeing it again so many years later and understanding more… bravo! What a great teacher!
