Arithmetic mean vs Geometric mean | inequality among means | visual proof



hi~

It’s quite hard to upload videos from china because of YouTube being banned, but I’ll be back home in two/three months and will be uploading more frequently (i will try at least).

Same thing with Patreon..

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Support my animations on:

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Any further questions or ideas:

Email – thinktwiceask@gmail.com

Twitter –

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Programs used:

– Cinema 4D

– Adobe Premiere Pro

– Processing
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Music:

“so far away” by outlax

Nguồn: https://alexakopyan.com

Xem thêm bài viết khác: https://alexakopyan.com/tong-hop/

42 Comments

  • awesome!!! when harmonic mean?

    Moonwatcher
    Posted July 28, 2020
  • Awesome ✴️✴️

    Mahmoud El-Bahnasawi
    Posted July 28, 2020
  • The explanation is great, though the music a bit "Silent Hill"-ish 🙂

    Pavel Sapehin
    Posted July 28, 2020
  • You didn't do it for negative numbers 🙁

    Bananaforscale
    Posted July 28, 2020
  • Great animation! It's very clear that h must always be less than or equal to r, but how would you prove that rigorously?

    Nick Georgopoulos
    Posted July 28, 2020
  • very nice. keep going.

    Rasoul Khoshravan
    Posted July 28, 2020
  • This is my motivation to start reading the 6th Book of Euclid.

    zeuperm
    Posted July 28, 2020
  • Simply loved it!

    Shailesh Dagar
    Posted July 28, 2020
  • My Mind: Booooooooooom

    Valor Kurzatx
    Posted July 28, 2020
  • What is this genre of music called and what else is similar? It's not something I would normally listen to but I really like it.

    Brett Cooper
    Posted July 28, 2020
  • Awesome, thanks

    Kerstin
    Posted July 28, 2020
  • What is this type of music called? Links to anything similar?

    Brett Cooper
    Posted July 28, 2020
  • What a superb geometrical proof! 🙂

    Nasim Hussain
    Posted July 28, 2020
  • Everything about this is wonderful.

    Brett Cooper
    Posted July 28, 2020
  • amazing!

    石安
    Posted July 28, 2020
  • Wait.. can someone explain how the 2 triangles had all equal angles?

    Rajdeep Gadgil
    Posted July 28, 2020
  • Can someone please explain this to me!

    I'm being very basic and saying that a and b are equal to 1 and 2, respectively.

    (a+b)/2= 1.5
    √ ab= √ 3= 1.732…

    Um……

    Omri Weininger
    Posted July 28, 2020
  • song??

    Valentina Balcazar Nuñez(Student)
    Posted July 28, 2020
  • what about harmonic mean?

    Hakan Ahmad Fatahillah
    Posted July 28, 2020
  • Can you create some visualization for milanimum questions ?

    Sanskar Suryawanshi
    Posted July 28, 2020
  • Nice visualization of the geometric mean. BTW how do you visualize the geometric mean of 3 numbers?

    Michal Nemecek
    Posted July 28, 2020
  • those who disliked thought it meant "download"

    Garo Garabed
    Posted July 28, 2020
  • Beautiful animation!

    HPP
    Posted July 28, 2020
  • Cool, what program for this animation?

    Farhan Karim
    Posted July 28, 2020
  • Sexy

    Natasa Djurdjevic
    Posted July 28, 2020
  • Nailed it

    Satvik Sharma
    Posted July 28, 2020
  • This only applies if a+b is equal or greater than 2

    The Guy That makes you mad
    Posted July 28, 2020
  • from 3b1b

    Lord Neo
    Posted July 28, 2020
  • From 3b1b amazing recommendation it was

    Mohit Jani
    Posted July 28, 2020
  • You're doing a great job. Keep it up. Your channel surely deserve more followers.

    Satyam Bhatia
    Posted July 28, 2020
  • Now how do we add the harmonic mean?

    Moises Moises
    Posted July 28, 2020
  • Can you do one on why n/2.5+n is roughly the square root of 2n^2

    Khai Quan-Nicholls
    Posted July 28, 2020
  • what if 1 number is -ve? then lhs could be +ve or -ve but rhs would always be imaginary. i think abs(rhs) would be larger than abs(lhs)

    and if both numbers are -ve? lhs would always be -ve and rhs always +ve. but abs both side will satisfy the original inequality

    Joel Koh
    Posted July 28, 2020
  • nice!

    erika mayumi
    Posted July 28, 2020
  • everything about this is perfect

    Jorge C. M.
    Posted July 28, 2020
  • This also shows that AM = GM only if a = b 🙂

    Nicholas Eugene
    Posted July 28, 2020
  • Mind blown

    Mayyousay HD
    Posted July 28, 2020
  • That smooth animation woah

    DrWaffles
    Posted July 28, 2020
  • very nice my friend

    Joe Siu
    Posted July 28, 2020
  • before watching: Is it because a square is the maximal way to get an area rather than a rectangle?

    edit: nope, your proof is much more visually appealing. I'm thinking of how to approximate square roots, and modeling them as rectangles is the easiest way to do so (which is why I thought of the comparison). The math also agrees

    Pharph
    Posted July 28, 2020
  • Lol, I still don't get why geometric mean is called geometric mean. It isn't as if it is the only mean with geometric significance.

    Rishabh Dhiman
    Posted July 28, 2020
  • Amazing. Please do upload more content.

    The Bnbrkr
    Posted July 28, 2020

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