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fermatslibrary's profile
Fermat's Library
Fermat's Library
Fermat's Library
@fermatslibrary

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Fermat's Library

@fermatslibrary

A platform for illuminating academic papers. We publish an annotated paper every week. Our chrome extension for arXiv: https://fermatslibrary.com/librarian 

fermatslibrary.com
Joined September 2015

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    Fermat's Library‏ @fermatslibrary 13 Apr 2019
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    • Report NetzDG Violation

    Arith. mean ≥ Geom. mean √a √b ░░ ░░ ▓▓ ▓▓ ▓▓ ▓▓ ░░ ░░ ▓▓ ▓▓ ▓▓ ▓▓ ▓▓ ▓▓ |||||| ||||||| ▓▓ ▓▓ ▓▓ ▓▓ |||||| ||||||| ▓▓ ▓▓ ▓▓ ▓▓ ▓▓ ▓▓ ░░ ░░ ▓▓ ▓▓ ▓▓ ▓▓ ░░ ░░ 2(√a)²+2(√b)²≥(√a+√b)² (a+b)/2≥√ab

    7:27 AM - 13 Apr 2019
    • 179 Retweets
    • 821 Likes
    • Melis Pavel V., MD PhD Sirved Azhak Abad Abad's Mathematical world s1291 David Olof von Unge darkness زَهراء نورالدين
    11 replies 179 retweets 821 likes
      1. Jonathan Mboyo Esole‏ @JMEsole 13 Apr 2019
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        Replying to @fermatslibrary

        The fact that the algebraic mean is greater or equal to the geometric mean can be seen as a direct consequence of the non-negativity of squares of real numbers. Here is a one-line proof using the binomial formula:pic.twitter.com/17ZBqSLF5B

        0 replies 13 retweets 88 likes
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      2. DℝOℕ∈‏ @d_r_o_n_e 13 Apr 2019
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        Replying to @fermatslibrary

        Interesting fact about geometric mean by Martin Rees: 'The geometric mean of the mass of a proton and the mass of the sun, ~ 55 kg; not far off the mass of an average person. It would take about as many human bodies to make up the mass of the sun as there are atoms in each of us.

        1 reply 6 retweets 28 likes
      3. Nicolò Bellini‏ @BelliniNicolo 13 Apr 2019
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        Replying to @d_r_o_n_e @fermatslibrary

        The geometric mean of the mass of a proton and the mass of the Sun is 57.687 +/- 0.007 kg while the mass of an avarage person is 62 +/- 5 kg so the two are perfectly compatible.

        0 replies 0 retweets 3 likes
      4. End of conversation
      1. Timothy Peterson‏ @nsquaredcrypto 13 Apr 2019
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        Replying to @fermatslibrary

        I wrote a book on this topic: http://riskbooks.com/performance-measurement-for-alternative-investments …pic.twitter.com/OwVcDgpn0f

        0 replies 0 retweets 2 likes
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      1. Anoop Manghat‏ @anoopman 13 Apr 2019
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        Replying to @fermatslibrary

        Isn't the starting point to state the following square can never be negative i.e. (√a - √b)^2 >=0 ...and then expand the right to get: √a+√b>=2√(ab) (√a+√b)/2 >= √(ab) A.M. >= G.M.

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      2. Gabor Szarnyas‏ @szarnyasg 13 Apr 2019
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        The large square has two ░ squares with an area of 2(√a)² and two ▓ squares with an area of 2(√b)², with the two dark ones potentially overlapping in the middle (denoted with ||). Therefore, the total area of these four squares is ≥ the area of the large square, (√a+√b)².

        0 replies 0 retweets 2 likes
      3. End of conversation
      1. Roger Sauer‏ @rsauer3473 13 Apr 2019
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        Replying to @fermatslibrary

        Laszlo Krepakian (1923-2002) during his formative grade school years teased Philomena Potterman excessively during math. In high school he let up some, but he was still mean when he put gum in her hair during geometry class.

        0 replies 0 retweets 1 like
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      1. baq domalaq‏ @baqdomalaq 13 Apr 2019
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        Replying to @fermatslibrary

        OK I got how you proved it. But didn't get the picture.

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      1. Benjamin Slayton‏ @SlaytonBenjamin 13 Apr 2019
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        Replying to @fermatslibrary

        I don’t understand what the block symbols are supposed to represent.

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