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Post con #BaselProblem

#BaselProblem

Post pubblici su X che usano #BaselProblem.

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  1. Logic Geometry, Information@LGcommaI
    Velleman's simplification of Matsuoka's solution is the easiest rigorous solution of the #BaselProblem I've ever seen. It's easier than anything given by the English #Wikipedia as of 2020-09-23. No Fourier Analysis, no infinite-product-representation of sinc, no complex analysis.
    Scarica
    1412
  2. MathType@MathType
    Solving the #BaselProblem made Euler famous, but he did not stop there: within 5 years of calculating the infinite sum of the reciprocals of squares, he generalized his solution to any even power. The odd ones, however, remain mysterious #MathType #math #mathematics #mathfacts
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    1603039.7K
  3. MathType@MathType
    Solving the #BaselProblem made Euler famous, but he did not stop there: within 5 years of calculating the infinite sum of the reciprocals of squares, he generalized his solution to any even power. The odd ones, however, remain mysterious #MathType #math #mathematics #mathfacts
    Scarica
    0402328.9K
  4. Logic Geometry, Information@LGcommaI
    #BaselProblem in a tweet (Velleman). I(·):=∫_0^{pi/2}(·)dx,h(n,x):=(cos x)^{2n}, I_n:=I(h(n,x)), J_n:=I(x^2*h(n,x)). Integration by parts yields recursions that imply 1/n^2=2*(J_{n-1}/I_{n-1}-J_n/I_n), hence (1+..+1/n^2) =pi^2/6-2*J_n/I_n. Elementary to show: Remainder term→0.
    Logic Geometry, Information @LGcommaI
    Velleman's simplification of Matsuoka's solution is the easiest rigorous solution of the #BaselProblem I've ever seen. It's easier than anything given by the English #Wikipedia as of 2020-09-23. No Fourier Analysis, no infinite-product-representation of sinc, no complex analysis.
    113
  5. MathType@MathType
    Solving the #BaselProblem made Euler famous, but he did not stop there: within 5 years of calculating the infinite sum of the reciprocals of squares, he generalized his solution to any even power. The odd ones, however, remain mysterious #MathType #math #mathematics #mathfacts
    Scarica
    1392015.7K
  7. MathType@MathType
    Solving the #BaselProblem made Euler famous, but he did not stop there: within 5 years of calculating the infinite sum of the reciprocals of squares, he generalized his solution to any even power. The odd ones, however, remain mysterious #MathType #math #mathematics #mathfacts
    Scarica
    05723913.2K
  8. MathType@MathType
    Solving the #BaselProblem made Euler famous, but he did not stop there: within 5 years of calculating the infinite sum of the reciprocals of squares he generalised his solution to any even exponent. The odd ones, however, remain mysterious #Analysis #NumberTheory #MathType
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    0925
  9. Cliff Pickover✓@pickover
    Coin showing mathematician Leonhard Euler next to a beautiful formula. Russia.
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    22872
  11. The Huskies Pep Band@DaWGs
    You guys are probably familiar with the fact that you only need 39 digits of pi to calculate the diameter of the observable universe to within the width of a hydrogen atom... But did you know that Σ (1/n)^2 as n goes from 1 to infinity equals (π^2)/6 ? #baselproblem #happypiday
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    1417
  12. Paul Painlevé@Paul_Painleve
    @Paul_Painleve
    SG. Moreno, A One-Sentence and Truly Elementary Proof of the Basel Problem Chapman, Evaluating ζ(2) Josef Hofbauer, A Simple Proof of... Ed Sandifer, How Euler Did It #BaselProblem
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  13. Paul Painlevé@Paul_Painleve
    バーゼル問題 ζ(2)=1 + 1/2^2 + 1/3^2 + 1/4^2 + ... =π^2/6 には個人的に強い思い入れはないのですが、気がつけば何度かツイートしていたので、まとめというかわかりやすい文献紹介 #BaselProblem
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  14. Hal Tasaki@Hal_Tasaki
    Opening from Episode 6 of “Kamen-Rider Build”, a program (mainly) for kids. How nice that they are exposed to beautiful math! #BaselProblem
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    26281
  15. Cory Miller@vccmac
    💥 Think the Basel problem is “solved”? Think again. I just reframed it using the zero pattern of sin(x)/x—and it clicks in a way Euler never wrote down. \sum_{n=1}^{\infty} 1/n^2 = \pi^2/6, seen through a fresh lens. 🧠✨ #MathHack #BaselProblem #EulerWho #MindBlown
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  16. Paul Painlevé@Paul_Painleve
    @Paul_Painleve
    BW. Sullivan, Numerous Proofs of... D Daners, A short elementary proof of... INTEGERSブログ, バーゼル問題の高校数学範囲内で分かる証明 杉本敏夫, バーゼル問題とオイラー #BaselProblem
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  17. Paul Painlevé@Paul_Painleve
    @Paul_Painleve
    あとおまけ #BaselProblem
    Hal Tasaki @Hal_Tasaki
    Opening from Episode 6 of “Kamen-Rider Build”, a program (mainly) for kids. How nice that they are exposed to beautiful math! #BaselProblem
    012
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