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3/14なので円周率を計算する

Masayuki Mizuno
April 04, 2024
260

 3/14なので円周率を計算する

Masayuki Mizuno

April 04, 2024
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  1. ©2024 Wantedly, Inc. ڞ௨͢Δ܎਺ΛׅΓग़͢ ϗʔφʔ๏ͷཁྖ #JOBSZTQMJUUJOH๏ͷ࣮ྫ $IVEOPWTLZͷެࣜ΁ͷద༻  6403203 12π

    = ∞ ∑ k=0 (−1)n(6n)! (3n)!(n!)3 545140134n + 13591409 6403203n = 13591409 1 + (−1)6!(13591409 + 545140134) 3!(1!)36403203 + (−1)212!(13591409 + 2 ⋅ 545140134) 6!(2!)36403206 ⋯ = 13591409 + 1 ⋅ 1 ⋅ 5 1310939058860032000 ( (−1)(13591409 + 545140134) + 3 ⋅ 7 ⋅ 11 2310939058860032000 ((−1)2(13591409 + 2 ⋅ 545140134) + 5 ⋅ 13 ⋅ 17 3310939058860032000 (⋯)))
  2. ©2024 Wantedly, Inc. ༗ཧ਺ͰܭࢉΛਐΊΔͱߦྻੵʹؼணͰ͖Δ #JOBSZTQMJUUJOH๏ͷ࣮ྫ $IVEOPWTLZͷެࣜ΁ͷద༻  M N =

    1 ⋅ 1 ⋅ 5 1310939058860032000 ((−1)(13591409 + 545140134) + 3 ⋅ 7 ⋅ 11 2310939058860032000 ((−1)2(13591409 + 2 ⋅ 545140134) + 5 ⋅ 13 ⋅ 17 3310939058860032000 (⋯))) π = 4270934400N 10005(M + 13591409N) ( M N) = ( 1 ⋅ 1 ⋅ 5 1 ⋅ 1 ⋅ 5 ⋅ (−1)(13591409 + 545140134) 0 1310939058860032000 ) ( 3 ⋅ 7 ⋅ 11 3 ⋅ 7 ⋅ 11 ⋅ (−1)2(13591409 + 2 ⋅ 545140134) 0 2310939058860032000 )⋯( 0 1) আࢉ͸ߴίετͳͷͰ࠷ޙʹ·ͱΊͯߦ͏
  3. ©2024 Wantedly, Inc. CJHEFDJNBM ೚ҙਫ਼౓ͷුಈখ਺఺਺ϥΠϒϥϦ w ಺෦తʹ͸ਐ਺Ͱදݱ͍ͯ͠Δ w  

    ͕ͽͬͨΓʹͳΔ w ύϑΥʔϚϯε͸͋·Γྑ͘ͳ͍ σϑΥϧτHFN w 3VCZ࣌఺Ͱ͸ॲཧܥʹಉࠝ͞Ε͍ͯΔ w 3VCZ͔ΒCVOEMFEHFNʹͳΔΒ͍͠
  4. ©2024 Wantedly, Inc. HNQ (.1ٴͼ.1'3ͷ3VCZόΠϯσΟϯά w $Ͱ࣮૷͞Εͨஶ໊ͳϥΠϒϥϦ w ੑೳ͸ંΓࢴ෇͖ 3VCZόΠϯσΟϯάͷํ͸͋·Γϝϯς͞Εͯͳ͍

    w 3VCZҎ߱Ͱ͸CVOEMFJOTUBMMͷڍಈ͕ո͍͠ w ة͏͘3VCZͰ͔͠ಈ͔ͳ͍ԁप཰ܭࢉϓϩάϥϜ͕ੈʹग़Δॴͩͬͨ w 3BDUPS΋ରԠͯ͠ͳ͍
  5. ©2024 Wantedly, Inc. ࢖༻ͨ͠ϥΠϒϥϦຖͷԁप཰ܭࢉ଎౓ͷൺֱ ສܻ ສܻ ສܻ ສܻ ԯܻ *OUFHFS

    #JH%FDJNBM ඵ     *OUFHFS (.1' ඵ ඵ ඵ ඵ  (.1; (.1' ඵ ඵ ඵ ඵ ඵ
  6. ©2024 Wantedly, Inc. 3BDUPS 3VCZͰฒྻͳϓϩάϥϜΛهड़͢ΔͨΊͷػߏ w 3VCZ͔Βಋೖ͞Εͨ w "DUPSϞσϧʹجͮ͘ w

    3BDUPSؒͰϝοηʔδͷૹड৴͕ߦΘΕΔ͜ͱͰܭࢉ͕ਐΉ ֦ுϥΠϒϥϦ͸جຊNBJO3BDUPSͰ͔͠ಈ͔ͳ͍ w ޓ׵ੑͷͨΊ w ֦ுϥΠϒϥϦଆͰ3BDUPSʹରԠ͍ͯ͠ΔࣄΛද໌͢Δඞཁ͕͋Δ w HNQ͸ରԠͯ͠ͳ͍
  7. ©2024 Wantedly, Inc. ฒྻԽલޙͰͷԁप཰ܭࢉ଎౓ͷൺֱ ສܻ ສܻ ສܻ ສܻ ԯܻ 3BDUPSಋೖલ

    ඵ ඵ ඵ ඵ ඵ 3BDUPSಋೖޙ ඵ ඵ ඵ ඵ ඵ
  8. ©2024 Wantedly, Inc. ·ͱΊ 3VCZʹΑΔԁप཰ܭࢉϓϩάϥϜΛ࣮૷ ೚ҙਫ਼౓ܭࢉϥΠϒϥϦຖʹੑೳΛൺֱ w ಛผͳࣄ৘͕ແ͚Ε͹HNQΛ࢖͏ͱ଎͍ 3BDUPSͰฒྻ࣮ߦΛߦ͕ͬͨɺੑೳ͸৳ͼͳ͔ͬͨ w

    ฒྻ࣮ߦͰ͖ͳ͍($͕ϘτϧωοΫʹͳ͍ͬͯΔ w ࠷దԽΛߦ͏લʹTUBDLQSPGͰϘτϧωοΫΛ֬ೝ͠·͠ΐ͏ w ֦ுϥΠϒϥϦ͕3BDUPSʹରԠ͍ͯ͠ͳ͍৔߹΋͋ΔͷͰؾΛ෇͚͍ͨ