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算数の闇、世界の光

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August 23, 2019

 算数の闇、世界の光

社内 Tech Talk で算数について喋ったときのスライドです

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Y Enokida

August 23, 2019
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  1. ઌ΄Ͳͷओுͷݴ༿Λิ͏ ʮখֶߍͰʢ۩ମతͰ൚༻ੑͷͳ͍ʣ xx ࢉΛ΍Δͷແବ͔ͩΒʢΑΓந৅ తͰ൚༻ੑͷ͋ΔʣํఔࣜΛڭ͑Ε͹͍͍͡ΌΜʯ ҰൠԽ ʮখֶߍͰʢ۩ମతͰ൚༻ੑͷͳ͍ʣ xx Λ΍Δͷແବ͔ͩΒʢΑΓந৅త Ͱ൚༻ੑͷ͋Δʣ

    yy Λڭ͑Ε͹͍͍͡ΌΜʯ ۩ମྫΛ୅ೖ ʮখֶߍͰʢ۩ମతͰ൚༻ੑͷͳ͍ʣ௕ํܗͷ໘ੵͷެࣜΛ΍Δͷແବ͔ͩ ΒʢΑΓந৅తͰ൚༻ੑͷ͋Δʣଌ౓࿦Λڭ͑Ε͹͍͍͡ΌΜʯ
  2. খֶੜ޲͚ͱݴΘΕ͍ͯΔ໰୊ ͨͯ 3cmɼΑ͜ 5cm ͷ௕ํܗ͕͋Γ·͢ɽ໘ੵ͸͍ͭ͘Ͱ͔͢ɽ ౴͑ɿ15cm2 ͖ͬ͞ͷ๫࿦ʹج͍ͮͨ৔߹ ໰୊ͷਤܗ A ͸

    R2 ಺ͷۣܗͳͷͰɺಛʹՄଌू߹Ͱ͋Δɻ͕ͨͬ͠ ͯ A ͷࢦࣔവ਺͸ՄଌͰɺͦͷ Lebesgue ଌ౓ʹؔ͢Δੵ෼͸ Riemann ੵ෼ͰܭࢉͰ͖Δ͔Βɺࢦࣔവ਺ʹର͢Δ Fubini ͷఆཧ ͱซͤͯ R 1Ad— = R 3 0 R 5 0 dxdy = R 3 0 5dy = 15ɻ͕ͨͬͯ͠ٻ ΊΔ໘ੵ͸ 15cm2 Ͱ͋Δɻ ͜ΕΛখֶੜʹڭ͑Δ͜ͱʹͳΔ ͖͋Β͔ͳਓݖ৵֐
  3. ྫ୊ ࢞ͱຓͷஷۚͷ߹ܭ͸ 6600 ԁͰɺຓͷஷۚͷ 2 ഒ͸࢞ͷஷۚΑΓ΋ 1800 ԁଟ͍ͱ͖ɺຓͷஷۚ͸͍͘ΒͰ͔͢ɻ ղ౴ ຓͷஷۚΛ

    1 ‚ͱ͢Δͱɺ࢞ͷஷۚ͸ 2 ‚-1800 ͳͷͰɺ 3 ‚-1800=6600 Ͱ͋Δɻ͕ͨͬͯ͠ 3 ‚=8400 ͔ͩΒ 1 ‚=2800ɻͳͷͰ 2800 ԁɻ ஫ҙ 1 ‚Λ x ͱॻ͚͹ͨͩͷҰ࣍ํఔࣜͷ໰୊
  4. ઌఔͷղ౴ 6 ೥ੜʹ͸͍͍ͨͯཧղͯ͠΋Β͑Δ 5 ೥ੜ΋ଟ͘͸ཧղͯ͘͠ΕΔ 4 ೥ੜ͸ཧղͯ͘͠Εͳ͍ 1 ‚͕Կͳͷ͔Λཧղͯ͘͠Εͳ͍έʔε͕ଟൃ͢Δ ղܾ๏

    ઢ෼ਤΛॻ͘ 1 ‚ Λ໨Ͱݟͯ෼͔ΔܗͰද͢͜ͱͰɺ ʮม਺֓೦΁ͷ׳ΕʯΛ࡞Δ தߴͷ਺ֶͲ͜Ζ͔ੜ֔࢖͑ΔεΩϧɺແବʹ͢Δ΄͏͕೉͍͠