㸳 ᅗ㸯ࡢࡼ࠺㸪ᗏ㠃ࡢ༙ᚄࡀ 㸼 㸪㧗ࡉࡀ ࡒࢀⅬ 㸪 ࡀ࠶ࡿࠋࡇࡢᰕࡢഃ㠃ࢆ㸪Ⅼ 㸼 ࡢᰕࡀ࠶ࡾ㸪㸰ࡘࡢᗏ㠃ࡢ࿘ୖࡑࢀ ࡽⅬ ࡲ࡛㸪ୖࡽぢ࡚ィᅇࡾࡢᩳࡵ᪉ྥࡢ᭱ ▷⤒㊰ࡑࡗ࡚ษࡾ㛤࠸ࡓᖹ⾜ᅄ㎶ᙧࡢࡑࢀࡒࢀࡢ㡬Ⅼࢆ㸪ᅗ㸰ࡢࡼ࠺㸪 ′ ′ ࡍࡿࠋ ᅗ㸯 ᅗ㸰 ͛ ͛ ͛ ͛ ࠸ࡲ㸪ᅗ㸰ࡢᖹ⾜ᅄ㎶ᙧ ′ ′ ࠾࠸࡚㸪Ⅼ ࡀⅬ ′ 㸪Ⅼ ′ ࡀⅬ 㔜࡞ࡿࡼ࠺ࡵ㸪᪂ࡓ ࡞ᰕࢆࡘࡃࡿࠋ ඖࡢᰕࡢయ✚ࢆ 㸪᪂ࡓ࡞ᰕࡢయ✚ࢆ ඖࡢᰕ࠾࠸࡚ഃ㠃ࢆⅬ ࡽⅬ ࡕࡻ࠺ഃ㠃ࢆ㸯࿘ࡍࡿࡼ࠺㸪Ⅼ ࡍࡿࡁ㸪ḟࡢၥ࠸⟅࠼࡞ࡉ࠸ࠋ ࡲ࡛ษࡾ㛤ࡃࡁ㸪Ⅼ ࢆࡿⅬ ࡽᩳࡵ᪉ྥ ࡢࡕࡻ࠺┿ୗⅬ㹀ࡀ࠶ ࡾࡲࡍࠋࡇࡢࡁ㸪 ձ 㸻 㸪 㸻 ࡍࡿ㸪 㸪 ࡣ࠸ࡃࡽ࡞ࡿồࡵ࡞ࡉ࠸ࠋ ࡞࠾㸪ゎ⟅⏝⣬ࡣ⟅࠼ࡢࡳࢆ᭩ࡁ࡞ࡉ࠸ࠋ ղ 㸪 ࡀࡢࡼ࠺࡞್ࡢࡁ࡛ࡶ㸪 㸻 㸺 ࡞ࡿࡇࢆ♧ࡋ࡞ࡉ࠸ࠋ ࡞ࡿࡓࡵࡣ㸪ඖࡢᰕ࠾࠸࡚ഃ㠃ࢆⅬ ࠸ࡃࡽ࡞ࡿࡼ࠺Ⅼ 㸪 ࡽⅬ ࡲ࡛ษࡾ㛤ࡃࡁ㸪ࡑࡢ㛗ࡉࡀ ࢆࢀࡤࡼ࠸㸪ồࡵ࡞ࡉ࠸ࠋࡲࡓ㸪ࡑࡢࡁࡢ㸪 ࡀ‶ࡓࡍࡁ ᮲௳ࢆồࡵ࡞ࡉ࠸ࠋ 㹙ฟ㢟ࡢࡡࡽ࠸㹛 ✵㛫ᅗᙧࢆࡑࡢࡲࡲࡢᙧ࡛ᖹ㠃ୖ⾲⌧ࡍࡿࡇࡣ࡛ࡁ࡞࠸ࡓࡵ㸪✵㛫ᅗᙧࡢ≉ᚩࢆㄪࡿࡓࡵᒎ 㛤ᅗࢆ࠸ࡓࡾ㸪ᖹ㠃ୖࡢ⾲⌧ࡽ✵㛫ᅗᙧࡢᛶ㉁ࢆㄞࡳྲྀࡗࡓࡾࡍࡿࡇࢆ㸪୰ᏛᰯᩘᏛ࡛Ꮫ⩦ࡋ࡚ ࠸ࡿࠋ ࡇࡢၥ㢟࡛ࡣ㸪ࡑࡢࡇࢆ㋃ࡲ࠼㸪✵㛫ᅗᙧ㸦ᰕ㸧ࡢᒎ㛤ᅗ࡛࠶ࡿᖹ㠃ᅗᙧ㸦ᖹ⾜ᅄ㎶ᙧ㸧ࢆࡁ㸪 ࡉࡽ㸪ࡑࡢᖹ㠃ᅗᙧࡽ㸪ู࡞✵㛫ᅗᙧࡢᛶ㉁ࢆㄞࡳྲྀࡿࡇࢆ㏻ࡋ࡚㸪ᅗᙧࡢᛶ㉁ࡢ᰿ᗏ࠶ࡿᮏ ㉁ⓗ࡞ࡶࡢࢆぢᢤࡃ┤ほຊࡸ㸪ࡑࡢᛶ㉁ࢆㄽ⌮ⓗ⪃ᐹࡋ⾲⌧ࡍࡿ⬟ຊࢆぢࡿࡇࡋࡓࠋ 㹙ゎ⟅㹛 =π × × = π ᪂ࡓ࡞ᰕࡢᗏ㠃ࡢ༙ᚄ ′ 㸪㧗ࡉ ′ ࡍࡿ㸪 ձ π + π π π + ࡼࡾ㸪 ′ = π ′= π + ࣭ ′ = π ࡼࡾ㸪 ′ = ͛ π + = π π ͛ ͛ π + ղ ձྠᵝ π = =π π + π = π ′ ′ = π࣭ ࡼࡗ࡚㸪 㸪 + ′ π ࣭ = π + ͛ π + π + ࢆồࡵࡿ㸪 ࣭ π = + ࣭ = π ࣭ ࡇࡇ࡛㸪 π π + ࡢᑠࢆẚࡿ π 㸺 ࡼࡗ࡚㸪 㸪 ࡢ್ࢃࡽࡎ㸪 < π + ࡞ࡿࠋ ࡀᡂࡾ❧ࡘࠋ ษࡾྲྀࡿ㛗ࡉ ′= π ࡼࡗ࡚㸪 㸪 ′= ′ = ′ = ࡍࡿ㸪ྠᵝ㸪 ͛ π = π ′ ′ = π࣭ π π ࣭ ͛ = ͛ = ࡼࡾ㸪 π = ∴ = π ′ = ′ = π ࡞ࡿࡼ࠺Ⅼ 㸪 ࢆࢀࡤࡼ࠸ࠋ ′ ′ ࡣࡦࡋᙧ࡞ࡾ㸪 ′ = 㸪 ′ = 㸧 㸦ᅄゅᙧ ࡇࡇ࡛㸪 > ࡞ࡽ࡞ࡅࢀࡤ࡞ࡽ࡞࠸ࡢ࡛㸪 < π ࡛࠶ࡿࠋ ࡼࡗ࡚㸪ษࡾཱྀࡢ㛗ࡉࡣ π 㸪 ࡀ‶ࡓࡍࡁ᮲௳ࡣ㸪 < π ࡍ࡞ࢃࡕ ͛ 㹙ㅮホ㹛 ၥ㢟ࢆゎࡃࡣ㸪᪂ࡓ࡞ᰕࡢᗏ㠃ࡢ༙ᚄ㧗ࡉࢆ㸪ඖࡢᰕࡢᗏ㠃ࡢ༙ᚄ㧗ࡉ࡛⾲ࡍࡇࡀᚲせ ࡞ࡿࠋ࣏ࣥࢺ࡞ࡿࡢࡣḟࡢ㸰Ⅼࠋ ࣭ഃ㠃ࢆษࡾ㛤ࡃᩳࡵࡢ┤⥺ࡀ㸪᪂ࡓ࡞ᰕࡢᗏ㠃ࡢ࿘࡞ࡿࡇẼࡃࠋ ࣭ഃ㠃ࢆษࡾ㛤࠸ࡓᅗᙧ㸦ᖹ⾜ᅄ㎶ᙧ㸧ࡢ㠃✚ࢆ㸰㏻ࡾࡢ᪉ἲ࡛⾲ࡏࡿࠋ ࡲࡓ㸪ᖹ⾜ᅄ㎶ᙧࢆࡵ࡚㸰✀㢮ࡢᰕࢆࡘࡃࡿࡁ㸪ࡑࡢయ✚ࡀ➼ࡋࡃ࡞ࡿࡢࡣ㸪ࡶࡢᖹ⾜ᅄ㎶ ᙧࡀࡦࡋᙧࡢࡁ࡛࠶ࡿࠋࡇࡢࡇẼࡅࡤ㸪ṇゎ㏆࠸ࡇࢁࡲ࡛ゎ⟅࡛ࡁࡓࡢ࡛ࡣ࡞࠸ࠋ ࡇࢀࡽࢆぢᢤࡃࡓࡵᚲせ࡞ࡢࡣ㸪ᅗᙧᑐࡍࡿ┤ほຊࡸὝᐹຊ㸪ࡘࡲࡾ㸪ᅗᙧࡢᛶ㉁ࡢ᰿ᗏ࠶ࡿ ᮏ㉁ⓗ࡞ࡶࡢࢆぢᢤࡃ㈨㉁࣭⬟ຊ࡛࠶ࡿࠋࡑࢀࡽࡣ㸪ㄽ⌮ⓗ࡞ᛮ⪃ຊᡴࡕࡉࢀ࡚࠸ࡿࡇࡀᚲせ࡛ ࠶ࡾ㸪㏫㸪ㄽ⌮ⓗ࡞ᛮ⪃ࢆᑟࡃࡣࡓࡽࡁࢆࡍࡿࡇࡶ࠶ࡿࠋ㧗➼Ꮫᰯ࠾ࡅࡿᩘᏛᏛ⩦⯡ࢆ㏻ࡋ࡚㸪 ࡑࢀࡽࢆࡋࡗࡾ㌟ࡅ࡚ࡶࡽ࠸ࡓ࠸ࠋ
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