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1 A IT
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4 AV AV IT IT IT P P P (0<k<1 ) P A Grapes P Grapes P a P P P 8 4
5 相似な三角形における対応する点を結んだ直線の交点 P の描く軌跡 B` C C` a P θ a A B 4ABC 4AB`C` AC AB xrx AB` 辺比, AB xkx 相似比 {BACx{B`AC`xa 4AB`C`を,Aを中心に回転させたときの, 直線 ABから測った回転角を µ A(0, 0), B(1, 0), C(rcosa, rsina),b`(kcosµ, ksinµ),c`(krcos(µoa),krsin(µoa)) BB ksinµ xp(kcosµp1) yxksinµ 1 CC fksin(µoa)psinag xpfkcos(µoa)pcosag yxkrsinµ 2 a 1 xob 1 yxc 1 a 2 xob 2 yxc 2 x x c 1b 2 Pb 1 c 2, y x a 1c 2 Pc 1 a 2 a 1 b 2 Pb 1 a 2 a 1 b 2 Pb 1 a 2 P (x, y) a 1 b 2 Pb 1 a 2 xsina(k 2 O1P2kcosµ) c 1 b 2 Pb 1 c 2 xksinµfpkcos(µoa)ocosaokrcosµprg a 1 c 2 Pa 2 c 1 xksinµfkrsinµpksin(µoa)osinag x x ksinµfpkcos(µoa)ocosaokrcosµprg sina(k 2 O1P2kcosµ) 5
6 y x ksinµfkrsinµpksin(µoa)osinag sina(k 2 O1P2kcosµ) B` C P C` θ a α O B A BB` 2xk 2 O1P2kcosµ BC sina x2r BC 2 x1or 2 P2rcosa BCx 1Or 2 P2rcosa Rx 1Or 2 P2rcosa 2sina O POA AP 2 xr 2 OR 2 P2R 2 cos x2r 2 (1Pcos ) x (1Or 2 P2rcosa)(1Pcos ) 2sin 2 a AP 6
7 AP 2 xx 2 Oy 2 x k 2 sin 2 µ ËfPkcos(µOa)OcosaOkrcosµPrg 2 OfkrsinµPksin(µOa)Osinag 2 Ì sin 2 a(k 2 O1P2kcosµ) 2 x k 2 sin 2 µf(k 2 O1)(r 2 O1P2rcosa)P2kcosµ(r 2 O1P2rcosa)g... 付記 1 sin 2 a(k 2 O1P2kcosµ) 2 x k 2 sin 2 µ(r 2 O1P2rcosa)(k 2 O1P2kcosµ) sin 2 a(k 2 O1P2kcosµ) 2 x k 2 sin 2 µ(r 2 O1P2rcosa) sin 2 a(k 2 O1P2kcosµ) ( ) cos x1p 2sin2 a AP 2 1Or 2 P2rcosa x1p 2sin2 ak 2 sin 2 µ(r 2 O1P2rcosa) (1Or 2 P2rcosa)sin 2 a(k 2 O1P2kcosµ) x1p 2k 2 sin 2 µ k 2 O1P2kcosµ x k 2 O1P2kcosµP2k 2 sin 2 µ k 2 O1P2kcosµ x k 2 cos2µp2kcosµo1 k 2 O1P2kcosµ à xarccos k 2 cos2µp2kcosµo1 k 2 O1P2kcosµ k Ä cos x (k 2 cos2µp2kcosµo1) (k 2 O1P2kcosµ)P(k 2 cos2µp2kcosµo1)(k 2 O1P2kcosµ) (k 2 O1P2kcosµ) 2 8 の分子 x(p2k 2 sin2µo2ksinµ)(k 2 O1P2kcosµ)P2ksinµ(k 2 cos2µp2kcosµo1) xp4k 2 (k 2 O1)sinµcosµO8k 3 sinµcos 2 µo2k 3 sinµp2k 3 (1P2sin 2 µ)sinµ x4k 2 sinµf2kpk(1pcos 2 µ)p(k 2 O1)cosµg x4k 2 sinµfkcos 2 µp(k 2 O1)cosµOkg x4k 2 sinµ(kcosµp1)(cosµpk) 0 0<k<1 sinµx0, cosµxk cosµ 0 xk à xarccos k 2 (2k 2 P1)P2k 2 O1 k 2 O1P2k 2 xarccos 2k 4 P3k 2 O1 à 1Pk 2 xarccos (2k 2 P1)(k 2 P1) à 1Pk 2 Ä Ä Ä 7
8 xarccos(p(2k 2 P1)) xarccos(pcos2µ 0 ) x¼parccos(cos2µ 0 ) x¼p2µ 0 P AP ACP /2 2 x ¼ 2 Pµ 0 sin à 2 Äxsinà ¼ 2 Pµ 0 xcosµ 0 xk {ACPx 2 x arcsin k Ä P 2 2 x 4Aarcsin k (AP 2 )/k 2 sin 2 µ fpkcos(µoa)ocosaokrcosµprg 2 OfkrsinµPksin(µOa)Osinag 2 xk 2 (rcosµpcos µoa ) 2 O2k(rcosµPcos µoa )(cosapr)o(cosapr) 2 O fk 2 (rsinµpsin µoa ) 2 O2ksina(rsinµPsin µoa )Osin 2 ag xk 2 fr 2 (cos 2 µosin 2 µ)p2rfcosµcos µoa Osinµsin µoa gocos 2 µoa Osin 2 µoa g O2kfrcosµcosaPcos µoa cosapr 2 cosµorcos µoa gocos 2 ap2rcosaor 2 O2kfrsinµsinaPsin µoa sinagosin 2 a xk 2 fr 2 P2rcosaO1gO2kfrcos µpa PcosµPr 2 cosµorcos µoa go(r 2 P2rcosaO1) x(k 2 O1)(r 2 P2rcosaO1)O2k(2rcosµcosaPcosµPr 2 cosµ) x(k 2 O1)(r 2 P2rcosaO1)P2kcosµ(r 2 P2rcosaO1) x(r 2 P2rcosaO1)(k 2 P2kcosµO1) k=0.5 P POA y O θ α= Acos( ( k 2 cos2 θ 2 k cos θ + 1)/ ( k 2 2 k cos θ + 1) ) -20 k = 0.5 のとき 8
9 0<k<1 P 2 2α O 2α=4Asin(k) 180 /π k P b a P 0.5 a b k P k P Grapes 9
10 1 y y = a x O x 2-1 Grapes -2 y=ax 2 a -3-4 y=ax 2 +q q 9-5 Grapes y 10 y=a(x p) No.29 URL 9 PDF y = ax 2 + q 6 nal.html y=a(x p) 2 5 a =1, q =7 p 4 のとき, 3 y = x y O x y=ax 2 8 y = a ( x + p) +q 7 a =1,p =1 6 のとき, 5 x y = ( x + 1) 2 4 x O x
11 y=ax 2 y=ax 2 +q y=a(x p) 2 y=a(x p) 2 4 Grapes Grapes
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18 P80 2 (6/18) 1 Grapes PC 2 P81 26 (6/18) 1 Grapes PC
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More information1 26 ( ) ( ) 1 4 I II III A B C (120 ) ( ) 1, 5 7 I II III A B C (120 ) 1 (1) 0 x π 0 y π 3 sin x sin y = 3, 3 cos x + cos y = 1 (2) a b c a +
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2 3 4 (Neural Network) (Deep Learning) (Deep Learning) ( x x = ax + b x x x ? x x x w σ b = σ(wx + b) x w b w b .2.8.6 σ(x) = + e x.4.2 -.2 - -5 5 x w x2 w2 σ x3 w3 b = σ(w x + w 2 x 2 + w 3 x 3 + b) x,
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2 3 4 (Neural Network) (Deep Learning) (Deep Learning) ( x x = ax + b x x x ? x x x w σ b = σ(wx + b) x w b w b .2.8.6 σ(x) = + e x.4.2 -.2 - -5 5 x w x2 w2 σ x3 w3 b = σ(w x + w 2 x 2 + w 3 x 3 + b) x,
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