A B 5 C mm, 89 mm 7/89 = 3.4. π 3 6 π 6 6 = 6 π > 6, π > 3 : π > 3

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1 π π π p N p N

2 A B 5 C mm, 89 mm 7/89 = 3.4. π 3 6 π 6 6 = 6 π > 6, π > 3 : π > 3

3 . r πr πr n n n n r πr r πr = πr : (4.3 B a O C A 3: N p N N s N s N p N 3

4 N a p N = (N a/ = Na 3 OA =, BC = a OAB s N = (N a = a ( a = Na = p N ( N s N N p N N s N = p N π π.4 π a r = na S S = πr = πn a M B Ma < S = πn a < (M + Ba, M n < π < M + B n a =, r = n ( n π (. n = 4 π (M, B /4 4.5 ( ( x- y- k /4 N x- P k = N,, k =,,..., N P k y- Q k Q k = k ( k N, N 4

5 4: π 5

6 Q k R k Q k O P k P k 5: (N = A Q k Q k+ O P k P k+ 6: (N = A 6

7 Q k x- P k Q k R k /4 π/4 P k P k Q k R k k =,,..., N ( 5 /4 π/4 P k P k+ Q k+ Q k k =,,..., N ( 6 N k= ( k < π N N 4 N N k= N 4 < k= N k < π < 4 N ( k. N N N k= N k. ( N π ( 4/N N = 3.4 < π < N = ( π. N N a N b N a N b 7 OBA = EBD OAB EDB OA =, ED = AE = b, AB = b OA : ED = AB : DB, : b = b : DB, DB = bb. (3 ODC = EBD OCD EDB OD =, EB = AB AE = b b, CD = a OD : EB = CD : BD, : (b b = a : BD, BD = a(b b. (4 (3 (4 bb = a(b b, b (a + b = ab, b = ab a + b. (5 OAF = DAC OF A DCA OA =, DA = F A = a, AF = a OA : DA = AF : AC, : a = a : AC, AC = a. (6 7

8 D B a F E b a b O C A 7: EOA = AOF OAE OF A OAE DCA OA =, DC = a, AE = b OA : DC = AE : CA, : a = b : CA, CA = ab. (7 (6 (7 a = ab, ab a =. (8 N p N N q N p N = Na, q N = Nb, p N = Na, q N = Nb a = p N /N, b = q N /N, a = p N /(N, b = q N /(N (5, (8. q N = p Nq N p N + q N p N = p N q N (p N q N, (p N q N. 8

9 6, 4, p 6 = 3, q 6 = 3 q = = ( 3, p = 3 ( 3 = 6 3. p N < π < q N n =, 3.58 < π < 3.53, n = 4, 3.36 < π < 3.596, n = 48, < π < 3.46, n = 96, 3.4 < π < 3.47, n = 9, 3.44 < π < π p N, q N N =, 4, 48, 96, 9. a, b A(a, b = a + b, G(a, b= ab, H(a, b = ab a + b A(a, b a b, G(a, b, H(a, b A(a, b G(a, b a = b 4(A(a, b G(a, b = (a + b 4ab = a + ab + b 4ab ( A a, = b = a ab + b = (a b. ( a + = a + b b ab = H(a, b 9

10 ( H(a, b = A a, ( G b a, = b ab, H(a, b ab = G(a, b H(a, b G(a, b A(a, b max(a, b = { a, a b, b, a < b, min(a, b = { a, a b, b, a > b, a max(a, b, b max(a, b A(a, b = (a + b (max(a, b + max(a, b = max(a, b a min(a, b, b min(a, b ( A a, = ( b a + ( b min(a, b + = min(a, b min(a, b, H(a, b = A (, min(a, b. a b min(a, b H(a, b G(a, b A(a, b max(a, b p N < q N q N = H(p N, q N, p N = G(p N, q N p N < p N < q N < q N p 3 n q 6 α q 3 n p 6 β n q 3 n+ = H(p 3 n, q 3 n β = H(α, β = αβ α + β α + αβ = αβ, α = αβ, α = β α π

11 3 3. p N p N N 6 p N p N 7 DCA DC = a, CA = a, DA = a a + (a = (a a = p N /N, a = p N /(N p N N + p4 N 4N = p N 4 N, p4 N 4N p N + 4N p N =, p N = N ± = N ( N ± p N = N 4N 4 4N p N = N ± N N p N. N p N p N < q N < q 6 = 3 ( N, p N = N N p N ( N N p N. (9 3. (64? 78 a n = p 3 n {a n } a n+ a n a n+ a n+ a n+ a n.5 = 4 t N = N N p N N p N = Nt N, N ( t N = p N, N t N = N p N N N (9 p N = N ( N (N t N = (N p N N p N = N ( t N, (N t N = (N p N = 4N N ( t N = N ( + t N.

12 n 3 n a n+ a n+ a n a n+ a n a n+ a n : t N = ( + t N, p Nt N = N ( t N ( + t N = N ( t N = p N. p N t N = p N, t N = ( + t N ( ( N = 3 n a n = p N, a n+ = p N ( t N = p N (N a n+ a n = p N p N = p N p N t N = p N ( t N = p N( t N + t N p 3 N = (N ( + t N. a n+ a n+ = p 4N t 4N = p N a n+ a n+ = p 3 4N (4N ( + t 4N. p 3 N (4N t 3 4N ( + t 4N.

13 a n+ a n+ a n+ a n = p3 N (N ( + t N p 3 N (4N t 3 4N ( + t 4N = + t N 4t 3 4N ( + t 4N n N = 3 n p N π t N = N N p N = p N N t N, t 4N ( a n+ a n+ a n+ a n = + t N 4t 3 4N ( + t 4N + 4( + = 4 (. n a n+ a n+ a n+ a n a n π b n b n = 4a n+ a n ( 3 n b n 4π π 3 = π b n+ b n = 4a n+ a n+ 4a n+ a n 3 3 = 4(a n+ a n+ a n+ a n 3 = 4(a n+ a n 3 ( 3 an+ a n+ a n+ a n 4 n b n a n π π 6 4. a n ( b, b, b 3, b 4, b 5 3

14 ([] ( ([] 4. < r < S n = + r + r + + r n + r n rs n = r + r + r r n + r n+ S n rs n = r n+, ( rs n = r n+, S n = rn+ r n r n+ + r + r + + r n + r n + = lim n S n = r (3 r = = OA =, AC = a OAB S(a < a S(a a < r < n AC C n AC n = ar n C = C OC n B n B n OC n D n OC n C n C n C n = r n a r n a = a( rr n a( rrn OB n D n OC n C n OB n =, OC n = + a r n 4

15 : = C B D D B D 3 B B 3 C C C 3 a O 9: A 5

16 OB n D n OC n C n : ( + a r n OB n D n a( rr n ( + a r n = a( rrn n =,,... n= a( rr n ( + a r n ( a r n + a 4 r 4n a 6 r 6n + a( r a( rr a( rr a( rr3 = ( + a r ( + a r 4 ( + a r 6 ( + a r 8 + a( r ( = a r + a 4 r 4 a 6 r 6 + a( rr ( + a r 4 + a 4 r 8 a 6 r + a( rr ( + a r 6 + a 4 r a 6 r 8 + a( rr3 ( + a r 8 + a 4 r 6 a 6 r a( r ( = a r + a 4 r 4 a 6 r 6 + a( r ( + r a r 5 + a 4 r 9 a 6 r 3 + a( r ( + r a r 8 + a 4 r 4 a 6 r + a( r ( + r 3 a r + a 4 r 9 a 6 r

17 a( rr n a( r = ( + r + r + r 3 + ( + a r n n= a( r (a r + a r 5 + a r 8 + a( r + (a 4 r 4 + a 4 r 9 + a 4 r 4 + a 4 r 9 + a( r (a 6 r 6 + a 6 r 3 + a 6 r + a 6 r 7 + a( r = ( + r + r + r 3 a( r + a r ( + r 3 + r 6 + a( r + a 4 r 4 ( + r 5 + r + r 5 + a( r a 6 r 6 ( + r 7 + r 4 + r + ( a( r = r a r r + a4 r 4 3 r a6 r 6 5 r + 7 = (a a3 r + r + r + a 5 r 4 + r + r + r 3 + r a 7 r r + + r +. 6 r OB n D n OAB S(a r a n+ r n an+ + r + + rn n + S(a = (a a3 3 + a5 5 a (4 a = OAB π /8 8 π = S( = ( , 3 (. π = 4 ( π π (4 π 7

18 C G b + a F E B a O D : A OA =, AB = a, BC = b OB, OAB = 9, OBC = 9, < a, b < C OA CD CD OB E B CD BF c = DC/OD OAG S(c = S(a + S(b c a, b OAB ODE, ODE BF E, BF E CF B OAB CF B OB : CB = AB : F B, OA : CF = AB : F B CB = b OB, AB = a OB : b OB = a : F B, F B = ab OA = : CF = a : ab, CF = b CD = DF + F C = AB + F C = a + b, OD = OA DA = OA F B = ab, c = CD OD = a + b ab. 8

19 S ( a + b = S(a + S(b (5 ab (5 a =, b = = π 8 = S( = S ( + S ( 3 : S(/ + S(/3 = S( 4 (. ( π = ( (6 9

20 [ ] (5 S ( = S 5 ( + S 5 ( = S = S ( 5. (5 4S ( ( ( 5 5 = S + S = S = S (. 9 S( + S ( = S 39 S( + S = S ( ( = 4S, 39 5 ( ( S( = 4S S (. 9 S( = π 4 (4 5. (6 5 6 π 5 5. a > b a = a, b = b, a n+ = a n + b n, b n+ = a n b n n =,,,... {a n }, {b n } b < b < b < < b n < b n+ < a n+ < a n < < a < a < a.

21 b n b n+ a n+ a n lim n a n = α, lim n b n = β α = lim n a n+ = lim n a n + b n = α + β α = β α a b M(a, b. M(, n a n b n a n b n (a n+ b n+ = (a n + b n a n b n = ( an b n (a n b n = ( an +. (7 b n a n > b n < a n b n < N < a n+ b n+ < N (. a =, b = c =, a n+ = a n + b n, b n+ = a n b n, c n+ = a n b n, n =,,... π = M (, n c n n=. s n = n k= k c k, p n = a n s n

22 p p p p p π p 3 9 p 4 p 5 4 π π p π ( p, p, p 3 A a a k a = k a a k k a b = k a > b b = b n + b n + + b n + b n + b n+ + b n+ 4 + b i 99 b ( n b < n+ n b < n+ i =,,... Y i = b i + b i + + b i + b i X i X i Y i X i = c i + c i + + c i + c i, c, c,..., c i 9 X i = Z + c i, Z = c i + c i + + c i

23 Z (X i + c i = X i Y i = Y i + b i < (Y i + Z < Y i +, Z Y i (Z+ > Z+c i = X i X i (Z + > Y i = Y i + b i Y i. (Z + > Y i Z Z Y i Z = X i c i Z + Zc i + c i = X i Y i = Y i + b i, Zc i + c i (Y i Z + b i (8 (Y i Z + b i Z Q ZQ (Y i Z + b i < Z(Q + Z(Q + + (Q + > Z(Q + > (Y i Z + b i c i Q c i c i = Q c i = Q c i = Q X n Y n b < (X n + X n X n b = k a < X n + k X n a < k X n + k a k

24 c 3 7 ( + c c (c = 9 c = 8 3 ( 7 + c c ( 89 = ( 34 3, c = 3 3 ( 73 + c 3 c 3 ( 9 = 7 (7 346, c 3 = 3 = =.73 3 = = =.57 3 =.57 q = ( 3 <.68 = 3.6 4

25 7 p = = 6.57 < p < 6.58 = 3.8 p < π < q 3. < π < 3.6 B ([3] k <. K(k = E(k = dx ( x ( k x = dθ k sin θ (, k x π dx = k x sin θ dθ (. x = sin θ. a > b >, k = b a I(a, b = J(a, b = cos θ = sin θ I(a, b = J(a, b = dθ a (a b sin θ = a a (a b sin θ dθ = a dθ a cos θ + b sin θ, a cos θ + b sin θ dθ dθ k sin θ = a K(k, k sin θ dθ = ae(k. I(a, b = K(k, J(a, b = ae(k. (9 a 5. I ( a + b, ab = I(a, b. 5

26 [ ] b tan θ = u du dθ = dθ cos θ du = cos θ b cos θ = cos θ b I(a, b = = I = b + u. dθ a cos θ + b sin θ = (a + u (b + u du = ( a + b, ab = b cos θ, cos θ = + tan θ = (( a+b dθ cos θ a + b tan θ b b + u, (a + u (b + u du. + u (ab + u u = ( v ab ab + u = v 4v (ab + v du, ab + u dv = v, ( a + b + u = 4 (a + v ( + b v = 4v (a + v (b + v v u ( a + b I, ab = dv = I(a, b. (a + v (b + v du. 6. k = k K(k = π M(, k. [ ] a =, b = k n =,,... a n+ = a n + b n, b n+ = an b n m = M(, k lim a n = lim b n = m n n 5 I(, k = I(a, b = = I(a n, b n n K(k = I(, k = I(m, m = m dθ = π m = π M(, k. ( a + b J, ab J(a, b. de dk = dk (E K, k dk = kk (E k K. 6

27 . (a K(k = + k K (c E(k = + k E 7. [ ] J ( k + k ( k + k J k = b a, k = ( a + b, ab = a + b E, (b K(k = + k K + k K(k, (d E(k = ( + k E ( a + b, ab J(a, b = abi(a, b. b a, k = a b + k a + b ( 4ab (a + b, + k ( k k K(k. + k ( k J(a, b = ae(k = a + b E ( a b. a + b J(a, b = ae(k I(a, b = K(k (d a ( a + b J, ( a b ab J(a, b = (a + be ae(k a + b ( k = (a + be ae(k + k ( k = (a + b E(k + + k + k K(k ae(k = bk(k = abi(a, b. 3. lim n n c n =. [ ] (7 8. [ ] ( J(a, b = a n c n I(a, b. n= A n = n (J(a n, b n a ni(a n, b n 7 5 A n+ A n = n (J(a n+, b n+ J(a n, b n n+ a n+i(a n+, b n+ + n a ni(a n, b n = n a n b n I(a n, b n n+ a n+i(a n, b n + n a ni(a n, b n = ( n a n b n (a n + b n + an I(an, b n = n (a n b ni(a n, b n = n c ni(a, b. 7

28 n A n = a ni(a n, b n J(a n, b n = = = c n a n a n cos θ + b n sin θ dθ a n a n cos θ b n sin θ a n cos θ + b n sin θ dθ = sin θ a n cos θ + b n sin θ dθ c n a n cos θ + b n sin θ dθ (a n b n sin θ a n cos θ + b n sin θ dθ dθ a n cos θ + b n sin θ = c ni(a n, b n. < A n n c ni(a n, b n = n c ni(a, b. 3 lim n n c n = A + n= (A n+ A n = lim N A N+ =. J(a, b a I(a, b = A = (A n+ A n = n c ni(a, b J(a, b = = I(a, b ( a n= n c n, n= n c n I(a, b. n= n= 9 (. E(kK(k + E(k K(k K(kK(k = π. [ ] a =, b = k = k = 9 E ( ( ( K K = π. 8 E ( ( = n c n K n= (. 8

29 ( 6 ( K n c n K n= ( = M n c n 4M n= ( = π. π (, π (, = π. C 3. a, b, c C c n Z, n a (n = a(a + (a + n (a + n, a ( = F (a, b, c; u = n= a (n b (n n!c (n un (. f(u = F (a, b, c; u u < u( u d f df + (c (a + b + u abf = ( du du ( x / K(k. K(k = π F (,, ; k. 4. K (k = K(k K(k, K (k (k 3 k d y dk + (3k dy + ky = ( dk 9

30 K K ( 5. K (k = K(k, E (k = E(k EK + E K KK [ ] 5 W = EK + E K KK lim W K( = π k E( = W = (E KK + E K sin θ dθ = cos θ dθ = [ sin θ ] π =. lim W = lim (E k k KK + E(K( = lim (E KK + π k. lim k (E KK = (K EK = = k ( ( = kk kk ( dθ k sin θ ( k sin π θ k sin θ dθ ( k sin θ dθ k dθ cos θ + k sin θ k dθ k cos θ + k sin θ = kk π k sin θ dθ K(k dθ ( k sin θ k dθ ( k sin θ < (K EK < kk π (k. [] π. [],,, 999. [3] π 7 3

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