() 800 ( p.38) r ( r r ) ( ) 6 = r = 56 8 r r = 56 8 = AD BC ( ) ( ) = 8 8 = = 8 ( ) ( 3 = 8 )

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Download "() 800 ( p.38) 50 8 8 8 64 64 r ( r r ) ( ) 6 = r = 56 8 r r = 56 8 = 3.60438 3.6 3.6 3.6 800 8 AD BC ( ) ( 4 3 3 ) = 8 8 = 63 63 64 = 8 ( ) ( 3 = 8 )"

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1 3 (r) (r ) 3.4 r l l r dx x 0 εριϕέρεια (William Oughtred : ?) 8 (Leonhard Euler (707783) (Introductio in Analysin Innitorum : 748 ) ( 8 ) a 0x n + a x n + + a n x + a n = 0 (algebraic number) (transcendental number) k x k = 0 a x a = 0 ( p e = lim + ) n = = n n n! n= p e e pi + = 0 (i : i = ) (Johann Heinrich Lambert : 78777) 76 (Carl Louis Ferdinand von Lindemann : 853) 88 n 500 =

2 () 800 ( p.38) r ( r r ) ( ) 6 = r = 56 8 r r = 56 8 = AD BC ( ) ( ) = 8 8 = = 8 ( ) ( 3 = 8 ) ( ) ( ) 4 6 =.44 ( ) 4 ( ) 8 B A 8 D C 3

3 () BM854 ( 4 pp.505) A B,0 C,0 AB ( ) AC 0 6,40 BC = 6 4,6 4,6 6,40 AB =,4,4 ABC AB 0, 0 = ( 4 p.56) 3; 7, 30 = = 5 = YBC8600 ( 4 p.56) kù² 0;5 0;5 ( ) 0;0,5 4,48 sìla sìla ( ) 4,48 0;0,,30 sìla 0;0,5 0;0,5 0;5 kù² d l h = 6 ²u-si V = h = 6 ²u-si ( 0cm) l d h = 6 ²u-si ( ) l h = 4 l h V 4,48 4 4,48 0;4,48 0; 4, 48 = = 5 4 = 5 = 5 8 3

4 6 ( 3 p.7) : rod nindan = cubit kù² 6 m (5.4 m) cubit kù² = 30 nger ²u-si 0.5 m (0.45 m) chain = 60 cubit kù² = 5 rod nindan cable U = 60 rod nindan league = 30 cable U : sar ( ) = rod nindan 36 m ( m ) sar ( ) = sar ( ) cubit kù² 8 m 3 ( m 3 ) ubu = 50 sar iku = ubu = 00 sar eshe e²è = 6 iku bùr = 3 eshe e²è : sìla l bán = 0 sìla bariga PI = 6 bán gur = 5 bariga PI : mina ma-na = 60 shekel gín 0.5 kg (0.505 kg) talent gù = 60 mina ma-na shekel gín = 80 grain ²e YBC8600 kù² 0; 5 = 5 60 = rod nindan S A O O A B P B Q C Q C R T R 4 8 ( pp ) OABC OAC OABC = = S = 6 = BQ = CQ = CR = x OST OB = BT = OT = BT = OQT = OBT OBQ OT CQ = BT OB BQ OB x = x 3 3 x = + 3 = ( 3) OQR = QR OC = 4( 3) S = 4( 3) = 48( 3) 4 < 4 < 48( 3) + 3 < 4 < 3 4 = 5 (OB : OT = BQ : QT ) x 4

5 (3) (Anaxagorac (Anaxagoras) : 500? 48?) (<IppokrĹthc Qĩoc (Hippocrates of Chios) : 440 ) E C G ACB ABC F H AC BC AEC BGC AECF A BGCHB ABC A D B (Euclid (Eukleides : EÎkleÐdhc) : 300 ) (StoiqeÐwsic) ( 5 p.367) 5 3 () ( ( ) ) () ( ) (3) 3 ( 3 ) 3 3 p (?) 3 ( ) (>Arqimădhc (Archim ed es) : 87? ) (KÔklou mètrhsic (Dimensio Circuli)) ( ) : 4 ( 5 p.483) 5

6 < < 3 7 K L C M K L C Z H J J H Z B ( 5 pp ) E E A A CZ 6 CH CJ 4 CK 48 CL = CM 6 EC : CZ = 3 : > 65 : 53 EC : CH > 57 : 53 EC : CJ > 6 + /8 : 53 EC : CK > /4 : 53 EC : CL > / : 53 AC EC 6 LM CL AC : ( 6 ) > / : / < < CB 6 CH CJ 4 CK 48 CL 6 AC : CB = 560 : 780 AC : CH < / + /4 : 780 AC : CJ < / : 40 AC : CK < 00 + /6 : 66 AC : CL < 07 + /4 : 66 CL 6 ( 6 ) : AC < 6336 : 07 + / /4 > > = < < =

7 (4) ( ) (834) 3 3 : 0.50 m = 0 = 0 = 6 = m = 0 = = 0 0 = 0 : = 40 = 00 : 0.4 dl = 0 = 0 = 0 = 0 = 0 : 6 g = 6 = 5 = = 4 = 4 = 6 (6807) 30 ( ) 63 (74) ( ) ( ) 46 7

8 ( : ) ( 6 pp.3536) 4 8 < > (l = S x S = xr l = xr = 3x r = (r) 3x l = = r x ) ( 6 p.3) < < ( : 4500) 7 ) 355 ( ) 3 (636 ) < < (

9 (5) (Chandraguputa : 37? 3?) 37 3 (Ashoka : 68? 3?) 3 (Kanishka : 30?55?) 5 (Chandraguputa : 30?355?) 6 5 (Mahabharata) (R am ayana) 5 (±ulbas utra : ) (Bakhshali manuscript) 4 5 ( Apastamba ulbas utra) ( 7 p.40) 3 ( ABCD) ( ) ( ) (M) ( ) ( ) (M ) (M AD AD G E ME ) (GE) 3 (GF) (MG ) (M MF ) ( ) ( )

10 A B E F M G D C a ABCD M MA 3 4 AD ME AD ME G ME GE 3 F MF ( ) ( MF = a + ) a = + a 3 6 ( + 6 ( ) a) = a 6 = + = 8(3 ) ( Aryabhaṭa : 476?550?) ( Aryabhaṭ ya) ( 7 p.6 p.8) 7 ( ) ( ) l d S V S = l d V = S S 3 ( = = 0000 ) (Bh askara : 4?85?) (L l avat ) ( 7 p.3) ( ) ( ) 7 ( ) 4 0

11 (6) n l n n L n ( l n < < L n ) L n = l nl n l n + L n ( p.8) O M n N n M n N n P n P n A Q n Q n l n = l n L n O r OA P n OQ n = 360 n P n OQ n = 360 n OP n OQ n AOP n AOQ n M n N n n P n Q n n M n N n n P n Q n n l n = M n N n n L n = P n Q n n l n = M n N n n L n = P n Q n n 50 6 ( 60 ) ( ) 50 l 6 = 50 6 = 300 L 6 = 6 = L = (43) l = (4647) L = = (3 + 3) = = = 00( 3) (7347) l = ( 3) = ( 3) = = 600 = = 300 ( 3 ) = 300( 6 ) (305)

12 00 l L < < < < = L 4 = L 4 = 300( 6 ) 00( 3) 300( 6 ) + 00( 3) l 4 = l 4 = 300( 6 ) 400( 3)( 6 ) = 00( 3 ) = 400( 3)( 6 ) l 4 + L = ( ) p n l n L n

13 (7) (François Viète : ) = (John Wallis : 66703) = (k)(k) (k )(k ) = k= (James Gregory : ) (Gottfried Wilhelm Freiherrvon Leibniz : 64676) 4 = arctan x = x 3 x3 + 5 x5 7 x7 + x (Isaac Newton : 6477) 6 = arcsin = (Carl Friedrich Gauss : ) 4 = arctan arctan 57 5 arctan = arctan + arctan 3 6 (John Machin : 68075) 4 = 4 arctan 5 arctan (Charles Hutton : 73783) 4 = 3 arctan 4 + arctan 5 3

14 arctan x = x 3 x3 + 5 x5 ( ) k 7 x7 + = k + xk+ ( x ) arctan 5 5 ( ) 3 + ( ) 5 ( ) 7 + ( k=0 = arctan arctan ( ) ( ) ) ( ) = = ( ) arctan 5 5 ( ) 3 ( ) ( 5 ) 7 + ( 5 ) ( 5 ) + 3 = arctan 5 arctan ( ) ( 3 ) 3 ( ) ( ) ( ) 3 = ( 5 ) 3 ( ) 3 4

15 (8) (Georges Louis Leclerc Comte de Buon : ) (Monte-Carlo method) 45 (John von Neumann : 0357) a l l < a l a l < a O x θ 0 x a 0 θ p x θ a x O l θ x a x = l sin θ θ x l sin θ p = = pa p 0 l sin θdθ = l pa ( ) 855 (Augustus de Morgan : 80687) a = 5 l = ( p.6) 3 5 = = = =

16 = = (Johann Rudolf Wolf : 8683) a = 45 mm l = 36 mm ( p.) ? 80 ( 55) 77 ( 5) 3 M. ( ) ( ) 6 ( 37) ( ) 5 ( ) ( ) 7 ( 47) 6 ( ) ( ) 80 ( 55) 7 ( ) ( ) 80 ( 55) 8 ( 55) 3 ( 5) 77 ( 5) 0 G. ( ) ( ) 6 ( 8) ( ) ( A3) 78 ( 53) 3 Victor J. Katz(ed.) The Mathematics of Egypt, Mesopotamia, China, India, and Islam. A Sourcebook Princeton U. P

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